Toroidal surface. More...

#include <surf_torus_surface.h>

Inheritance diagram for MbTorusSurface:

Collaboration diagram for MbTorusSurface:

Public Member Functions
	MbTorusSurface (const MbPlacement3D &pl, double initMajorR, double initMinorR)
	Constructor by local coordinate system, major and minor radii.

	MbTorusSurface (double initMajorR, double initMinorR, const MbPlacement3D &pl, double vin, double vax)
	Constructor by major and minor radii, local coordinate system, minimal and maximal parameters by V. More...

	MbTorusSurface (const MbCartPoint3D &c0, const MbCartPoint3D &c1, const MbCartPoint3D &c2)
	Constructor by three points. More...

	MbTorusSurface (const MbCartPoint3D &c0, const MbCartPoint3D &c1, const MbCartPoint3D &c2, double initMinorR)
	Constructor by three points and minor radius. More...

Initialization functions
void	Init (const MbTorusSurface &)
	The initialization by toroidal surface.

Common functions of a geometric object
MbeSpaceType	IsA () const override
	Get the type of the object.

MbSpaceItem &	Duplicate (MbRegDuplicate *=nullptr) const override
	Create a copy of the object. More...

bool	IsSame (const MbSpaceItem &other, double accuracy=LENGTH_EPSILON) const override
	Determine whether an object is equal. More...

bool	SetEqual (const MbSpaceItem &) override
	Make objects equal if they are similar. More...

void	Transform (const MbMatrix3D &matr, MbRegTransform *=nullptr) override
	Convert the object according to the matrix. More...

void	GetProperties (MbProperties &properties) override
	Outstanding properties of the object. More...

void	SetProperties (const MbProperties &properties) override
	Change the properties of an object. More...

Functions for surface domain description
double	GetUMin () const override
	Get the minimum value of u.

double	GetVMin () const override
	Get the minimum value of v.

double	GetUMax () const override
	Get the maximum value of u.

double	GetVMax () const override
	Get the maximum value of v.

bool	IsUClosed () const override
	Determine whether a surface is closed in u-parameter direction. More...

bool	IsVClosed () const override
	Determine whether a surface is closed in v-parameter direction. More...

double	GetUPeriod () const override
	Return period for smoothly closed surface or 0.

double	GetVPeriod () const override
	Return period for smoothly closed surface or 0.

Functions for working at surface domain
Functions PointOn, Derive... correct parameters when getting out of rectangular domain bounds.
void	PointOn (double &u, double &v, MbCartPoint3D &) const override
	Calculate a point on the surface. More...

void	DeriveU (double &u, double &v, MbVector3D &) const override
	Calculate first derivative with respect to u.

void	DeriveV (double &u, double &v, MbVector3D &) const override
	Calculate first derivative with respect to v.

void	DeriveUU (double &u, double &v, MbVector3D &) const override
	Calculate second derivative with respect to u.

void	DeriveVV (double &u, double &v, MbVector3D &) const override
	Calculate second derivative with respect to v.

void	DeriveUV (double &u, double &v, MbVector3D &) const override
	Calculate second derivative.

void	DeriveUUU (double &u, double &v, MbVector3D &) const override
	Calculate third derivative.

void	DeriveUUV (double &u, double &v, MbVector3D &) const override
	Calculate third derivative.

void	DeriveUVV (double &u, double &v, MbVector3D &) const override
	Calculate third derivative.

void	DeriveVVV (double &u, double &v, MbVector3D &) const override
	Calculate third derivative.

void	Normal (double &u, double &v, MbVector3D &) const override
	Calculate normal.

void	NormalU (double &u, double &v, MbVector3D &) const override
	Calculate derivative of normal with respect to U.

void	NormalV (double &u, double &v, MbVector3D &) const override
	Calculate derivative of normal with respect to V.

Functions for working inside and outside the surface domain.
functions _PointOn, _Derive... of surfaces don't correct parameters when getting out of rectangular domain bounds.
void	_PointOn (double u, double v, MbCartPoint3D &) const override
	Calculate a point on the surface. More...

void	_DeriveU (double u, double v, MbVector3D &) const override
	Calculate first derivative with respect to u on extended surface.

void	_DeriveV (double u, double v, MbVector3D &) const override
	Calculate first derivative with respect to v on extended surface.

void	_DeriveUU (double u, double v, MbVector3D &) const override
	Calculate second derivative with respect to u on extended surface.

void	_DeriveVV (double u, double v, MbVector3D &) const override
	Calculate second derivative with respect to v on extended surface.

void	_DeriveUV (double u, double v, MbVector3D &) const override
	Calculate second derivative on extended surface.

void	_DeriveUUU (double u, double v, MbVector3D &) const override
	Calculate third derivative on extended surface.

void	_DeriveUUV (double u, double v, MbVector3D &) const override
	Calculate third derivative on extended surface.

void	_DeriveUVV (double u, double v, MbVector3D &) const override
	Calculate third derivative on extended surface.

void	_DeriveVVV (double u, double v, MbVector3D &) const override
	Calculate third derivative on extended surface.

void	_Normal (double u, double v, MbVector3D &) const override
	Calculate a normal on extended surface.

void	_NormalU (double u, double v, MbVector3D &) const override
	Calculate derivative of normal vector on extended surface.

void	_NormalV (double u, double v, MbVector3D &) const override
	Calculate derivative of normal vector on extended surface.

void	_NormalUU (double u, double v, MbVector3D &) const override
	Calculate second derivative of normal vector on extended surface.

void	_NormalUV (double u, double v, MbVector3D &) const override
	Calculate second derivative of normal vector on extended surface.

void	_NormalVV (double u, double v, MbVector3D &) const override
	Calculate second derivative of normal vector on extended surface.

Functions for get of the group of data inside and outside the surface's domain of parameters.
void	Explore (double &u, double &v, bool ext, MbCartPoint3D &pnt, MbVector3D &uDer, MbVector3D &vDer, MbVector3D uuDer, MbVector3D vvDer, MbVector3D uvDer, MbVector3D nor) const override
	Calculate point and derivatives of object for given parameters. More...

void	_PointNormal (double u, double v, MbCartPoint3D &pnt, MbVector3D &deru, MbVector3D &derv, MbVector3D &norm, MbVector3D &noru, MbVector3D &norv, MbVector3D &deruu, MbVector3D &dervv, MbVector3D &deruv) const override
	Calculate all derivatives at point. More...

Functions of moving on surface
double	StepU (double u, double v, double sag) const override
	Calculate parameter step. More...

double	StepV (double u, double v, double sag) const override
	Calculate parameter step. More...

double	DeviationStepU (double u, double v, double angle) const override
	Calculate parameter step. More...

double	DeviationStepV (double u, double v, double angle) const override
	Calculate parameter step. More...

double	MetricStepU (double u, double v, double length) const override
	Calculate parameter step. More...

double	MetricStepV (double u, double v, double length) const override
	Calculate parameter step. More...

size_t	GetUCount () const override
	The number of splittings by u-parameter for a check of events.

size_t	GetVCount () const override
	The number of splittings by v-parameter for a check of events.

Common functions of surface
double	CurvatureU (double u, double v) const override
	Calculate line curvature along the direction of u. More...

double	CurvatureV (double u, double v) const override
	Calculate line curvature along the direction of v. More...

MbSplineSurface *	NurbsSurface (double, double, double, double, bool bmatch=false) const override
	Construct a NURBS copy of trimmed surface. More...

MbSurface *	NurbsSurface (const MbNurbsParameters &uParam, const MbNurbsParameters &vParam) const override
	Construct a NURBS copy of a surface. More...

MbSurface *	Offset (double d, bool same) const override
	Create an offset surface. More...

MbCurve3D *	CurveU (double v, MbRect1D *pRgn, bool bApprox=true) const override
	Construct spatial copy of the line v = const. More...

MbCurve3D *	CurveV (double u, MbRect1D *pRgn, bool bApprox=true) const override
	Construct spatial copy of the line u = const. More...

void	DirectPointProjection (const MbCartPoint3D &p, const MbVector3D &vect, SArray< MbCartPoint > &uv, bool ext, MbRect2D *uvRange=nullptr) const override
	Find all a point projection onto the surface along a vector in either of two directions. More...

void	CurveIntersection (const MbCurve3D &curv, SArray< MbCartPoint > &uv, SArray< double > &tt, bool ext0, bool ext, bool touchInclude=false) const override
	Determine points of intersection between a surface and a curve. More...

MbeNewtonResult	SurfaceTangentNewton (const MbSurface &surf1, MbeParamDir switchPar, double funcEpsilon, size_t iterLimit, double &u0, double &v0, double &u1, double &v1, bool ext0, bool ext1) const override
	Solution of equation system for determination of surfaces tangency. For internal use only.

MbeNewtonResult	CurveTangentNewton (const MbCurve3D &curv, double funcEpsilon, size_t iterLimit, double &u, double &v, double &t, bool ext0, bool ext1) const override
	Solution of equation system for determination of tangency between a surface and a curve. For internal use only.

bool	GetCylinderAxis (MbAxis3D &axis) const override
	Get rotation axis of a surface.

bool	GetCenterLines (std::vector< MbCurve3D * > &clCurves) const override
	Get center lines of a surface.

bool	IsSimilarToSurface (const MbSurface &surf, VERSION version, double precision=METRIC_PRECISION) const override
	Define whether the surfaces are similar for merge. More...

bool	GetMatrixToSurface (const MbSurface &surf, MbMatrix &matr, VERSION version, double precision=METRIC_PRECISION) const override
	Get two-dimensional matrix of transformation from its parametric region to the parametric region of 'surf'. More...

double	GetFilletRadius (const MbCartPoint3D &p, double accuracy=METRIC_REGION) const override
	Get fillet radius if the surface is a fillet surface with the set accuracy. More...

ThreeStates	Salient () const override
	Determine whether the surface is convex. More...

void	GetTesselation (const MbStepData &stepData, double u1, double u2, double v1, double v2, SArray< double > &uu, SArray< double > &vv) const override
	Determine a splitting of parametric region of a surface by verticals and horizontals. More...

bool	SetLimit (double u1, double v1, double u2, double v2) override
	Set surface limits. For internal use only.

void	SetExtendedParamRegion (double u1, double v1, double u2, double v2) override
	Set extended limits of surface. For internal use only.

void	IncludePoint (double u, double v) override
	Include a point into domain. For internal use only.

bool	GetPoleVMin () const override
	Whether a pole exists on parametric region boundary.

bool	GetPoleVMax () const override
	Whether a pole exists on parametric region boundary.

bool	IsPole (double u, double v, double paramPrecision=PARAM_PRECISION) const override
	Whether the point is a pole.

size_t	GetUMeshCount () const override
	The the number of splittings in u-direction.

size_t	GetVMeshCount () const override
	The the number of splittings in v-direction.

double	GetUParamToUnit () const override
	Get increment of u-parameter, corresponding to the unit length in space.

double	GetVParamToUnit () const override
	Get increment of v-parameter, corresponding to the unit length in space.

double	GetUParamToUnit (double u, double v) const override
	Get increment of u-parameter, corresponding to the unit length in space.

double	GetVParamToUnit (double u, double v) const override
	Get increment of v-parameter, corresponding to the unit length in space.

void	GetParamsToUnit (double u, double v, double &uParam, double &vParam) const override
	Get increment of parameters, corresponding to the unit length in space.

bool	IsShift (const MbSpaceItem &, MbVector3D &, bool &isSame, double accuracy=LENGTH_EPSILON) const override
	Determine whether the object is a translation. More...

double	GetRadius () const override
	Get the physical radius of the object or null if it impossible. More...

Functions of elementary surfaces.
bool	GetPointProjection (const MbCartPoint3D &p, bool init, double &u, double &v, bool ext, MbRect2D *uvRange=nullptr) const override
	The nearest point projection onto the surface. More...

Public Member Functions inherited from MbElementarySurface
MbeSpaceType	Type () const override
	Get the group object type.

void	Move (const MbVector3D &to, MbRegTransform *=nullptr) override
	Move an object along a vector. More...

void	Rotate (const MbAxis3D &axis, double angle, MbRegTransform *=nullptr) override
	Rotate an object around an axis at a given angle. More...

double	DistanceToPoint (const MbCartPoint3D &to) const override
	Determine the distance to the point. More...

void	GetBasisItems (RPArray< MbSpaceItem > &s) override
	Get the base objects.

void	GetBasisPoints (MbControlData3D &) const override
	Get control points of object.

void	SetBasisPoints (const MbControlData3D &) override
	Change the object by control points.

MbeNewtonResult	PointProjectionNewton (const MbCartPoint3D &p, size_t iterLimit, double &u, double &v, bool ext) const override
	Finding of point projection on surface. For internal use only.

bool	NearPointProjection (const MbCartPoint3D &p, double &u, double &v, bool ext, MbRect2D *uvRange=nullptr) const override
	Find the projection of a point onto the surface. More...

bool	IsRectangular () const override
	Determine whether derivatives with respect to u and v are orthogonal.

void	AddTesselation (double step, size_t maxCount, double w1, double w2, SArray< double > &ww) const
	Add parameters to the array with given step. More...

const MbPlacement3D &	GetPlacement () const
	A local coordinate system.

MbPlacement3D &	SetPlacement ()

void	InitPlacement (const MbPlacement3D &p)
	Set the local coordinate system.

bool	IsPositionNormal () const
	Whether the coordinate system is orthonormalized.

bool	IsPositionIsotropic () const
	Whether the coordinate system is orthogonal and isotropic by the axes.

bool	IsPositionCircular () const
	Whether the coordinate system is orthogonal with X and Y axes equal by length.

Public Member Functions inherited from MbSurface
virtual	~MbSurface ()
	Destructor.

virtual void	Accept (Visitor &visitor)
	Implementation of a function initializing a visit of an object.

MbeSpaceType	Type () const override
	Get the group object type.

MbeSpaceType	Family () const override
	Get family of objects.

double	DistanceToPoint (const MbCartPoint3D &) const override
	Determine the distance to the point. More...

void	AddYourGabaritTo (MbCube &c) const override
	Expand sent bounding box (a.k.a. gabarit), so that it included the object. More...

void	Refresh () override
	Translate all the time (mutable) data objects in an inconsistent (initial) state.

virtual void	PrepareIntegralData (const bool forced) const
	Calculate temporary (mutable) data of an object. More...

void	CalculateMesh (const MbStepData &stepData, const MbFormNote &note, MbMesh &mesh) const override
	Build polygonal copy mesh. More...

MbProperty &	CreateProperty (MbePrompt name) const override
	Create your own property with the name.

void	GetBasisPoints (MbControlData3D &) const override
	Get control points of object.

void	SetBasisPoints (const MbControlData3D &) override
	Change the object by control points.

size_t	size () const
	Number of objects if object is interpreted as vector of objects.

const MbSurface *	operator[] (size_t) const
	An access operator.

virtual bool	IsUTouch () const
	Determine whether a surface is closed in u-parameter direction regardless of the smoothness of the closure. More...

virtual bool	IsVTouch () const
	Determine whether a surface is closed in v-parameter direction regardless of the smoothness of the closure. More...

virtual bool	IsUPeriodic () const
	Determine whether a surface is closed in u-parameter direction. More...

virtual bool	IsVPeriodic () const
	Determine whether a surface is closed in v-parameter direction. More...

virtual double	GetPeriod (ptrdiff_t i) const
	Return period. More...

virtual size_t	Periodicity () const
	Determine periodicity. More...

virtual bool	GetPoleUMin () const
	Whether a pole exists on parametric region boundary.

virtual bool	GetPoleUMax () const
	Whether a pole exists on parametric region boundary.

bool	IsPole (const MbCartPoint &uv, double paramPrecision=PARAM_PRECISION) const
	Whether the point is a pole.

virtual void	TangentU (double &u, double &v, MbVector3D &) const
	Calculate tangent vector in u.

virtual void	TangentV (double &u, double &v, MbVector3D &) const
	Calculate tangent vector in v.

virtual void	Explore (double &u, double &v, MbCartPoint3D &pnt, MbVector3D &uDer, MbVector3D &vDer) const
	Calculate point and first derivatives with respect to u and with respect to v. More...

virtual void	_TangentU (double u, double v, MbVector3D &) const
	Calculate tangent vector in u direction on extended surface.

virtual void	_TangentV (double u, double v, MbVector3D &) const
	Calculate tangent vector in v direction on extended surface.

virtual void	_NormalD (double u, double v, double du, double dv, MbVector3D &der) const
	Calculate derivative of normal vector at the point with the given parameters u and v along the line with the given direction (du,dv).

virtual void	_NormalDD (double u, double v, double du, double dv, MbVector3D &der) const
	Calculate second derivative of normal vector at the point with the given parameters u and v along the line with the given direction (du,dv).

double	SurfaceStep (const double &u, const double &v, bool alongU, const MbStepData &stepData) const
	Calculate parameter step. More...

virtual const MbSurface &	GetSurface () const
	Get itself (it is overloaded only in CurveBoundedSurface).

virtual const MbSurface &	GetBasisSurface () const
	Get the base surface if exists or itself.

virtual MbSurface &	SetSurface ()
	Get itself (it is overloaded only in CurveBoundedSurface).

virtual MbSurface &	SetBasisSurface ()
	Get the base surface if exists or itself.

virtual void	GetLimitPoint (ptrdiff_t number, MbCartPoint3D &pnt) const
	Calculate the boundary point. More...

virtual void	GetLimitPoint (ptrdiff_t number, MbCartPoint &pnt) const
	Calculate the boundary two-dimensional point. More...

MbCartPoint3D	GetLimitPoint (ptrdiff_t number) const
	Calculate the boundary point. More...

double	NormalCurvatureU (double u, double v) const
	Calculate a normal curvature of line along the direction of u. More...

double	NormalCurvatureV (double u, double v) const
	Calculate a normal curvature of line along the direction of v. More...

double	NormalCurvature (double u, double v, double du, double dv) const
	Calculate a normal curvature of surface. More...

bool	MeanGaussCurvature (double u, double v, double &mean, double &gauss) const
	Calculate the mean and the Gaussian curvature. More...

bool	MainCurvatures (double u, double v, double &c1, double &c2, double &du, double &dv) const
	Calculate the mean and the Gaussian curvature. More...

virtual bool	IsSameBase (const MbSurface &) const
	Whether a base surface is a copy of the base surface of the given object.

virtual bool	IsPlanar (double accuracy=METRIC_EPSILON) const
	Whether a surface is planar.

virtual MbeParamDir	GetFilletDirection (double accuracy=METRIC_REGION) const
	Direction of fillet surface with accuracy. More...

virtual bool	GetCentre (MbCartPoint3D &c) const
	Give the center of sphere surface.

virtual void	ChangeCarrier (const MbSpaceItem &item, MbSpaceItem &init)
	Changing of carrier. More...

virtual bool	ChangeCarrierBorne (const MbSurface &item, MbSurface &init, const MbMatrix &matr)
	Changing of carrier elements. More...

virtual bool	IsSpinePeriodic () const
	Periodicity of the guide. More...

MbSplineSurface *	NurbsSurface (bool bmatch=false) const
	Construct a NURBS copy of a surface. More...

bool	NurbsParam (const MbNurbsParameters &tParam, bool uParam, double op1, double op2, bool &isClosedNurbs, double &epsilon, SArray< double > &params) const
	Prepare parameters for the transformation to NURBS surface. More...

void	CheckApproxPointParamsOpen (bool isU, double par, size_t degree, size_t pCount, SArray< double > &tList, SArray< double > &aKnots) const
	Chose points for approximation along the parameter. More...

void	CheckApproxPointParamsClosed (bool isU, double par, size_t degree, size_t pCount, SArray< double > &tList, SArray< double > &aKnots) const
	Chose points for approximation along the parameter. More...

virtual MbCurve3D *	CurveUV (const MbLineSegment &segm, bool bApprox=true) const
	Construct spatial copy of line by parametric line. More...

virtual MbeItemLocation	PointRelative (const MbCartPoint3D &pnt, double eps=ANGLE_REGION) const
	Get point location relative to the surface. More...

virtual MbeItemLocation	PointClassification (const MbCartPoint &pnt, bool ignoreClosed=false) const
	A point is located inside the region on a surface. More...

virtual double	DistanceToBorder (const MbCartPoint &point, double &epsilon) const
	Calculate the parametric distance to the nearest boundary. More...

virtual size_t	CurveClassification (const MbCurve &curve, SArray< double > &tcurv, SArray< MbVector > &dir) const
	Determine points of intersections between the curve and the surface contours. More...

size_t	SurfaceBorderIntersection (const MbCurve &curve, SArray< double > &tcurv, SArray< MbVector > &dir) const
	Determine points of intersections between the curve and the surface contours. More...

virtual MbeNewtonResult	DirectPointProjectionNewton (const MbCartPoint3D &p, const MbVector3D &vect, size_t iterLimit, double &u, double &v, double &w, bool ext) const
	Finding of point projections to the surface in direction of the vector. For internal use only.

virtual bool	NearDirectPointProjection (const MbCartPoint3D &pnt, const MbVector3D &vect, double &u, double &v, bool ext, MbRect2D *uvRange=nullptr, bool onlyPositiveDirection=false) const
	Find the nearest point projection to the surface in the vector direction. More...

virtual MbeNewtonResult	CurveIntersectNewton (const MbCurve3D &curv1, double funcEpsilon, size_t iterLimit, double &u0, double &v0, double &t1, bool ext0, bool ext1) const
	Solution of equation system for determination of intersections between a surface and a curve. For internal use only.

virtual MbeNewtonResult	SurfaceIntersectNewton (const MbSurface &surf1, MbeParamDir switchPar, double funcEpsilon, size_t iterLimit, double &u0, double &v0, double &u1, double &v1, bool ext0, bool ext1) const
	Solution of equation system for determination of surfaces intersections. For internal use only.

virtual MbeNewtonResult	SilhouetteNewton (const MbVector3D &eye, bool perspective, const MbAxis3D *axis, MbeParamDir switchPar, double funcEpsilon, size_t iterLimit, double &u, double &v, bool ext) const
	Solution of equation system for determination of surface silhouette points. For internal use only.

virtual bool	IsSpecialSimilarToSurface (const MbSurface &surf, VERSION version, double precision=METRIC_PRECISION) const
	Whether the surfaces are similar to merge. Special case. For internal use only.

virtual bool	ProjectCurveOnSimilarSurface (const MbCurve3D &spaceCurve, const MbCurve &curve, const MbSurface &surfNew, MbCurve *&curveNew) const
	Construction of projection of a surface curve on coincident surface. More...

bool	ProjectCurveOnSimilarSurface (const MbCurve3D &spaceCurve, const MbCurve &curve, const MbSurface &surfNew, SPtr< MbCurve > &curveNew) const
	Construction of projection of a surface curve on coincident surface. More...

virtual double	DistanceToCurve (const MbCurve3D &curve, double &u, double &v, double &t, bool tCalc=false) const
	Calculate the nearest distance to a curve. More...

virtual double	DistanceToSurface (const MbSurface &surf1, double &u0, double &v0, double &u1, double &v1) const
	Calculate the nearest distance to a surface. More...

virtual bool	CreateNormalPlacements (const MbVector3D &axisZ, double angle, SArray< MbPlacement3D > &places, VERSION version=Math::DefaultMathVersion()) const
	Construct normal placements of constructive planes.

virtual bool	CreateTangentPlacements (const MbVector3D &axisZ, SArray< MbPlacement3D > &places) const
	Construct tangent placements of constructive planes.

MbeNewtonResult	PlacementNewton (const MbVector3D &vec, double angle, MbeParamDir switchPar, size_t iterLimit, double &u, double &v) const
	Construct tangent placements of constructive planes. For internal use only.

bool	CreateVconstPlacements (const MbVector3D &axisZ, double angle, bool normalPlace, SArray< MbPlacement3D > &places) const
	Construct the normal or tangent placements on v-lines.

bool	CreateUconstPlacements (const MbVector3D &axisZ, double angle, bool normalPlace, SArray< MbPlacement3D > &places) const
	Construct the normal or tangent placements on u-lines.

virtual double	ParamArea () const
	Calculate the area of parameters domain.

virtual size_t	GetUPairs (double v, SArray< double > &u) const
	Calculate U-pairs by V. More...

virtual size_t	GetVPairs (double u, SArray< double > &v) const
	Calculate V-pairs by U. More...

MbeNewtonResult	IsoclinalNewton (const MbVector3D &dir, size_t iterLimit, double &u, double &v) const
	Determination of parameters of a surface isocline point. For internal use only.

virtual void	GetIsoclinal (const MbVector3D &nor, SArray< MbCartPoint > &uv) const
	Find all isoclines of a surface. More...

virtual void	CalculateGabarit (MbCube &cube) const
	Calculate bounding box of surface. It is recommended to use GetGabarit.

void	CalculateLocalGabarit (const MbMatrix3D &into, MbCube &cube) const override
	Calculate bounding box in the local coordinate system.

const MbCube &	GetGabarit () const
	Calculate bounding box of surface.

const MbCube &	Cube () const
	Return saved bounding box. It should be empty. It is recommended to use GetGabarit.

void	SetDirtyGabarit () const
	Make the bounding box empty. For internal use only.

void	CopyGabarit (const MbSurface &s, const MbVector3D *to=nullptr)
	Copy the bounding box from the copy. More...

double	GetGabDiagonal () const
	Calculate the diagonal of the bounding box.

void	CalculateRect (const MbPlacement3D &place, MbRect &rect) const
	Calculate the rectangular bounding box of a surface in the given plane. More...

virtual MbContour &	MakeContour (bool sense) const
	Return the bounding two-dimensional contour. More...

virtual MbCurve &	MakeSegment (size_t i, bool sense) const
	Return a segment of the bounding two-dimensional contour. More...

MbCurve &	MakeCurve (size_t number1, size_t number2) const
	Return a segment of the bounding two-dimensional contour. More...

bool	SetLimit (const MbRect &)
	Set surface limits. For internal use only.

double	GetMaxParamDeltaU () const
	Get the maximum increment of U-parameter.

double	GetMaxParamDeltaV () const
	Get the maximum increment of V-parameter.

virtual double	GetParamDelta () const
	Get the maximum increment of parameter.

virtual double	GetParamPrice () const
	Get the minimum distinguishable value of parameter.

double	GetUParamToUnit (const MbCartPoint &uv) const
	Get increment of u-parameter, corresponding to the unit length in space.

double	GetVParamToUnit (const MbCartPoint &uv) const
	Get increment of v-parameter, corresponding to the unit length in space.

double	GetUEpsilon () const
	Get the minimum distinguishable value of u-parameter. It corresponds to the length Math::metricEpsilon in space.

double	GetVEpsilon () const
	Get the minimum distinguishable value of v-parameter. It corresponds to the length Math::metricEpsilon in space.

double	GetUEpsilon (double u, double v) const
	Get the minimum distinguishable value of u-parameter. It corresponds to the length Math::metricEpsilon in space.

double	GetVEpsilon (double u, double v) const
	Get the minimum distinguishable value of v-parameter. It corresponds to the length Math::metricEpsilon in space.

double	GetURegion () const
	Get the minimum distinguishable value of u-parameter. It corresponds to the length Math::metricRegion in space.

double	GetVRegion () const
	Get the minimum distinguishable value of v-parameter. It corresponds to the length Math::metricRegion in space.

double	GetURegion (double u, double v) const
	Get the minimum distinguishable value of u-parameter. It corresponds to the length Math::metricRegion in space.

double	GetVRegion (double u, double v) const
	Get the minimum distinguishable value of v-parameter. It corresponds to the length Math::metricRegion in space.

void	CalculatePolygon (double minPar, double maxPar, double constPar, MbeParamDir dir, const MbStepData &stepData, MbPolygon3D &polygon) const
	Calculate polygon by u or v. More...

virtual void	CalculateSurfaceWire (const MbStepData &stepData, size_t beg, MbMesh &mesh, size_t uMeshCount=c3d::WIRE_MAX, size_t vMeshCount=c3d::WIRE_MAX) const
	Calculate mesh. More...

void	AddTesselation (const MbStepData &stepData, MbeParamDir dir, double u1, double u2, double v1, double v2, SArray< double > &uu, SArray< double > &vv) const
	Determine splitting of the surface parametric region according to direction. More...

virtual void	CalculateSurfaceGrid (const MbStepData &stepData, bool sense, MbGrid &grid) const
	Approximate a surface by triangular plates. More...

virtual bool	IsLineU () const
	Check that all derivatives of surface with respect to u which have more than first order are equal to null.

virtual bool	IsLineV () const
	Check that all derivatives of surface with respect to v which have more than first order are equal to null.

virtual void	CheckSurfParams (double &u, double &v) const
	Check parameters. Analogue of the global function _CheckParams, optimized for caches usage. More...

bool	GetPlacement (MbPlacement3D *place, bool exact=false) const
	Get a local coordinate system of planar surface (or only a possibility of getting it).

bool	GetPlanePlacement (MbPlacement3D &place) const
	Get a local coordinate system if a surface is a plane.

bool	GetControlPlacement (MbPlacement3D &place, bool sameSense=true) const
	Construct a local coordinate system of a surface with origin at the middle point of base surface parametric limits. More...

bool	OrientPlacement (MbPlacement3D &place, bool normalSense=true) const
	Orient an axis X of a placement along the line of its intersection with surface.

bool	IsPointOn (const MbCartPoint3D &, double eps=METRIC_PRECISION) const
	Determine whether a point is located on a surface or not.

void	PointOn (MbCartPoint &uv, MbCartPoint3D &p) const
	Calculate the point on a surface inside the domain of surface.

void	_PointOn (const MbCartPoint &uv, MbCartPoint3D &p) const
	Calculate a point on a surface extension.

void	Normal (MbCartPoint &uv, MbVector3D &v) const
	Calculate the normal vector to a surface inside the domain of surface.

bool	GetMatrix (double xMin, double xMax, double yMin, double yMax, MbMatrix &matr) const
	Find a matrix of transformation for the curves on a surface when the parameterization is changed. More...

double	GetUMid () const
	The middle value of u.

double	GetVMid () const
	The middle value of v.

double	GetURange () const
	Parametric length by u.

double	GetVRange () const
	Parametric length by v.

void	GetRect (MbRect &r) const
	Get parametric bounding box.

void	GetRect (MbRect2D &r) const
	Get parametric bounding box.

Public Member Functions inherited from MbSpaceItem
virtual	~MbSpaceItem ()
	Destructor.

void	PrepareWrite () const
	Register object. More...

MbeRefType	RefType () const override
	Get a registration type (for copying, duplication).

bool	IsFamilyRegistrable () const override
	Whether the object belongs to a registrable family.

virtual bool	IsSimilar (const MbSpaceItem &item) const
	Determine whether an object is similar. More...

void	CalculateWire (const MbStepData &stepData, MbMesh &mesh) const

void	CalculateWire (double sag, MbMesh &mesh) const

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.

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.

CommonRecursiveMutex *	GetLock () const
	Get a pointer to the mutex object. Return nullptr if no parallelism. For use in ScopedLock.

Functions of toroidal surface
double	GetMajorRadius () const
	Get physical major radius.

double	GetMinorRadius () const
	Get physical minor radius.

void	SetMajorR (double r)
	Changing of major radius.

void	SetMinorR (double r)
	Changing of minor radius.

double	GetMajorR () const
	Major radius.

double	GetMinorR () const
	Minor radius.

double	GetR (double v) const
	Radius of v-parallel.

void	GetMinorCentre (double u, MbCartPoint3D &c) const
	Get center of torus u-line.

double	MinorCentreProjection (MbCartPoint3D &p) const
	Get projection of the point to the line of centers of minor radius.

bool	GetVPoles (double &poleVMin, double &poleVMax) const
	Define position of the poles. More...

Additional Inherited Members
Protected Member Functions inherited from MbSurface
	MbSurface ()
	Constructor.

	MbSurface (const MbSurface &)
	Copy-constructor.

void	MoveGabarit (const MbVector3D &v)
	Move bounding box.

void	NormalCalculation (const MbVector3D &uDer, const MbVector3D &vDer, double u, double v, bool ext, MbVector3D &nor) const
	Normal calculation by derivatives uDer and vDer on point with parameters u, v.

double	StepAlong (double u, double v, double sag, bool alongU, double stepMinCoeff, const MbVector3D &der, const MbVector3D &sec) const
	Step calculation by sