C3D Toolkit  Kernel - 117978, Vision - 2.9.1.5

Elliptical arc in two-dimensional space. More...

#include <cur_arc.h>

+ Inheritance diagram for MbArc:
+ Collaboration diagram for MbArc:

Public Member Functions

 MbArc ()
 Constructor of a circle with default parameters. More...
 
 MbArc (double rad)
 Constructor of a circle by radius. More...
 
 MbArc (const MbCartPoint &p, double rad)
 Constructor of a circle. More...
 
 MbArc (const MbCartPoint &pc, const MbCartPoint &on)
 Create a circle. More...
 
 MbArc (const MbCartPoint &pc, double rad, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
 Constructor of a circular arc. More...
 
 MbArc (const MbCartPoint &pc, double rad, double t1, double t2, int initSense)
 Constructor of a circular arc. More...
 
 MbArc (const MbArc &init, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
 Constructor of an elliptic arc based on a sample and bounding points. More...
 
 MbArc (const MbCartPoint &pc, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
 Constructor of a circular arc. More...
 
 MbArc (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3)
 Constructor of a circular arc. More...
 
 MbArc (const MbCartPoint &p1, const MbCartPoint &p2, double a4)
 Constructor of a circular arc. More...
 
 MbArc (double aa, double bb, const MbPlacement &place, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
 Constructor of an elliptical arc. More...
 
 MbArc (double aa, double bb, const MbPlacement &place, double t1, double t2, int initSense)
 Constructor of an elliptical arc. More...
 
 MbArc (const MbArc &ellipse, double t1, double t2, int initSense)
 Constructor of an elliptical arc. More...
 
 MbArc (double aa, double bb, const MbPlacement &pos)
 Constructor of an ellipse. More...
 
 MbArc (double aa, double bb, const MbCartPoint &c, double angle)
 Constructor of an ellipse. More...
 
 MbArc (const MbArc &init)
 Copy-constructor.
 
virtual ~MbArc ()
 Destructor.
 
Common functions of a geometric object.
MbePlaneType IsA () const override
 Get the object type.
 
MbPlaneItemDuplicate (MbRegDuplicate *=nullptr) const override
 Create a copy. More...
 
bool IsSame (const MbPlaneItem &other, double accuracy=LENGTH_EPSILON) const override
 Determine whether objects are equal. More...
 
bool SetEqual (const MbPlaneItem &) override
 Make the objects equal. More...
 
void Transform (const MbMatrix &matr, MbRegTransform *ireg=nullptr, const MbSurface *newSurface=nullptr) override
 Transform according to the matrix. More...
 
void Move (const MbVector &, MbRegTransform *=nullptr, const MbSurface *newSurface=nullptr) override
 Translate along a vector. More...
 
void Rotate (const MbCartPoint &pnt, const MbDirection &angle, MbRegTransform *=nullptr, const MbSurface *newSurface=nullptr) override
 Rotate about a point. More...
 
double DistanceToPoint (const MbCartPoint &) const override
 Calculate the distance to a point.
 
bool DistanceToPointIfLess (const MbCartPoint &toP, double &d) const override
 Calculate the distance to a point. More...
 
void AddYourGabaritTo (MbRect &r) const override
 Extend the given bounding rectangle so that it encloses this object.
 
void CalculateGabarit (MbRect &r) const override
 Detect the bounding box of a curve. More...
 
bool IsInRectForDeform (const MbRect &r) const override
 Determine visibility of a curve in rectangle.
 
MbeState Deformation (const MbRect &, const MbMatrix &) override
 Deform the curve. More...
 
void Refresh () override
 Set all temporary (mutable) data of object to undefined (initial) state.
 
void PrepareIntegralData (const bool forced) const override
 Calculate temporary (mutable) data of an object. More...
 
bool IsVisibleInRect (const MbRect &r, bool exact=false) const override
 Determine visibility of an object in rectangle. More...
 
bool IsCompleteInRect (const MbRect &r) const override
 Determine whether an object is fully visible in rectangle. More...
 
bool IsVisibleInRect (const MbRect &rect, bool exact=false) const override
 Determine visibility of an object in rectangle. More...
 
Functions for curve domain description
double GetTMax () const override
 Get the maximum value of parameter.
 
double GetTMin () const override
 Get the minimum value of parameter.
 
bool IsClosed () const override
 Define whether the curve is periodic. More...
 
double GetPeriod () const override
 Return period. More...
 
Functions for working in the domain of a curve.

PointOn, FirstDer, SecondDer, ThirdDer,... functions correct parameter when it runs out the domain.

void PointOn (double &t, MbCartPoint &) const override
 Calculate a point on the curve. More...
 
void FirstDer (double &t, MbVector &) const override
 Calculate first derivative.
 
void SecondDer (double &t, MbVector &) const override
 Calculate second derivative.
 
void ThirdDer (double &t, MbVector &) const override
 Calculate third derivative.
 
virtual void Normal (double &t, MbVector &) const
 
Functions for working inside and outside of the curve domain.

_PointOn, _FirstDer, _SecondDer, _ThirdDer,... functions don't correct parameter when it runs out the domain. The bounded curve is extended due to the equations of curve.

void _PointOn (double t, MbCartPoint &) const override
 Calculate point at curve and its extension. More...
 
void _FirstDer (double t, MbVector &) const override
 Calculate first derivative at curve and its extension.
 
void _SecondDer (double t, MbVector &) const override
 Calculate second derivative at curve and its extension.
 
void _ThirdDer (double t, MbVector &) const override
 Calculate third derivative at curve and its extension.
 
virtual void _Normal (double t, MbVector &) const
 
Functions for get of the group of data inside and outside the curve's domain of parameter.
void Explore (double &t, bool ext, MbCartPoint &pnt, MbVector &fir, MbVector *sec, MbVector *thir) const override
 Calculate point and derivatives of object for given parameter. More...
 
Functions of moving along the curve
double Step (double t, double sag) const override
 Calculate parameter step. More...
 
double DeviationStep (double t, double angle) const override
 Calculate parameter step. More...
 
Common functions of the curve
void Inverse (MbRegTransform *iReg=nullptr) override
 Set the opposite direction of curve.
 
double GetMetricLength () const override
 Calculate the metric length of a curve. More...
 
double CalculateMetricLength () const override
 Calculate the metric length of a curve.
 
double GetLengthEvaluation () const override
 Calculate the metric length of a curve. More...
 
double Curvature (double t) const override
 Calculate curvature of curve.
 
double CalculateLength (double t1, double t2) const override
 Calculate the metric length of a curve. More...
 
bool DistanceAlong (double &t, double len, int curveDir, double eps=Math::LengthEps, VERSION version=Math::DefaultMathVersion()) const override
 Translate parameter along the curve. More...
 
double PointProjection (const MbCartPoint &pnt) const override
 Calculate the point projection to the curve. More...
 
bool NearPointProjection (const MbCartPoint &pnt, double xEpsilon, double yEpsilon, double &t, bool ext, MbRect1D *tRange=nullptr) const override
 Find the point projection to the curve. More...
 
void TangentPoint (const MbCartPoint &pnt, SArray< double > &tFind) const override
 Find tangents to a curve. More...
 
void PerpendicularPoint (const MbCartPoint &pnt, SArray< double > &tFind) const override
 Find perpendiculars to a curve. More...
 
bool SmallestPerpendicular (const MbCartPoint &pnt, double &tProj) const override
 Find the nearest perpendicular to the curve. More...
 
void IntersectHorizontal (double y, SArray< double > &cross) const override
 Find intersections of a curve with horizontal line. More...
 
void IntersectVertical (double x, SArray< double > &cross) const override
 Find intersections of a curve with vertical line. More...
 
bool GetCentre (MbCartPoint &c) const override
 Return the center of an ellipse or a circle.
 
virtual const MbCartPointGetCentre () const
 Return the center of an ellipse or a circle.
 
bool GetMiddlePoint (MbCartPoint &p) const override
 Calculate a middle point of a curve.
 
bool GetWeightCentre (MbCartPoint &p) const override
 Calculate the center of gravity of a curve.
 
double GetRadius (double accuracy=PARAM_REGION) const override
 Get the physical radius of the curve or zero if it impossible. More...
 
bool IsSimilarToCurve (const MbCurve &curve, double precision=PARAM_PRECISION) const override
 Define whether the curves are similar for the merge.
 
size_t GetCount () const override
 Define the number of splittings for one passage in operations.
 
void GetPointsByEvenLengthDelta (size_t n, std::vector< MbCartPoint > &pnts) const override
 Get n points of a curve with equal intervals by arc length.
 
bool HasLength (double &length) const override
 Calculate the metric length of a curve. More...
 
bool IsDegenerate (double eps=Math::LengthEps) const override
 Define whether the curve is degenerate..
 
MbNurbsNurbsCurve (const MbCurveIntoNurbsInfo &) const override
 Construct a NURBS copy of a curve. More...
 
MbCurveNurbsCurve (const MbNurbsParameters &) const override
 Construct a NURBS copy of a curve. More...
 
MbContourNurbsContour () const override
 Approximate of a curve by the contour from NURBS curves.
 
MbCurveTrimmed (double t1, double t2, int sense, const MbDimAccuracy &xyEps, bool saveParamLenAndLaw) const override
 Construct a trimmed curve with the given two-dimensional accuracy. More...
 
MbCurveOffset (double rad) const override
 Construct the equidistant curve which is shifted by the given value.
 
MbeItemLocation PointRelative (const MbCartPoint &pnt, double eps=Math::LengthEps) const override
 Define the point position relative to the curve. More...
 
MbeState DeletePart (double t1, double t2, MbCurve *&part2) override
 Delete the piece of a curve. More...
 
MbeState TrimmPart (double t1, double t2, MbCurve *&part2) override
 Keep the piece of a curve. More...
 
bool ModifyByPoint (size_t ind, const MbCartPoint &pnt)
 Modify the ellipse by a characteristic point. More...
 
bool GetSpecificPoint (const MbCartPoint &from, double &dmax, MbCartPoint &pnt) const override
 Return a specific point of a curve. More...
 
void Isoclinal (const MbVector &angle, SArray< double > &tFind) const override
 Construct isoclines. More...
 
bool GetAxisPoint (MbCartPoint &p) const override
 Calculate a point to construct an axis. More...
 
MbResultType Extend (const MbCurveExtensionParameters &parameters, c3d::PlaneCurveSPtr &resCurve) const override
 Extend the curve. More...
 
bool IsCircle (double eps=PARAM_REGION) const
 Check whether the ellipse is a circle with a given tolerance.
 
virtual MbCurveTrimmed (double t1, double t2, int sense, bool saveParamLenAndLaw=false) const
 Construct a trimmed curve. More...
 
virtual MbCurveTrimmed (double t1, double t2, int sense, const MbDimAccuracy &xyEps, bool saveParamLenAndLaw) const=0
 Construct a trimmed curve with the given two-dimensional accuracy. More...
 
Functions in the local coordinate system of object placement.
const MbPlacementGetPlacement () const
 Get the local coordinate system of an object.
 
void SetPlacement (const MbPlacement &pl)
 Modify the local coordinate system of the object.
 
bool IsPositionNormal () const
 Determine whether the local coordinate system is orthonormalized.
 
bool IsPositionCircular () const
 Determine whether the local coordinate system is orthogonal with X and Y axes equal by length.
 
bool IsPositionIsotropic () const
 Determine whether the local coordinate system is orthogonal and isotropic by the axes.
 
double GetPositionAngle (const MbCartPoint &p) const
 Calculate the angle in the local coordinate system. More...
 
void InitByPositionAngles (double a1, double a2, int initSense, const MbDimAccuracy &xyEps=MbDimAccuracy::twoDimRgn)
 Initialization of the ellipse parameters. More...
 
Functions for working with data.
double GetR () const
 Return the radius and the length of semiaxis along X for the ellipse.
 
double GetRadiusA () const
 Return the length of semiaxis along X.
 
double GetRadiusB () const
 Return the length of semiaxis along Y.
 
void SetRadiusA (double aa)
 Set the length of semiaxis along X.
 
void SetRadiusB (double bb)
 Set the length of semiaxis along Y.
 
double GetAngle () const
 Return the arc opening angle. Set the arc opening angle. The start point of the arc remains unchanged.
 
void SetAngle (double ang)
 
double GetMajorAxisAngle () const
 Calculate the angle between OX axes of the local and the global coordinate systems.
 
double GetTrim1 () const
 Return the parameter of the start point.
 
double GetTrim2 () const
 Return the parameter of the end point.
 
int GetSense () const
 Determine the flag of coincidence of the direction with the base curve direction.
 
void SetTrim1 (double t)
 Set the parameter of the start point.
 
void SetTrim2 (double t)
 Set the parameter of the end point.
 
void SetRadius (double rad)
 Set the radius of the circular arc.
 
void SetCentre (const MbCartPoint &c)
 Set the center.
 
void SetDirection (bool clockwise)
 Set the arc orientation.
 
void Init (const MbArc &)
 Initialize elliptical arcs with the given arc.
 
void Init (const MbCartPoint &pc, double rad)
 Initialize a circle by the center and the radius

 
void Init (double t1, double t2)
 Initialize arc by parameters for begin point and end point.
 
bool Init3Points (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3, bool cl)
 Initialize a circular arc. More...
 
void InitCircle (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3)
 Initialize a circular arc. More...
 
void InitArc (MbCartPoint &pc, const MbCartPoint &p1, const MbCartPoint &p2)
 Initialize a circular arc. More...
 
void Init (const MbCartPoint &pc, double rad, const MbCartPoint &p1, const MbCartPoint &p2, bool clockwise)
 Initialize a circular arc. More...
 
void Init (const MbCartPoint &pc, const MbCartPoint &p)
 Initialize a circle. More...
 
void Init (const MbCartPoint &p1, double angle, double rad)
 Initialize a circle. More...
 
void Init (const MbCartPoint &pc, const MbCartPoint &pnt, double angle)
 Initialize a circle. More...
 
void Init (const MbCartPoint &pc, double angle1, double angle2, double rad, bool clockwise)
 Initialize a circular arc. More...
 
void Init (const MbCartPoint &pc, const MbCartPoint &pnt, bool firstPoint, double angle, bool clockwise)
 Initialize a circular arc. More...
 
void Init (const MbCartPoint &pc, double angle1, const MbCartPoint &p2, double rad, bool clockwise)
 Initialize a circular arc. More...
 
void Init (MbArc *obj, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
 Initialize a circular arc. More...
 
void Init (const MbCartPoint &p1, const MbCartPoint &p2, double angle, bool firstAngle, bool clockwise)
 Initialize a circular arc. More...
 
void Init (MbCartPoint &pc, double angle1, double angle2, const MbCartPoint &pnt, bool firstPoint, bool clockwise)
 Initialize a circular arc. More...
 
void Init (MbCartPoint &pc, const MbCartPoint &p, bool firstPoint, double angle, double rad, bool clockwise)
 Initialize a circular arc. More...
 
void Init (const MbCartPoint &pc, const MbCartPoint &p1, const MbCartPoint &p2, int initSense)
 Initialize a circular arc. More...
 
bool Init (double a2, MbCartPoint &p1, MbCartPoint &p2, const DiskreteLengthData *diskrData=nullptr, bool correctFirstPnt=true)
 Initialize a circular arc. More...
 
void Init (double aa, double bb, const MbPlacement &place)
 Initialize an ellipse. More...
 
void Init (double aa, double bb, const MbCartPoint &pc, double ang)
 Initialize an ellipse. More...
 
void Init1 (const MbCartPoint &c, const MbCartPoint &p1, double &len, double &angle)
 Initialize an ellipse. More...
 
void Init2 (const MbCartPoint &c, const MbCartPoint &p1, MbCartPoint &p2, double &lenB)
 Initialize an ellipse. More...
 
void Init3 (const MbCartPoint &c0, const MbCartPoint &p1, double angle, double &aa, double &bb)
 Initialize an ellipse. More...
 
void Init4 (const MbCartPoint &p1, const MbCartPoint &p2, double angle, double &aa, double &bb)
 Initialize an ellipse. More...
 
void Init5 (const MbCartPoint &c, const MbCartPoint &p1, const MbCartPoint &p2, double &aa, double &bb, double &angle)
 Initialize an ellipse. More...
 
void Init6 (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3, double &aa, double &bb, double &angle)
 Initialize an ellipse. More...
 
void Init7 (const MbCartPoint &pc, MbCartPoint p1, MbCartPoint p2, MbCartPoint p3, double &aa, double &bb, double &angle)
 Initialize an ellipse. More...
 
void Init8 (const MbCartPoint &p1, const MbDirection &dir1, const MbCartPoint &p2, const MbDirection &dir2, const MbCartPoint &p3, double &aa, double &bb, double &angle)
 Initialize an ellipse. More...
 
void Init (double aa, double bb, const MbPlacement &place, double t1, double t2, int initSense)
 Initialize an elliptical arc. More...
 
void Init (double aa, double bb, const MbPlacement &place, const MbCartPoint &p1, const MbCartPoint &p2, bool clockwise)
 Initialize an elliptical arc. More...
 
void Init4 (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &pB, const MbCartPoint &pE, bool clockwise=false)
 Initialize an elliptical arc. More...
 
bool OnSector (const MbCartPoint &pnt) const
 Determine whether the ray from the center to the point is in the arc's sector.
 
bool OnSector (double angle) const
 Determine whether the ray hits the arc's sector. More...
 
void SetLimitPoint (ptrdiff_t number, const MbCartPoint &pnt)
 Replace the arc's point. More...
 
bool IsClockwise () const
 Return the arc direction: true - clockwise, false - counterclockwise.
 
double GetLimitAngle (ptrdiff_t number) const
 Return the angle of the end point. More...
 
void SetLimitAngle (ptrdiff_t number, const MbCartPoint &pnt)
 Modify the end angle of the arc. More...
 
double CheckParam (double &t) const
 Set the parameter to the range of the allowable values.
 
void ParamToAngle (double &t) const
 Convert the parameter of the curve to the angle.
 
void AngleToParam (double &t) const
 Convert the curve angle to the curve parameter.
 
void ParameterInto (double &t) const
 Convert parameter of the base curve to the local parameter.
 
void ParameterFrom (double &t) const
 Convert the local parameter to the parameter of the base curve.
 
bool IsBaseParamOn (double t, double eps=Math::paramEpsilon) const
 Determine whether the parameter of the base curve is in range of the trimmed curve.
 
void PointOnBaseEllipse (double &t, MbCartPoint &pnt) const
 Evaluate a point on ellipse. More...
 
double PointProjectionOnBaseEllipse (const MbCartPoint &pnt) const
 Find the projection of a point onto the ellipse. More...
 
void MakeAsBaseEllipse ()
 Initialize as complete ellipse.
 
void CopyBaseEllipse (const MbArc &init)
 Copy the base ellipse.
 
bool IsSelfIntersectOffset (double d) const
 Determine whether the ellipse offset has self-intersections. More...
 
bool ParametricToCanonicConic (double &A, double &B, double &C, double &D, double &E, double &F, double &X1, double &Y1, double &X2, double &Y2) const
 
bool Normalize ()
 Orthonormalize the local coordinate system.
 
void GetControlPoints (SArray< MbCartPoint > &points)
 Fill the array with the control points.
 
void NormalizeTransform (const MbMatrix &mt)
 Orthonormalize the placement when transforming.
 
ptrdiff_t EllipticIntersect (const MbLine &pLine, double cross[2], double eps0=PARAM_PRECISION) const
 Determine the parameters of intersection of a line with an ellipse. More...
 
const MbArcoperator= (const MbArc &init)
 Overrides the assignment operator.
 
void GetProperties (MbProperties &properties) override
 Get properties of the object. More...
 
void SetProperties (const MbProperties &properties) override
 Change properties of the object. More...
 
void GetBasisPoints (MbControlData &) const override
 Get control points of object.
 
void SetBasisPoints (const MbControlData &) override
 Change the object by control points.
 
- Public Member Functions inherited from MbCurve
virtual ~MbCurve ()
 Destructor.
 
MbePlaneType Type () const override
 Get the group type of the object.
 
MbePlaneType Family () const override
 Get family of object.
 
void Refresh () override
 Set all temporary (mutable) data of object to undefined (initial) state.
 
size_t size () const
 Number of objects if object is interpreted as vector of objects.
 
const MbCurveoperator[] (size_t) const
 An access operator.
 
virtual void AddYourGabaritMtr (MbRect &rect, const MbMatrix &matr) const
 Add a bounding box to rectangle. More...
 
virtual void CalculateLocalGabarit (const MbMatrix &into, MbRect &local) const
 Calculate bounding box in the local coordinate system. More...
 
bool IsVisibleInRect (const MbRect &rect, bool exact=false) const override
 Determine visibility of an object in rectangle. More...
 
double DistanceToPoint (const MbCartPoint &toP) const override
 Calculate the distance to a point.
 
bool DistanceToPointIfLess (const MbCartPoint &toP, double &d) const override
 Calculate the distance to a point. More...
 
virtual bool IsPeriodic () const
 Define whether the curve is periodic. More...
 
bool IsTouch (double eps=Math::LengthEps) const
 Determine whether a curve is closed regardless of the smoothness of the closure. More...
 
void Tangent (double &t, MbVector &v) const
 Calculate tangent vector (normalized).
 
void Tangent (double &t, MbDirection &d) const
 Calculate tangent vector (normalized).
 
void Normal (double &t, MbVector &v) const
 Calculate main normal vector (normalized).
 
void Normal (double &t, MbDirection &d) const
 Calculate main normal vector (normalized).
 
void _Tangent (double t, MbVector &v) const
 Calculate tangent vector (normalized).
 
void _Tangent (double t, MbDirection &d) const
 Calculate tangent vector (normalized).
 
void _Normal (double t, MbVector &v) const
 Calculate main normal vector (normalized) at curve and its extension.
 
void _Normal (double t, MbDirection &d) const
 Calculate main normal vector (normalized) at curve and its extension.
 
double CurvatureDerive (double t) const
 Calculate derivative of curvature by parameter.
 
double CurvatureRadius (double t) const
 Calculate radius of curve with a sign.
 
virtual bool IsBounded () const
 Define whether the curve is bounded.
 
virtual bool IsStraight (bool ignoreParams=false) const
 Define whether the curve is rectilinear..
 
virtual bool IsSmoothConnected (double angleEps) const
 Define whether joints of contour/curve are smooth.
 
double GetParamLength () const
 Calculate the parametric length of a curve.
 
virtual void ResetTCalc () const
 Reset the current value of parameter.
 
virtual bool BeginApprox (double sag, double &tbeg, double &tend, MbCartPoint &pnt, bool &existNextPoint) const
 Start approximation for the drawing. More...
 
virtual bool GetNextPoint (double sag, double tend, double &tcur, MbCartPoint &pnt) const
 Calculate the next point. More...
 
virtual void CalculatePolygon (double sag, MbPolygon &poligon) const
 Calculate an array of points for drawing. More...
 
MbNurbsNurbsCurve (const MbCurveIntoNurbsInfo *nInfo=nullptr) const
 Construct a NURBS copy of a curve. More...
 
virtual MbCurveTrimmed (double t1, double t2, int sense, bool saveParamLenAndLaw=false) const
 Construct a trimmed curve. More...
 
virtual MbeLocation PointLocation (const MbCartPoint &pnt, double eps=Math::LengthEps) const
 The point position relative to the curve.
 
MbeNewtonResult PointProjectionNewton (const MbCartPoint &p, double xEpsilon, double yEpsilon, size_t iterLimit, double &t, bool ext) const
 Find the point projection to the curve. More...
 
void PointProjection (const MbCartPoint &pnt, MbCartPoint &on) const
 Calculate the point projection to the curve. More...
 
void BasePointProjection (const MbCartPoint &pnt, MbCartPoint &on) const
 Calculate the point projection to the curve. More...
 
void PointProjectionAndAngle (MbCartPoint &on, double &angle) const
 Calculate the point projection to the curve. More...
 
bool DirectPointProjection (const MbCartPoint &pnt, const MbDirection &dir, MbCartPoint &pp) const
 Calculate the point projection to the curve. More...
 
void HorzIsoclinal (SArray< double > &tFind) const
 Construct horizontal isoclines. More...
 
void VertIsoclinal (SArray< double > &tFind) const
 Construct vertical isoclines. More...
 
void LowestPoint (MbCartPoint &lowestPoint, double &tLowest) const
 Find the lowest point of a curve and the corresponding parameter.
 
virtual void SelfIntersect (SArray< MbCrossPoint > &, double metricEps=Math::LengthEps) const
 Find self-intersections of curve. More...
 
virtual void OffsetCuspPoint (SArray< double > &tCusps, double dist) const
 Find the special points of an offset curve. More...
 
virtual bool GoThroughPoint (MbCartPoint &pnt)
 Create a curve through a point. More...
 
virtual void GetStartPoint (MbCartPoint &) const
 Calculate a start point of a curve.
 
virtual void GetEndPoint (MbCartPoint &) const
 Calculate an end point of a curve.
 
void GetPointsByEvenParamDelta (size_t n, std::vector< MbCartPoint > &pnts) const
 Get n points of a curve with equal intervals by parameter.
 
void GetPointsByEvenParamDelta (size_t n, SArray< MbCartPoint > &pnts) const
 
void GetPointsByEvenLengthDelta (size_t n, SArray< MbCartPoint > &pnts) const
 
virtual double LengthBetween2Points (MbCartPoint &p1, MbCartPoint &p2, MbCartPoint *pc=nullptr) const
 Calculate minimal length of a curve between two points on it. More...
 
bool IsPointOn (const MbCartPoint &, double eps=Math::LengthEps) const
 Check whether the point is on a curve with the tolerance eps.
 
bool IsParamOn (double t, double eps=Math::paramEpsilon) const
 Check whether the parameter is inside a range with the tolerance eps.
 
void CorrectCyclicParameter (double &t, double eps=Math::paramRegion) const
 Correct parameter for closed curves. More...
 
void CorrectParameter (double &t) const
 Correct parameter. More...
 
MbCurveInverseDuplicate () const
 Create a copy with changed direction.
 
bool IsInverseSame (const MbCurve &curve, double accuracy=LENGTH_EPSILON) const
 Define whether an inversed curve is the same.
 
virtual bool IsReparamSame (const MbCurve &curve, double &factor) const
 Define whether a reparameterized curve is the same. More...
 
MbCartPoint GetLimitPoint (ptrdiff_t number) const
 Calculate the boundary point. More...
 
void GetLimitPoint (ptrdiff_t number, MbCartPoint &pnt) const
 Calculate the boundary point. More...
 
void GetLimitTangent (ptrdiff_t number, MbVector &v) const
 Calculate a tangent vector to the boundary point. More...
 
void GetLimitPointAndTangent (ptrdiff_t number, MbCartPoint &pnt, MbVector &v) const
 Calculate a tangent vector and point at the end of a curve. More...
 
bool AreLimitPointsEqual () const
 Are boundary points equal? More...
 
virtual const MbCurveGetBasisCurve () const
 Returns the base curve if exists or itself.
 
virtual MbCurveSetBasisCurve ()
 Returns the base curve if exists or itself.
 
virtual double GetParamDelta () const
 Return an indent by parameter of a curve.
 
virtual const MbCurveGetSubstrate () const
 Get a substrate or itself.
 
virtual MbCurveSetSubstrate ()
 Get a substrate or itself.
 
virtual int SubstrateCurveDirection () const
 Return direction of a substrate relative to a curve or vice versa.
 
virtual void SubstrateToCurve (double &) const
 Transform a substrate parameter to the curve parameter.
 
virtual void CurveToSubstrate (double &) const
 Transform a curve parameter to the substrate parameter.
 
virtual double GetParamToUnit () const
 Return increment of parameter, corresponding to the unit length in space.
 
virtual double GetParamToUnit (double t) const
 Return increment of parameter, corresponding to the unit length in space according to parameter.
 
virtual double GetTEpsilon (double epsilon) const
 Return the minimal discernible value of parameter with the given tolerance.
 
virtual double GetTEpsilon (double t, double epsilon) const
 Return the minimal discernible value of parameter with the given tolerance according to parameter.
 
virtual double GetTRegion (double epsilon) const
 Return the minimal discernible value of parameter with the given tolerance.
 
virtual double GetTRegion (double t, double epsilon) const
 Return the minimal discernible value of parameter with the given tolerance according to parameter.
 
virtual double GetTRegion (double t, const MbDimAccuracy &xyEps) const
 Return the minimal discernible value of parameter with the given two-dimensinal accuracy according to parameter. The method takes into account the direction of the curve at a point.
 
double GetTMid () const
 Return the middle of parametric range of a curve.
 
double GetTRange () const
 Return the parametric length of a curve.
 
MbCartPoint PointOn (double &t) const
 Calculate point on the curve.
 
MbVector FirstDer (double &t) const
 Calculate first derivative.
 
MbDirection Tangent (double &t) const
 Calculate tangent vector (normalized).
 
MbDirection Normal (double &t) const
 Calculate the normal vector.
 
double DerLength (double &t) const
 Calculate the length of derivative vector.
 
virtual void GetAnalyticalFunctionsBounds (std::vector< double > &params) const
 Get the boundaries of the curve sections that are described by one analytical function. More...
 
virtual void BreakPoints (std::vector< double > &vBreaks, double precision=ANGLE_REGION) const
 \ ru Определение точек излома кривой. The determination of curve smoothness break points.
 
MbPropertyCreateProperty (MbePrompt name) const override
 Create a custom property.
 
virtual bool IsContinuousDerivative (bool &contLength, bool &contDirect, c3d::DoubleVector *params=nullptr, double epsilon=EPSILON) const
 Get properties of the object. More...
 
virtual bool SetContinuousDerivativeLength (VERSION version, double epsilon=EPSILON)
 Eliminate the discontinuities of the first derivative at length. More...
 
bool IsSpaceNear (const MbCurve &curve, double eps, bool ext, double devSag=5.0 *Math::deviateSag) const
 Check whether the two curves are metrically close. More...
 
bool IsSpaceNear (const MbCurve &curve, double xEps, double yEps, bool ext, double xNear, double yNear, double devSag=5.0 *Math::deviateSag) const
 Check whether the two curves are metrically close. More...
 
SimpleName GetCurveName () const
 A curve name.
 
void SetCurveName (SimpleName newName)
 Set a curve name.
 
- Public Member Functions inherited from MbPlaneItem
virtual ~MbPlaneItem ()
 Destructor.
 
void PrepareWrite () const
 Object registration. More...
 
MbeRefType RefType () const override
 Get the registration type (for copying, duplication).
 
virtual void Rotate (const MbCartPoint &pnt, double angle, MbRegTransform *iReg=nullptr, const MbSurface *newSurface=nullptr)
 Rotate about a point. More...
 
virtual bool IsSimilar (const MbPlaneItem &item) const
 Determine whether the objects are similar. More...
 
- Public Member Functions inherited from TapeBase
 TapeBase (RegistrableRec regs=noRegistrable)
 Constructor.
 
 TapeBase (const TapeBase &)
 Copy-constructor.
 
virtual ~TapeBase ()
 Destructor.
 
RegistrableRec GetRegistrable () const
 Whether the stream class is registrable.
 
void SetRegistrable (RegistrableRec regs=registrable) const
 Set the state of registration of the stream class.
 
virtual const char * GetPureName (const VersionContainer &) const
 Get the class name.
 
virtual bool IsFamilyRegistrable () const
 Whether the object belongs to a registrable family.
 
- Public Member Functions inherited from MbRefItem
refcount_t GetUseCount () const
 Get count of references (get count of owners of an object).
 
refcount_t AddRef () const
 Increase count of references by one.
 
refcount_t DecRef () const
 Decrease count of references by one.
 
refcount_t Release () const
 Decrease count of references by one and if count of references became zero, then remove itself.
 
- Public Member Functions inherited from MbNestSyncItem
void Lock () const
 Switch lock on (locking happens only in parallel region).
 
void Unlock () const
 Switch lock off if locking has been set.
 
CommonRecursiveMutexGetLock () const
 Get a pointer to the mutex object. Return nullptr if no parallelism. For use in ScopedLock.
 

Static Public Member Functions

static MbArcCreate (const MbCartPoint &p1, const MbCartPoint &p2, const MbCartPoint &p3)
 Create circular arc. More...
 
static MbArcCreate (const MbCartPoint &p1, const MbCartPoint &p2, double a4)
 Create circular arc. More...
 

Protected Member Functions

double GetParamEpsilon (double eps=Math::LengthEps) const
 Get the parameter accuracy.
 
void SetClosed ()
 Make closed.
 
- Protected Member Functions inherited from MbCurve
 MbCurve ()
 Default constructor.
 
 MbCurve (const MbCurve &other)
 Copy-constructor.
 
- Protected Member Functions inherited from MbPlaneItem
 MbPlaneItem ()
 Constructor.
 
- Protected Member Functions inherited from MbRefItem
 MbRefItem ()
 Constructor without parameters.
 

Protected Attributes

MbPlacement position
 Local coordinate system.
 
double a
 Radius of semiaxis along X.
 
double b
 Radius of semiaxis along Y.
 
double trim1
 The start point parameters.
 
double trim2
 The end point parameters.
 
int sense
 Flag of coincidence with direction from axisX to axisY (sense==0 is not allowed).
 
bool circle
 Whether the object is a circle (true) or an ellipse (false).
 
bool closed
 Whether the object is a closed curve (true) or an arc (false).
 
MbRect rect
 Auxiliary data. More...
 
atomic_double metricLength
 Metric length of curve.
 
- Protected Attributes inherited from MbCurve
SimpleName name
 A curve name. The object data is temporary and used internally.
 

Detailed Description

Elliptical arc in two-dimensional space.

The elliptical arc is described by two radii a and b and two parameters trim1 and trim2 given in the local coordinate system 'position'.
Parameters 'trim1' and 'trim2' are measured along the arc in direction from position.axisX axis to position.axisY axis. Parameters 'trim1' and 'trim2' will be called parameters of trimming. Values of parameters of trimming equal to 0 and 2pi correspond to a point on position.axisX axis.
Parameter t of curve possesses the values in the range: 0<=t<=trim2-trim1. The curve can be closed. For closed curve: trim2-trim1=2pi.
Radius-vector of the curve in the method PointOn(double&t,MbCartPoint3D&r) is described by the function
r(t) = position.origin + (a cos(trim1+(sense)t) position.axisX) + (b sin(trim1+(sense)t) position.axisY).
Radii of the curve must be positive: a>0, b>0.
The following inequalities must be satisfied for the parameters of trimming: trim1<trim2 if sense==1 and trim1>trim2 if sense==-1.
The local coordinate system 'position' can be both right and left. If the local coordinate system is right and sense=+1 or the local coordinate system is left and sense=-1, then the arc is oriented counterclockwise.

Constructor & Destructor Documentation

◆ MbArc() [1/15]

MbArc::MbArc ( )

Constructor of a circle with default parameters.

A circle is created with center in the origin and zero radius.

◆ MbArc() [2/15]

MbArc::MbArc ( double  rad)

Constructor of a circle by radius.

A circle is created with center in the origin and the given radius.

Parameters
[in]rad- Radius.

◆ MbArc() [3/15]

MbArc::MbArc ( const MbCartPoint p,
double  rad 
)

Constructor of a circle.

A circle is created with center in point 'p' and with the given radius.

Parameters
[in]p- Center of circle.
[in]rad- Radius.

◆ MbArc() [4/15]

MbArc::MbArc ( const MbCartPoint pc,
const MbCartPoint on 
)

Create a circle.

A circle is created with center in point 'pc'. The radius is determined as the distance between points 'pc' and 'on'.

Parameters
[in]pc- Center of circle.
[in]on- Point on circle.

◆ MbArc() [5/15]

MbArc::MbArc ( const MbCartPoint pc,
double  rad,
const MbCartPoint p1,
const MbCartPoint p2,
int  initSense 
)

Constructor of a circular arc.

A circular arc is created with a center in point 'p' and with a given radius. Points 'p1' and 'p2' specify the bounds of arc. The start point of the arc lies on the ray starting from the circle center and passing through point 'p1'. The end point is on the ray passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]pc- Center of circle.
[in]rad- Radius.
[in]p1- A point specifying the beginning of the arc.
[in]p2- A point specifying the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense cannot be equal to zero.

◆ MbArc() [6/15]

MbArc::MbArc ( const MbCartPoint pc,
double  rad,
double  t1,
double  t2,
int  initSense 
)

Constructor of a circular arc.

A circular arc is created with a center in point 'p' and with a given radius. t1 and t2 specify the start and the end angles of the arc. The angles are measured from the OX axis counterclockwise. The angles are given in radians. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]pc- Center of circle.
[in]rad- Radius.
[in]t1- An angle specifying the beginning of the arc.
[in]t2- An angle specifying the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ MbArc() [7/15]

MbArc::MbArc ( const MbArc init,
const MbCartPoint p1,
const MbCartPoint p2,
int  initSense 
)

Constructor of an elliptic arc based on a sample and bounding points.

An arc based on the given sample of circle or ellipse is created. Points 'p1' and 'p2' specify the bounds of arc. The start point of the arc lies on the ray starting from the circle center and passing through point 'p1'. The end point is on the ray passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]init- A sample circle or ellipse.
[in]p1- A point specifying the beginning of the arc.
[in]p2- A point specifying the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ MbArc() [8/15]

MbArc::MbArc ( const MbCartPoint pc,
const MbCartPoint p1,
const MbCartPoint p2,
int  initSense 
)

Constructor of a circular arc.

An arc of a circle centered in point 'pc'. The radius is determined as the distance between points 'pc' and 'p1'. Points 'p1' and 'p2' specify the bounds of arc. The start point of the arc lies on the ray starting from the circle center and passing through point 'p1'. The end point is on the ray passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]pc- Center of circle.
[in]p1- A point determining the beginning of the arc and the radius.
[in]p2- A point specifying the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ MbArc() [9/15]

MbArc::MbArc ( const MbCartPoint p1,
const MbCartPoint p2,
const MbCartPoint p3 
)

Constructor of a circular arc.

A circular arc is created passing through 3 given points. Points p1 and p3 are the end points. Direction of moving along the arc is defined so as point p2 lay on the arc.

Deprecated:
The method is deprecated.
Parameters
[in]p1- Beginning of the arc.
[in]p2- A point on the arc.
[in]p3- End of the arc.

◆ MbArc() [10/15]

MbArc::MbArc ( const MbCartPoint p1,
const MbCartPoint p2,
double  a4 
)

Constructor of a circular arc.

An arc is created with ends at the given points. A circle radius is defined by the given tangent of 1/4 of arc opening angle.

Deprecated:
The method is deprecated.
Parameters
[in]p1- Beginning of the arc.
[in]p2- End of the arc.
[in]a4- Tangent of 1/4 of the arc opening angle.

◆ MbArc() [11/15]

MbArc::MbArc ( double  aa,
double  bb,
const MbPlacement place,
const MbCartPoint p1,
const MbCartPoint p2,
int  initSense 
)

Constructor of an elliptical arc.

An elliptical arc is created with the given semiaxes and the local coordinate system. Points 'p1' and 'p2' specify the bounds of arc. The start point of the arc lies on the ray starting from the circle center and passing through point 'p1'. The end point is on the ray passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]aa- Radius of semiaxis along X.
[in]bb- Radius of semiaxis along Y.
[in]place- The local coordinate system of the ellipse.
[in]p1- A point specifying the beginning of the arc.
[in]p2- A point specifying the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ MbArc() [12/15]

MbArc::MbArc ( double  aa,
double  bb,
const MbPlacement place,
double  t1,
double  t2,
int  initSense 
)

Constructor of an elliptical arc.

An elliptical arc is created with the given semiaxes and the local coordinate system. t1 and t2 specify the start and the end angles of the arc. The angles are measured from the OX axis counterclockwise. The angles are given in radians. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]aa- Radius of semiaxis along X.
[in]bb- Radius of semiaxis along Y.
[in]place- The local coordinate system of the ellipse.
[in]t1- An angle specifying the beginning of the arc.
[in]t2- An angle specifying the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ MbArc() [13/15]

MbArc::MbArc ( const MbArc ellipse,
double  t1,
double  t2,
int  initSense 
)

Constructor of an elliptical arc.

An elliptical arc is constructed with the local coordinate system and semiaxes of the given ellipse. t1 and t2 specify the start and the end angles of the arc. The angles are measured from the OX axis counterclockwise. The angles are given in radians. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]ellipse- A pattern ellipse.
[in]t1- An angle specifying the beginning of the arc.
[in]t2- An angle specifying the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ MbArc() [14/15]

MbArc::MbArc ( double  aa,
double  bb,
const MbPlacement pos 
)

Constructor of an ellipse.

An ellipse is created with the given local coordinate system and semiaxes.

Parameters
[in]aa- Radius of semiaxis along X.
[in]bb- Radius of semiaxis along Y.
[in]pos- The local coordinate system of the ellipse.

◆ MbArc() [15/15]

MbArc::MbArc ( double  aa,
double  bb,
const MbCartPoint c,
double  angle 
)

Constructor of an ellipse.

An ellipse is created with the given semiaxes. The local coordinate system of the ellipse has the origin in point 'c'; OX axis of the local coordinate system forms angle 'angle' with the OX axis of the current coordinate system. Direction of turning from the current coordinate system axis to the axis of the new coordinate system.

Parameters
[in]aa- Radius of semiaxis along X.
[in]bb- Radius of semiaxis along Y.
[in]c- Origin of local coordinate system of ellipse.
[in]angle- An angle between OX axes of the local and the current coordinate systems.

Member Function Documentation

◆ Create() [1/2]

static MbArc* MbArc::Create ( const MbCartPoint p1,
const MbCartPoint p2,
const MbCartPoint p3 
)
static

Create circular arc.

A circular arc is created passing through 3 given points. Points p1 and p3 are the end points. Direction of moving along the arc is defined so as point p2 lay on the arc.

Parameters
[in]p1- Beginning of the arc.
[in]p2- A point on the arc.
[in]p3- End of the arc.

◆ Create() [2/2]

static MbArc* MbArc::Create ( const MbCartPoint p1,
const MbCartPoint p2,
double  a4 
)
static

Create circular arc.

An arc is created with ends at the given points. A circle radius is defined by the given tangent of 1/4 of arc opening angle.

Parameters
[in]p1- Beginning of the arc.
[in]p2- End of the arc.
[in]a4- Tangent of 1/4 of the arc opening angle.

◆ Duplicate()

MbPlaneItem& MbArc::Duplicate ( MbRegDuplicate iReg = nullptr) const
overridevirtual

Create a copy.

Create a copy of the object using the registrator. The registrator is used for preventing multiple copying of an object. If the object contains references to other objects, then the included objects are copied too. It is allowed not to pass the registrator to a function. Then the new copy of the object will be created. It is allowed not to use the registrator while copying a single object or a set of disconnected objects. The registrator must be used to copy several correlated objects successively. It is possible that the objects' connection means that the objects contain references to the common objects. Then, while copying without using the registrator, one can get a set of copies which contain references to the different copies of a single included object, what leads to loss of connection between the copies.

Parameters
[in]iReg- Registrator.
Returns
Copy of the object.

Implements MbPlaneItem.

◆ IsSame()

bool MbArc::IsSame ( const MbPlaneItem item,
double  accuracy = LENGTH_EPSILON 
) const
overridevirtual

Determine whether objects are equal.

Objects of the same types with similar (equal) data are considered to be equal.

Parameters
[in]item- Object for comparison.
[in]accuracy- The accuracy.
Returns
Whether the objects are equal.

Implements MbPlaneItem.

◆ SetEqual()

bool MbArc::SetEqual ( const MbPlaneItem item)
overridevirtual

Make the objects equal.

It is possible to make equal only similar objects. Similar object is equated to a given one by changing of numerical data.

Parameters
[in]item- Object for initialization.
Returns
Whether the object is made equal to the given one.

Implements MbPlaneItem.

◆ Transform()

void MbArc::Transform ( const MbMatrix matr,
MbRegTransform iReg = nullptr,
const MbSurface newSurface = nullptr 
)
overridevirtual

Transform according to the matrix.

Transform the initial object according to the matrix using the registrator. If the object contains references to the other geometric objects, then the nested objects are transformed according to the matrix. The registrator is used for preventing multiple transformation of the object. The function can be used without the registrator to transform a single object. The registrator must be used to transform a set of interdependent objects to prevent repeated transformation of the nested objects, since it is not ruled out that several objects from the set contain references to one or several common objects subject to transformation.

Parameters
[in]matr- A transformation matrix.
[in]iReg- Registrator.
[in]surface- New base surface of object provided that 'matr' is a transformation matrix from the old surface to a new one. For transformation of projection curve. It isn't considered if the surface is planar.

Implements MbPlaneItem.

◆ Move()

void MbArc::Move ( const MbVector to,
MbRegTransform iReg = nullptr,
const MbSurface newSurface = nullptr 
)
overridevirtual

Translate along a vector.

Translate a geometric object along the vector using the registrator. If the object contains references to the other objects, then the translation operation is applied to the nested objects. The registrator is used for preventing multiple transformation of the object. The function can be used without the registrator to transform a single object. The registrator must be used to transform a set of interdependent objects to prevent repeated transformation of the nested objects, since it is not ruled out that several objects from the set contain references to one or several common objects subject to translation.

Parameters
[in]to- Translation vector.
[in]iReg- Registrator.
[in]surface- New base surface of object provided that 'matr' is a transformation matrix from the old surface to a new one. For transformation of projection curve. It isn't considered if the surface is planar.

Implements MbPlaneItem.

◆ Rotate()

void MbArc::Rotate ( const MbCartPoint pnt,
const MbDirection angle,
MbRegTransform iReg = nullptr,
const MbSurface newSurface = nullptr 
)
overridevirtual

Rotate about a point.

Rotate an object about a point by the given angle using the registrator. If the object contains references to the other geometric objects, then the rotation operation is applied to the nested objects too. The registrator is used for preventing multiple transformation of the object. The function can be used without the registrator to transform a single object. The registrator must be used to transform a set of interdependent objects to prevent repeated transformation of the nested objects, since it is not ruled out that several objects from the set contain references to one or several common objects subject to rotation.

Parameters
[in]pnt- Fixed point.
[in]angle- The rotation angle.
[in]iReg- Registrator.
[in]surface- New base surface of object provided that 'matr' is a transformation matrix from the old surface to a new one. For transformation of projection curve. It isn't considered if the surface is planar.

Implements MbPlaneItem.

◆ DistanceToPointIfLess()

bool MbArc::DistanceToPointIfLess ( const MbCartPoint to,
double &  d 
) const
overridevirtual

Calculate the distance to a point.

Calculate distance to object from a given point near the object. Distance is calculated and stored to 'd' variable if it is less then initial value of 'd'. There can be performance benefit in comparison with DistanceToPoint function due to primarily checking the distance from point to bounding box and performing the further calculations only if this distance is not greater than the given one.

Parameters
[in]to- Point.
[in,out]d- Specified distance from object on input. Distance from point to object on output if operation succeeded.
Returns
True if distance from point to the object is less than the given one, otherwise false. Calculate the distance from a point and change the given value of distance if the distance is less than the given one.

Implements MbPlaneItem.

◆ CalculateGabarit()

void MbArc::CalculateGabarit ( MbRect ) const
overridevirtual

Detect the bounding box of a curve.

The sent rectangle becomes empty for getting a bounding box. Then bounding boxes of an object are calculated and saved into a rectangle 'rect'.

Reimplemented from MbCurve.

◆ Deformation()

MbeState MbArc::Deformation ( const MbRect rect,
const MbMatrix matr 
)
overridevirtual

Deform the curve.

If the bounding rectangle of a curve intersects the given one, then the curve is transformed according to the matrix with a help of 'Transform' function.

Parameters
[in]rect- A rectangle, in which the visibility of a curve is checked.
[in]matr- A deformation matrix.
Returns
A state of a curve after deformation.

Reimplemented from MbCurve.

◆ PrepareIntegralData()

void MbArc::PrepareIntegralData ( const bool  forced) const
overridevirtual

Calculate temporary (mutable) data of an object.

Calculate the temporary data of an object depending of the "forced" parameter. Calculate only data that was not calculated earlier if parameter "forced" is equal false. Recalculate all temporary data of an object if parameter "forced" is equal true.

Parameters
[in]forced- Forced recalculation.

Reimplemented from MbCurve.

◆ IsVisibleInRect() [1/2]

bool MbArc::IsVisibleInRect ( const MbRect rect,
bool  exact = false 
) const
overridevirtual

Determine visibility of an object in rectangle.

It is considered that the object is visible in rectangle if bounds of an object is crossed with the given rectangle or (high requirements to accuracy, exact = true) at least one point of object is in the rectangle.

Parameters
[in]rect- Rectangle to check getting to.
[in]exact- Check accuracy. If exact = true, then at least one point of object gets to the rectangle. if exact = false, it is sufficient to find intersection between rectangle and bounding box of an object.
Returns
true, if the object is visible in the rectangle, otherwise false.

Implements MbPlaneItem.

◆ IsCompleteInRect()

bool MbArc::IsCompleteInRect ( const MbRect rect) const
overridevirtual

Determine whether an object is fully visible in rectangle.

An object is fully contained in the given rectangle if its bounding rectangle is included in the given rectangle.

Parameters
[in]rect- Rectangle to check inclusion to.
Returns
true, if the object is fully contained in the rectangle, otherwise false.

Reimplemented from MbCurve.

◆ IsClosed()

bool MbArc::IsClosed ( ) const
overridevirtual

Define whether the curve is periodic.

Define whether the curve is periodic.
A periodic curve is closed. A curve is considered as periodic if:

  • start point is coincident with end point;
  • derivatives in start point and end point coincide;
    if there are breaks at curve (in cases when a curve is contour or polyline), then derivatives may not coincide; in Bezier curve derivatives should coincide by direction, but they may differ by absolute value.
    Curves:
  • MbLine,
  • MbLineSegment,
  • MbCosinusoid,
  • MbContour (if it contains only a single segment of one of the listed types)
    are not considered periodic when the start and end points coincide. The IsClosed() method always returns false for them.
    Returns
    True if a curve is closed.

Implements MbCurve.

◆ GetPeriod()

double MbArc::GetPeriod ( ) const
overridevirtual

Return period.

Return the period value if a curve can be closed. Let unclosed curve return null.

Returns
The value of period for a closed curve or null - for unclosed curve.

Reimplemented from MbCurve.

◆ PointOn()

void MbArc::PointOn ( double &  t,
MbCartPoint p 
) const
overridevirtual

Calculate a point on the curve.

Correct parameter when getting out of domain bounds and calculate a point on the curve.

Parameters
[in]t- Curve parameter.
[out]p- A point on the curve.

Implements MbCurve.

◆ _PointOn()

void MbArc::_PointOn ( double  t,
MbCartPoint p 
) const
overridevirtual

Calculate point at curve and its extension.

Calculate a point on the curve including the outside area determination parameter.

Parameters
[in]t- Curve parameter.
[out]p- A point on the curve.

Reimplemented from MbCurve.

◆ Explore()

void MbArc::Explore ( double &  t,
bool  ext,
MbCartPoint pnt,
MbVector fir,
MbVector sec,
MbVector thir 
) const
overridevirtual

Calculate point and derivatives of object for given parameter.

Values of point and derivatives are calculated on parameter area and on extended curve.

Parameters
[in]t- Parameter.
[in]ext- On parameters area (false), on extended curve (true).
[out]pnt- Point.
[out]fir- Derivative with respect to t.
[out]sec- Second derivative with respect to t, if not nullptr.
[out]thir- Third derivative with respect to t, if not nullptr.

Reimplemented from MbCurve.

◆ Step()

double MbArc::Step ( double  t,
double  sag 
) const
overridevirtual

Calculate parameter step.

Calculate parameter step for the curve's approximation by its sag value. Calculation of the step is performed with consideration of curvature radius. A step of curve's approximation is chosen in such way, that the deviation of a curve from its polygon does not exceed the given sag value.

Parameters
[in]t- A parameter defining the point on a curve, at which a step should be calculated.
[in]sag- Maximum feasible sag value.
Returns
A sag value by parameter at given point.

Reimplemented from MbCurve.

◆ DeviationStep()

double MbArc::DeviationStep ( double  t,
double  ang 
) const
overridevirtual

Calculate parameter step.

Calculate parameter step for the curve's approximation by the deviation angle of the tangent vector. A step of curve's approximation is chosen in such way, that angular deviation of the tangent curve at the next point does not exceed the given value ang.

Parameters
[in]t- A parameter defining the point on a curve, at which a step should be calculated.
[in]ang- The maximum feasible deviation angle of tangent.
Returns
A sag value by parameter at given point.

Reimplemented from MbCurve.

◆ GetMetricLength()

double MbArc::GetMetricLength ( ) const
overridevirtual

Calculate the metric length of a curve.

If a length of a curve is already calculated and saved in the object then this function returns the existing result, without repeating of calculations. Otherwise the length is calculated by the function CalculateMetricLength().

Returns
Length of a curve.

Implements MbCurve.

◆ GetLengthEvaluation()

double MbArc::GetLengthEvaluation ( ) const
overridevirtual

Calculate the metric length of a curve.

The length of a curve is inaccurately calculated, by approximation of polyline. If the more accurate curve's length is required, then use the function CalculateMetricLength().

Reimplemented from MbCurve.

◆ CalculateLength()

double MbArc::CalculateLength ( double  t1,
double  t2 
) const
overridevirtual

Calculate the metric length of a curve.

Calculate the metric length of unclosed curve from parameter t1 to parameter t2. The condition t1 < t2 should satisfied.

Parameters
[in]t1- Start parameter of a curve section.
[in]t2- End parameter of a curve section.
Returns
Length of a curve.

Reimplemented from MbCurve.

◆ DistanceAlong()

bool MbArc::DistanceAlong ( double &  t,
double  len,
int  curveDir,
double  eps = Math::LengthEps,
VERSION  version = Math::DefaultMathVersion() 
) const
overridevirtual

Translate parameter along the curve.

Translate parameter along the curve by the given distance at the given direction. The new value of parameter is saved in the variable t. If the curve is not closed and the length of its part from the point with parameter t to the end at the given direction is less than the required shift, then calculations are performed on extension of the curve, if it possible to construct such extension.

Parameters
[in,out]t- Input - the initial value of parameter. Output - the new value of parameter.
[in]len- The value of shift along the curve.
[in]curveDir- The offset direction. If curveDir is non-negative, then the shift is directed to the side of increasing of parameter. Otherwise - to the side of decreasing of parameter.
[in]eps- Computational tolerance.
[in]version- Version.
Returns
True - if the operation is performed successfully, otherwise false.

Reimplemented from MbCurve.

◆ PointProjection()

double MbArc::PointProjection ( const MbCartPoint pnt) const
overridevirtual

Calculate the point projection to the curve.

Calculate the parameter of the curve corresponding to the projection of the given point on this curve.
This function does not allow the parameter to go beyond the parametric domain of the definition of an unclosed curve, unlike the NearPointProjection function.

Parameters
[in]pnt- A given point.
Returns
The found parameter for the projection of a point onto the curve.

Reimplemented from MbCurve.

◆ NearPointProjection()

bool MbArc::NearPointProjection ( const MbCartPoint pnt,
double  xEpsilon,
double  yEpsilon,
double &  t,
bool  ext,
MbRect1D tRange = nullptr 
) const
overridevirtual

Find the point projection to the curve.

Find the nearest projection of a point on a curve (in the range of the curve) or on its continuation by the given initial approximation. If the parameter ext = true, then also search for a projection on the continuation of the curve. If the range of change of the 'tRange' parameter is specified, then find the projection in the specified range. A range of parameter may not belong to the domain of a curve. The Newton method is used.

Note
Mathematical kernel provides a thread-safe function implementation for its objects.
Parameters
[in]pnt- A given point.
[in]xEpsilon- A tolerance of detection of the projection by x axis.
[in]yEpsilon- A tolerance of detection of the projection by y axis.
[in,out]t- Input - initial approximation, output - parameter of a curve corresponding to the nearest projection.
[in]ext- A flag defining whether to seek projection on the extension of the curve.
[in]tRange- A range of parameter changing in which the solution should be found.
Returns
Returns true if the found parameter is in a valid range (according to the given ext, tRange parameters), or false - otherwise.

Reimplemented from MbCurve.

◆ TangentPoint()

void MbArc::TangentPoint ( const MbCartPoint pnt,
SArray< double > &  tFind 
) const
overridevirtual

Find tangents to a curve.

Find all tangents to a curve from the given point. A point may belong to a curve. In this function a curve without extensions is considered.

Parameters
[in]pnt- A given point.
[in,out]tFind- An array of parameters of a curve, corresponding to the tangent points.

Reimplemented from MbCurve.

◆ PerpendicularPoint()

void MbArc::PerpendicularPoint ( const MbCartPoint pnt,
SArray< double > &  tFind 
) const
overridevirtual

Find perpendiculars to a curve.

Find all perpendiculars to a curve from the given point. In this function a curve without extensions is considered.

Parameters
[in]pnt- A given point.
[in,out]tFind- An array of parameter on a curve, corresponding to the points on a curve, which the perpendiculars are passed through.

Reimplemented from MbCurve.

◆ SmallestPerpendicular()

bool MbArc::SmallestPerpendicular ( const MbCartPoint pnt,
double &  tProj 
) const
overridevirtual

Find the nearest perpendicular to the curve.

Find the nearest perpendicular to the curve from the given point. In this function perpendiculars to an extension of a curve are not considered.

Parameters
[in]pnt- A given point.
[in,out]tProj- Parameter on a curve, corresponding to the point on a curve, which the perpendicular is passed through.
Returns
True if the required perpendicular is constructed.

Reimplemented from MbCurve.

◆ IntersectHorizontal()

void MbArc::IntersectHorizontal ( double  y,
SArray< double > &  cross 
) const
overridevirtual

Find intersections of a curve with horizontal line.

Find intersections of a curve with horizontal line.

Parameters
[in]y- An ordinate of points of a horizontal line.
[in,out]cross- An array of parameters of a curve corresponding to the intersection points.

Reimplemented from MbCurve.

◆ IntersectVertical()

void MbArc::IntersectVertical ( double  x,
SArray< double > &  cross 
) const
overridevirtual

Find intersections of a curve with vertical line.

Find intersections of a curve with vertical line.

Parameters
[in]x- An abscissa of points of a vertical line.
[in,out]cross- An array of parameters of a curve corresponding to the intersection points.

Reimplemented from MbCurve.

◆ GetRadius()

double MbArc::GetRadius ( double  accuracy = PARAM_REGION) const
overridevirtual

Get the physical radius of the curve or zero if it impossible.

Generally returns 0. A non-zero value may be obtained only when the curve is an arc or is equal to an arc with the set precision (PARAM_REGION by default). \params[in] accuracy - The maximum curve deviation from an arc (PARAM_REGION by default).

Returns
Radius value if it can be obtained or 0.0.

Reimplemented from MbCurve.

◆ HasLength()

bool MbArc::HasLength ( double &  length) const
overridevirtual

Calculate the metric length of a curve.

Calculate the metric length of a curve and save the result in the variable 'length'.

Parameters
[in,out]length- Calculated length of a curve.
Returns
True - if the length of a curve differs from null. Otherwise returns false.

Implements MbCurve.

◆ NurbsCurve() [1/2]

MbNurbs* MbArc::NurbsCurve ( const MbCurveIntoNurbsInfo nInfo) const
overridevirtual

Construct a NURBS copy of a curve.

Constructs a NURBS curve which approximates a given curve inside the range [t1, t2]. with a given direction. If it is possible, constructs the accurate curve, perhaps with multiple knots. The number of knots for NURBS is defined depending on the curve.

Parameters
[in,out]nurbs- A constructed NURBS-curve.
[in]t1- Parameter corresponding to start of approximated part of a curve.
[in]t2- Parameter corresponding to end of approximated part of a curve.
[in]sense- Does the direction of parameter increasing along the NURBS curve coincide with direction of the initial curve. 'sense' > 0 - direction coincide.
[in]nInfo- Parameters of conversion of a curve to NURBS.
Returns
The constructed NURBS curve or nullptr in a case of failure.

Implements MbCurve.

◆ NurbsCurve() [2/2]

MbCurve* MbArc::NurbsCurve ( const MbNurbsParameters tParameters) const
overridevirtual

Construct a NURBS copy of a curve.

Constructs a NURBS curve which approximates a given curve with the given parameters. In parameters the degree and the number of knots of a spline and the range of curve's parameters changing may be set. If the flag of accurate approximation is not set in parameters then NURBS without multiple knots is constructed.

Parameters
[in]tParameters- Parameters for the construction of a NURBS copy of the curve.
Returns
The constructed NURBS curve or nullptr in a case of failure.

Reimplemented from MbCurve.

◆ Trimmed() [1/3]

MbCurve* MbArc::Trimmed ( double  t1,
double  t2,
int  sense,
const MbDimAccuracy xyEps,
bool  saveParamLenAndLaw 
) const
overridevirtual

Construct a trimmed curve with the given two-dimensional accuracy.

Constructs a trimmed curve, a start point of which corresponds to a point with parameter t1 and an end point corresponds to a point with parameter t2. Direction of the constructed curve relative to the initial curve may be changed by the parameter 'sense'. If the curve is closed, then there may be obtained a trimmed curve, passing through the start of a curve.
In a case of closed curve (or for an arc - exception) three parameters 'sense', t1 and t2 clearly define the result. In a case of unclosed curve the parameter 'sense' and parameter of trimming should correspond each other:
1) if sense == 1, then t1 < t2,
2) if sense == -1, then t1 > t2,
If there is a discrepancy between 'sense' and parameters of trimming, then 'sense' parameter has higher priority. If parameters t1 and t2 are equal and the curve is closed, then in result a closed curve should be obtained.

Parameters
[in]t1- Parameter corresponding to start of a trimmed curve.
[in]t2- Parameter corresponding to end of a trimmed curve.
[in]sense- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]xyEps- Two-dimensional accuracy. It is used for estimations near the points corresponding to the parameters t1 and t2.
[in]saveParLenAndLaw- Save parametric length and law.
Returns
A constructed trimmed curve.
Warning
Under development.

Implements MbCurve.

◆ PointRelative()

MbeItemLocation MbArc::PointRelative ( const MbCartPoint pnt,
double  eps = Math::LengthEps 
) const
overridevirtual

Define the point position relative to the curve.

There is defined on which side from a curve the point is located, by the positive direction of a curve.

Parameters
[in]pnt- A given point.
[in]eps- A tolerance of detection.
Returns
Iloc_InItem = 1 - if the point is on the left from a curve,
iloc_OnItem = 0 - if the point is on a curve,
iloc_OutOfItem = 1 - if the point is on the right from a curve.

Reimplemented from MbCurve.

◆ DeletePart()

MbeState MbArc::DeletePart ( double  t1,
double  t2,
MbCurve *&  part2 
)
overridevirtual

Delete the piece of a curve.

Delete a part of a curve between parameters t1 and t2. If the curve is split into two parts after deletion, then the initial object corresponds to the start part of a curve, and parameter 'part2' contains the end part of a curve. If the curve remained simply connected, then only the initial object changes.

Parameters
[in]t1- Start parameter of trimming.
[in]t2- End parameter of trimming.
[in,out]part2- The end part of a curve after deletion, if an initial curve is split into parts. It may be the only part after deletions, \ if the curve did not change (e. g. for a curve of MbLine type), in this case the returned value is dp_Degenerated.
Returns
A state of a curve after modification.

Implements MbCurve.

◆ TrimmPart()

MbeState MbArc::TrimmPart ( double  t1,
double  t2,
MbCurve *&  part2 
)
overridevirtual

Keep the piece of a curve.

Leave a part of a curve between parameters t1 and t2.
In a case of success the returned value equals dp_Changed and a curve satisfies to the next conditions:

  • if an initial curve is closed then the start point of a trimmed curve should correspond to the parameter t1, the end point - to the parameter t2,
  • if an initial curve is not closed then the start point of a trimmed curve should correspond to the minimum parameter from t1 and t2, the end point - to the maximum one.
    Parameters
    [in]t1- Start parameter of trimming.
    [in]t2- End parameter of trimming.
    [in,out]part2- This may be filled by a result of trimming if the curve was not changed. In this case the returned value is dp_Degenerated. Otherwise nullptr is returned.
    Returns
    A state of a curve after modification:
    dp_Degenerated - the curve is degenerated and there are possible three cases: the curve was not changed, because it would degenerate in a result of transformation, or it it was not changed and the result of trimming is 'part2',
    dp_NoChanged - the curve was not changes,
    dp_Changed - the curve is changed.
    Warning
    The function is designed for internal use only.

Implements MbCurve.

◆ ModifyByPoint()

bool MbArc::ModifyByPoint ( size_t  ind,
const MbCartPoint pnt 
)

Modify the ellipse by a characteristic point.

Parameters
[in]ind- Index of a characteristic point. Possible values:
0 - Ellipse center.
1 - The point on ellipse corresponding to 0 degrees.
2 - The point on ellipse corresponding to 90 degrees.
3 - The point on ellipse corresponding to 180 degrees.
4 - The point on ellipse corresponding to 270 degrees.
[in]pnt- Characteristic point.
Returns
True - if the operation succeeded. Otherwise returns false.

◆ GetSpecificPoint()

bool MbArc::GetSpecificPoint ( const MbCartPoint from,
double &  dmax,
MbCartPoint pnt 
) const
overridevirtual

Return a specific point of a curve.

Return a specific point of a curve if the distance from it to the given point is less than dmax. Specific points of a bounded curve are its start and end points.

Parameters
[in]from- A control point
[in,out]dmax- Input - maximum distance for search of specific point. Output - a distance from the point 'from' to the found specific point.
[in,out]pnt- Tangent vector.
Returns
True - if the specific point is found.

Reimplemented from MbCurve.

◆ Isoclinal()

void MbArc::Isoclinal ( const MbVector angle,
SArray< double > &  tFind 
) const
overridevirtual

Construct isoclines.

Construct lines at an angle to the axis OX and tangent to the curve.

Parameters
[in]angle- A vector defining an inclination angle of line to the axis OX.
[in,out]tFind- An array of parameters of a curve, corresponding to the tangent points.

Reimplemented from MbCurve.

◆ GetAxisPoint()

bool MbArc::GetAxisPoint ( MbCartPoint p) const
overridevirtual

Calculate a point to construct an axis.

Calculates a point to construct an axis, if a curve may be constructed by rotation of a point around an axis.

Returns
true, if such axis exists.

Reimplemented from MbCurve.

◆ Extend()

MbResultType MbArc::Extend ( const MbCurveExtensionParameters parameters,
c3d::PlaneCurveSPtr resCurve 
) const
overridevirtual

Extend the curve.

Extend the curve according to the given parameters.

Parameters
[in]parameters- Parameters of extension.
[out]resCurve- The extended curve or nullptr if extension is impossible.
Returns
Returns error status or rt_Success if all is OK.

Reimplemented from MbCurve.

◆ GetPositionAngle()

double MbArc::GetPositionAngle ( const MbCartPoint p) const

Calculate the angle in the local coordinate system.

Calculate the angle between OX axis of the local coordinate system and the ray starting from the origin of local coordinate system and passing through point p.

Parameters
[in]p- A given point.
Returns
Value of angle.

◆ InitByPositionAngles()

void MbArc::InitByPositionAngles ( double  a1,
double  a2,
int  initSense,
const MbDimAccuracy xyEps = MbDimAccuracy::twoDimRgn 
)

Initialization of the ellipse parameters.

Parameters are calculated subject to the directions and angles corresponding to the beginning and the end of the arc calculated in the local coordinate system.

Parameters
[in]a1- The angle corresponding to the beginning of the arc.
[in]a2- The angle corresponding to the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.
[in]xyEps- The xyEps.x component corresponds to x-axis accuracy, xyEps.y corresponds to y-axis accuracy.
Returns
Value of angle.

◆ Init3Points()

bool MbArc::Init3Points ( const MbCartPoint p1,
const MbCartPoint p2,
const MbCartPoint p3,
bool  cl 
)

Initialize a circular arc.

Initialize a circular arc passing through all 3 given points. Points p1 and p3 are the end points. If the arc is not closed, then the direction of moving along the arc is defined so as the point p2 lies on the arc.

Parameters
[in]p1- Beginning of the arc.
[in]p2- A point on the arc.
[in]p3- End of the arc.
[in]cl- Closedness attribute.
Returns
True if initialization completed successfully.

◆ InitCircle()

void MbArc::InitCircle ( const MbCartPoint p1,
const MbCartPoint p2,
const MbCartPoint p3 
)

Initialize a circular arc.

Initialize a circular arc passing through all 3 given points. Points p1 and p3 are the end points. The direction of moving along the arc is defined so as the point p2 lies on the arc.

Parameters
[in]p1- Beginning of the arc.
[in]p2- A point on the arc.
[in]p3- End of the arc.

◆ InitArc()

void MbArc::InitArc ( MbCartPoint pc,
const MbCartPoint p1,
const MbCartPoint p2 
)

Initialize a circular arc.

A new position of the arc center is specified, the arc center will be located on the bisector of the opening angle.

Parameters
[in]pc- Center of circle.
[in]p1- Beginning of the arc.
[in]p2- End of the arc.

◆ Init() [1/17]

void MbArc::Init ( const MbCartPoint pc,
double  rad,
const MbCartPoint p1,
const MbCartPoint p2,
bool  clockwise 
)

Initialize a circular arc.

The center and the radius of the circle is being modified. Points 'p1' and 'p2' specify the bounds of arc. The start point of the arc lies on the ray starting from the circle center and passing through point 'p1'. The end point is on the ray passing through the point 'p2'. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]pc- Center of circle.
[in]rad- Radius.
[in]p1- A point specifying the beginning of the arc.
[in]p2- A point specifying the end of the arc.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

◆ Init() [2/17]

void MbArc::Init ( const MbCartPoint pc,
const MbCartPoint p 
)

Initialize a circle.

The source object is changed to a circle with center in point 'pc'. The radius is determined as a distance between points pc and p.

Parameters
[in]pc- Center of circle.
[in]p- Point on circle.

◆ Init() [3/17]

void MbArc::Init ( const MbCartPoint p1,
double  angle,
double  rad 
)

Initialize a circle.

The source object is changed to a circle passing through point p1 with the given radius. Angle 'angle' specifies a line the circle's center lies on. It is the angle between a ray starting from point p1 and directed to the circle's center and OX axis.

Parameters
[in]p1- Point on circle.
[in]angle- An angle specifying the position of the center on the circle.
[in]rad- Radius.

◆ Init() [4/17]

void MbArc::Init ( const MbCartPoint pc,
const MbCartPoint pnt,
double  angle 
)

Initialize a circle.

The source object is changed to a circle with the given center and passing through point pnt. The radius is determined as the distance between points pc and pnt.

Parameters
[in]pc- Center of circle.
[in]pnt- Point on circle.
[in]angle- Get the start parameter.

◆ Init() [5/17]

void MbArc::Init ( const MbCartPoint pc,
double  angle1,
double  angle2,
double  rad,
bool  clockwise 
)

Initialize a circular arc.

The source object is changed to a circular arc with the given center and radius. angle1 and angle2 specify the start and the end angles of the arc. The angles are measured from the OX axis counterclockwise. The angles are given in radians. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters
[in]pc- Center of circle.
[in]angle1- An angle specifying the beginning of the arc.
[in]angle2- An angle specifying the end of the arc.
[in]rad- Radius.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

◆ Init() [6/17]

void MbArc::Init ( const MbCartPoint pc,
const MbCartPoint pnt,
bool  firstPoint,
double  angle,
bool  clockwise 
)

Initialize a circular arc.

The source object is changed to a circular arc with the given center and passing through point pnt. The radius is determined as the distance between points pc and pnt. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters
[in]pc- Center of circle.
[in]pnt- End point of the circular arc.
[in]firstPoint- Flag determining whether the point pnt is the start point.
[in]angle- The angle between the radius to the second point and the OX axis.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

◆ Init() [7/17]

void MbArc::Init ( const MbCartPoint pc,
double  angle1,
const MbCartPoint p2,
double  rad,
bool  clockwise 
)

Initialize a circular arc.

The source object is changed to a circular arc with the given center and radius. The end point of the arc is determined as intersection of ray (pc, p2) and the circle. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters
[in]pc- Center of circle.
[in]angle1- The start parameter of the circle.
[in]p2- A point specifying the angle of the circular arc end.
[in]rad- Radius.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. initSense can't be equal to zero.

◆ Init() [8/17]

void MbArc::Init ( MbArc obj,
const MbCartPoint p1,
const MbCartPoint p2,
int  initSense 
)

Initialize a circular arc.

The source object is changed to a circular arc corresponding to a given object. The start and the end point of the arc is determined as intersection of rays passing from the center to points p1 and p2 with the circle. The end point of the arc is determined as intersection of ray (pc, p2) and the circle. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]obj- A pattern object.
[in]p1- A point determining the angle of the beginning of the circular arc.
[in]p2- A point specifying the angle of the circular arc end.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ Init() [9/17]

void MbArc::Init ( const MbCartPoint p1,
const MbCartPoint p2,
double  angle,
bool  firstAngle,
bool  clockwise 
)

Initialize a circular arc.

In the result of the operation the circular arc is obtained which starts at point p1 and ends at point p2. For one of points the angle between the direction from the point to the circle center and the OX axis is specified. Parameter firstAngle determines for which of points the angle is specified. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters
[in]p1- The start point of the circular arc.
[in]p2- The end point of the circular arc.
[in]angle- The angle between the direction from the point to the circle center and OX axis.
[in]firstAngle- Flag determining for which point the angle is specified. firstAngle == true - for the first one.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

◆ Init() [10/17]

void MbArc::Init ( MbCartPoint pc,
double  angle1,
double  angle2,
const MbCartPoint pnt,
bool  firstPoint,
bool  clockwise 
)

Initialize a circular arc.

In the result of the operation a circular arc is obtained one of ends of which is point pnt. For this point the angle between the line directed from the point to the circle center and OX axis is specified. Find projection pc onto this line to determine the circle center.
The second angle specifies the second end of the arc. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters
[in,out]pc- On input - the given point, on output - the circle center.
[in]angle1- Angle between the direction from the starting point of the arc to the circle center and OX axis.
[in]angle2- Angle between the direction from the end point of the arc to the circle center and OX axis.
[in]pnt- End point of the circular arc.
[in]firstPoint- Flag determining whether the point pnt is a starting point.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

◆ Init() [11/17]

void MbArc::Init ( MbCartPoint pc,
const MbCartPoint p,
bool  firstPoint,
double  angle,
double  rad,
bool  clockwise 
)

Initialize a circular arc.

The source object is changed to the circular arc with the given radius and passing through point p. The circle center should be defined so as it is as close to the given point pc as possible. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters
[in,out]pc- On input - the given point, on output - the circle center.
[in]p- End point of the circular arc.
[in]firstPoint- Flag determining whether the point pnt is a starting point.
[in]angle- The angle between the radius to the second point and the OX axis.
[in]rad- Radius.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

◆ Init() [12/17]

void MbArc::Init ( const MbCartPoint pc,
const MbCartPoint p1,
const MbCartPoint p2,
int  initSense 
)

Initialize a circular arc.

In the result of the operation the circular arc is obtained with the center in point pc. The radius is determined as the distance between points 'pc' and 'p1'. Directions from the center to points p1 and p2 specify the angles determining the start and the end of the circle. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters
[in]pc- Center of circle.
[in]p1- A point specifying the direction to the beginning of the circular arc.
[in]p2- A point specifying the direction to the end of the circular arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ Init() [13/17]

bool MbArc::Init ( double  a2,
MbCartPoint p1,
MbCartPoint p2,
const DiskreteLengthData diskrData = nullptr,
bool  correctFirstPnt = true 
)

Initialize a circular arc.

The initialization is performed by the starting and end points and 1/2 of the arc opening angle. If diskrData != nullptr, the radius is rounded and the first or the second point is corrected (depends on correctFirstPnt).

Parameters
[in]a2- 1/2 of the circular arc opening angle.
[in,out]p1- The starting point of the arc. Can be corrected after rounding the radius.
[in,out]p2- The end point of the arc. Can be corrected after rounding the radius.
[in]diskrData- The structure for rounding the radius.
[in]correctFirstPnt- Determines which point to be corrected after the rounding. correctFirstPnt == true - the first point is to be corrected.
Returns
True if initialization completed successfully.

◆ Init() [14/17]

void MbArc::Init ( double  aa,
double  bb,
const MbPlacement place 
)

Initialize an ellipse.

In the result of the operation the ellipse is obtained with the given local coordinate system and semiaxes.

Parameters
[in]aa- Radius of semiaxis along X.
[in]bb- Radius of semiaxis along Y.
[in]place- The local coordinate system of the ellipse.

◆ Init() [15/17]

void MbArc::Init ( double  aa,
double  bb,
const MbCartPoint pc,
double  ang 
)

Initialize an ellipse.

In the result of the operation the ellipse is obtained with the specified semiaxes. The ellipse local coordinate system has origin in point pc; OX axis of the local coordinate system forms angle ang with OX axis of the current coordinate system. The turning direction - from the axis of the current coordinate system to the axis of the new coordinate system.

Parameters
[in]aa- Radius of semiaxis along X.
[in]bb- Radius of semiaxis along Y.
[in]pc- Origin of local coordinate system of ellipse.
[in]ang- An angle between OX axes of the local and the current coordinate systems.

◆ Init1()

void MbArc::Init1 ( const MbCartPoint c,
const MbCartPoint p1,
double &  len,
double &  angle 
)

Initialize an ellipse.

In the result of the operation an ellipse is obtained with center in point c. The length of ellipse semiaxis along X-axis is determined as the distance between points c and p1. The length of the second semiaxis is 0. The angle between OX axes of the ellipse's local coordinate system and the current coordinate system.

Parameters
[in]c- The ellipse center.
[in]p1- A point on ellipse.
[out]len- The length of semiaxis along X.
[out]angle- An angle between OX axes of the local and the current coordinate systems.

◆ Init2()

void MbArc::Init2 ( const MbCartPoint c,
const MbCartPoint p1,
MbCartPoint p2,
double &  lenB 
)

Initialize an ellipse.

In the result of the operation an ellipse is obtained with center in point c. Point p1 determines the direction of OX axis of ellipse's local coordinate system and the length of semiaxis along X. Point p2 determines the length of semiaxis along Y as the distance from the point to the OX axis of the local coordinate system. Point p2 is changed so as it lies on intersection of the ellipse with OY axis of the local coordinate system.

Parameters
[in]c- The ellipse center.
[in]p1- A point on ellipse specifies OX axis.
[in,out]p2- Specifies the length of semiaxis along Y. On output - point on intersection of ellipse with OY axis of the local coordinate system.
[out]lenB- The length of semiaxis along Y.

◆ Init3()

void MbArc::Init3 ( const MbCartPoint c0,
const MbCartPoint p1,
double  angle,
double &  aa,
double &  bb 
)

Initialize an ellipse.

In the result of the operation an ellipse is obtained inscribed into the rotated rectangle specified by the point of center c, the vertex p1 and the slope angle 'angle'. OX-axis of the local coordinate system of the ellipse will be oriented according to the angle 'angle'.

Parameters
[in]c0- The center of the rectangle.
[in]p1- The rectangle vertex.
[in]angle- Slope angle of the rectangle.
[out]aa- The length of semiaxis along X.
[out]bb- The length of semiaxis along Y.

◆ Init4() [1/2]

void MbArc::Init4 ( const MbCartPoint p1,
const MbCartPoint p2,
double  angle,
double &  aa,
double &  bb 
)

Initialize an ellipse.

In the result of the operation an ellipse is obtained inscribed into the rotated rectangle specified by two diagonal points p1 and p2 and the slope angle 'angle'. OX-axis of the local coordinate system of the ellipse will be oriented according to the angle 'angle'.

Parameters
[in]p1- The rectangle vertex.
[in]p2- The rectangle vertex.
[in]angle- Slope angle of the rectangle.
[out]aa- The length of semiaxis along X.
[out]bb- The length of semiaxis along Y.

◆ Init5()

void MbArc::Init5 ( const MbCartPoint c,
const MbCartPoint p1,
const MbCartPoint p2,
double &  aa,
double &  bb,
double &  angle 
)

Initialize an ellipse.

In the result of the operation an ellipse is obtained inscribed into the parallelogram given by three points: center of parallelogram (c), middle of one of its sides (p1) and one of vertices of this side (p2). OX-axis of the local coordinate system of the ellipse will pass through the point p2.

Parameters
[in]c- The center of parallelogram.
[in]p1- The middle of a side of the parallelogram.
[in]p2- A vertex of the parallelogram.
[out]aa- The length of semiaxis along X.
[out]bb- The length of semiaxis along Y.
[out]angle- An angle between OX axes of the local and the current coordinate systems.

◆ Init6()

void MbArc::Init6 ( const MbCartPoint p1,
const MbCartPoint p2,
const MbCartPoint p3,
double &  aa,
double &  bb,
double &  angle 
)

Initialize an ellipse.

In the result of the operation an ellipse is obtained inscribed into the parallelogram given by three vertices. OX-axis of the local coordinate system of the ellipse will be parallel to the segment [p1 p2].

Parameters
[in]p1- A vertex of the parallelogram.
[in]p2- A vertex of the parallelogram.
[in]p3- A vertex of the parallelogram.
[out]aa- The length of semiaxis along X.
[out]bb- The length of semiaxis along Y.
[out]angle- An angle between OX axes of the local and the current coordinate systems.

◆ Init7()

void MbArc::Init7 ( const MbCartPoint pc,
MbCartPoint  p1,
MbCartPoint  p2,
MbCartPoint  p3,
double &  aa,
double &  bb,
double &  angle 
)

Initialize an ellipse.

In the result of the operation an ellipse is obtained constructed by the center pc and three points on it p1, p2, p3

Parameters
[in]pc- The ellipse center.
[in]p1- A point on ellipse.
[in]p2- A point on ellipse.
[in]p3- A point on ellipse.
[out]aa- The length of semiaxis along X.
[out]bb- The length of semiaxis along Y.
[out]angle- An angle between OX axes of the local and the current coordinate systems.

◆ Init8()

void MbArc::Init8 ( const MbCartPoint p1,
const MbDirection dir1,
const MbCartPoint p2,
const MbDirection dir2,
const MbCartPoint p3,
double &  aa,
double &  bb,
double &  angle 
)

Initialize an ellipse.

For ellipse construction we have two points on ellipse and tangent lines at these points and the third point on the ellipse.

Parameters
[in]p1- A point on ellipse.
[in]dir1- The direction of tangent line to ellipse at point p1.
[in]p2- A point on ellipse.
[in]dir2- The direction of tangent line to ellipse at point p2.
[in]p3- A point on ellipse.
[out]aa- The length of semiaxis along X.
[out]bb- The length of semiaxis along Y.
[out]angle- An angle between OX axes of the local and the current coordinate systems.

◆ Init() [16/17]

void MbArc::Init ( double  aa,
double  bb,
const MbPlacement place,
double  t1,
double  t2,
int  initSense 
)

Initialize an elliptical arc.

In the result of the operation an elliptical arc is obtained with the specified semiaxes and the local coordinate system. t1 and t2 specify the start and the end angles of the arc. The angles are measured from the OX axis counterclockwise. The angles are given in radians. Parameter 'initSense' specifies the arc direction. If initSense > 0, then the orientation is counterclockwise.

Parameters
[in]aa- Radius of semiaxis along X.
[in]bb- Radius of semiaxis along Y.
[in]place- The local coordinate system of the ellipse.
[in]t1- An angle specifying the beginning of the arc.
[in]t2- An angle specifying the end of the arc.
[in]initSense- Direction. initSense > 0 - counterclockwise, initSense < 0 - clockwise. initSense can't be equal to zero.

◆ Init() [17/17]

void MbArc::Init ( double  aa,
double  bb,
const MbPlacement place,
const MbCartPoint p1,
const MbCartPoint p2,
bool  clockwise 
)

Initialize an elliptical arc.

In the result of the operation an elliptical arc is obtained with the specified semiaxes and the local coordinate system. Points 'p1' and 'p2' specify the bounds of arc. The start point of the arc lies on the ray starting from the circle center and passing through point 'p1'. The end point is on the ray passing through the point 'p2'. Parameter 'clockwise' specifies the direction of the arc. If clockwise > 0, then the direction of moving is counterclockwise.

Parameters
[in]aa- Radius of semiaxis along X.
[in]bb- Radius of semiaxis along Y.
[in]place- The local coordinate system of the ellipse.
[in]p1- A point specifying the beginning of the arc.
[in]p2- A point specifying the end of the arc.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

◆ Init4() [2/2]

void MbArc::Init4 ( const MbCartPoint p1,
const MbCartPoint p2,
const MbCartPoint pB,
const MbCartPoint pE,
bool  clockwise = false 
)

Initialize an elliptical arc.

Ellipse is inscribed into the rectangle given by two diagonal points p1 and p2. Sides of the rectangle are parallel to the axes of the current coordinate system. The projections of points pB and pE onto ellipse determine the start and the end of the arc. 'clockwise' determines moving form the start point to the end point clockwise or counterclockwise.

Parameters
[in]p1- The rectangle vertex.
[in]p2- The rectangle vertex.
[in]pB- A point specifying the beginning of the arc.
[in]pE- A point specifying the end of the arc.
[in]clockwise- Direction. clockwise > 0 - moving counterclockwise, clockwise < 0 - clockwise. 'clockwise' can't be equal to zero.

◆ OnSector()

bool MbArc::OnSector ( double  angle) const

Determine whether the ray hits the arc's sector.

It is analyzed if the ray starting from the center and forming the angle 'angle' with OX-axis of the current coordinate system hits the arc's sector.

Parameters
[in]angle- The angle between the direction being analyzed and the OX-axis of the current coordinate system.
Returns
True if the direction hits the arc's sector.

◆ SetLimitPoint()

void MbArc::SetLimitPoint ( ptrdiff_t  number,
const MbCartPoint pnt 
)

Replace the arc's point.

The reconstruction of the elliptical arc by the end points is performed keeping the arc opening angle.

Parameters
[in]number- The index of end point of the arc. 1 - start of arc, 2 - end of arc.
[in]pnt- A new point.

◆ GetLimitAngle()

double MbArc::GetLimitAngle ( ptrdiff_t  number) const
inline

Return the angle of the end point.

The angle of the end point of the arc is measured relative to the OX-axis of the current coordinate system.

Parameters
[in]number- The index of end point of the arc. 1 - start of arc, 2 - end of arc.
Returns
The angle between the direction from the center to the end point and OX-axis of the current coordinate system.

◆ SetLimitAngle()

void MbArc::SetLimitAngle ( ptrdiff_t  number,
const MbCartPoint pnt 
)
inline

Modify the end angle of the arc.

Parameters
[in]number- The index of end point of the arc. 1 - start of arc, 2 - end of arc.
[in]pnt- The point specifying the direction to the new end of the arc.
Returns
The angle between the direction from the center to the end point and OX-axis of the current coordinate system.

◆ PointOnBaseEllipse()

void MbArc::PointOnBaseEllipse ( double &  t,
MbCartPoint pnt 
) const

Evaluate a point on ellipse.

The point is evaluated on a closed ellipse regardless of whether the object is an ellipse or is an elliptical arc.

Parameters
[in]t- Parameter.
[out]pnt- The required point.

◆ PointProjectionOnBaseEllipse()

double MbArc::PointProjectionOnBaseEllipse ( const MbCartPoint pnt) const

Find the projection of a point onto the ellipse.

A point is projected onto the closed ellipse regardless of whether the object is an ellipse or an elliptical arc.

Parameters
[in]pnt- A point to project.
Returns
Parameter corresponding to the projected point.

◆ IsSelfIntersectOffset()

bool MbArc::IsSelfIntersectOffset ( double  d) const

Determine whether the ellipse offset has self-intersections.

Parameters
[in]d- Offset distance.
Returns
True if it has self-intersections.

◆ EllipticIntersect()

ptrdiff_t MbArc::EllipticIntersect ( const MbLine pLine,
double  cross[2],
double  eps0 = PARAM_PRECISION 
) const

Determine the parameters of intersection of a line with an ellipse.

Parameters
[in]pLine- Line.
[out]cross- Array with parameters of ellipse at intersection points.
Returns
Count of intersection points.

◆ GetProperties()

void MbArc::GetProperties ( MbProperties properties)
overridevirtual

Get properties of the object.

Get internal data (properties) of an object for viewing and modification.

Parameters
[in]properties- Container for internal data of an object.

Implements MbPlaneItem.

◆ SetProperties()

void MbArc::SetProperties ( const MbProperties properties)
overridevirtual

Change properties of the object.

Change internal data (properties) of object is performed by copying of corresponding values from the given object.

Parameters
[in]properties- Container for internal data of an object.

Implements MbPlaneItem.

◆ IsVisibleInRect() [2/2]

bool MbCurve::IsVisibleInRect
override

Determine visibility of an object in rectangle.

Determine whether an object is visible in the given rectangle. There is a possibility to perform a fast check or more thorough check when the second parameter has a corresponding value.

Parameters
[in]rect- A given two-dimensional rectangle.
[in]exact- Whether to perform a more thorough check.
Returns
true, if the object is fully or partially contained in the rectangle, otherwise false.

◆ Trimmed() [2/3]

virtual MbCurve* MbCurve::Trimmed

Construct a trimmed curve.

Constructs a trimmed curve, a start point of which corresponds to a point with parameter t1 and an end point corresponds to a point with parameter t2. Direction of the constructed curve relative to the initial curve may be changed by the parameter 'sense'. If the curve is closed, then there may be obtained a trimmed curve, passing through the start of a curve.
In a case of closed curve (or for an arc - exception) three parameters 'sense', t1 and t2 clearly define the result. In a case of unclosed curve the parameter 'sense' and parameter of trimming should correspond each other:
1) if sense == 1, then t1 < t2,
2) if sense == -1, then t1 > t2,
If there is a discrepancy between 'sense' and parameters of trimming, then 'sense' parameter has higher priority. If parameters t1 and t2 are equal and the curve is closed, then in result a closed curve should be obtained.

Parameters
[in]t1- Parameter corresponding to start of a trimmed curve.
[in]t2- Parameter corresponding to end of a trimmed curve.
[in]sense- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]saveParLenAndLaw- Save parametric length and law.
Returns
A constructed trimmed curve.

◆ Trimmed() [3/3]

virtual MbCurve* MbCurve::Trimmed

Construct a trimmed curve with the given two-dimensional accuracy.

Constructs a trimmed curve, a start point of which corresponds to a point with parameter t1 and an end point corresponds to a point with parameter t2. Direction of the constructed curve relative to the initial curve may be changed by the parameter 'sense'. If the curve is closed, then there may be obtained a trimmed curve, passing through the start of a curve.
In a case of closed curve (or for an arc - exception) three parameters 'sense', t1 and t2 clearly define the result. In a case of unclosed curve the parameter 'sense' and parameter of trimming should correspond each other:
1) if sense == 1, then t1 < t2,
2) if sense == -1, then t1 > t2,
If there is a discrepancy between 'sense' and parameters of trimming, then 'sense' parameter has higher priority. If parameters t1 and t2 are equal and the curve is closed, then in result a closed curve should be obtained.

Parameters
[in]t1- Parameter corresponding to start of a trimmed curve.
[in]t2- Parameter corresponding to end of a trimmed curve.
[in]sense- Direction of a trimmed curve in relation to an initial curve. sense = 1 - direction does not change. sense = -1 - direction changes to the opposite value.
[in]xyEps- Two-dimensional accuracy. It is used for estimations near the points corresponding to the parameters t1 and t2.
[in]saveParLenAndLaw- Save parametric length and law.
Returns
A constructed trimmed curve.
Warning
Under development.

Member Data Documentation

◆ rect

MbRect MbArc::rect
mutableprotected

Auxiliary data.

Auxiliary data are used for fast calculations.
Bounding rectangle.


The documentation for this class was generated from the following file: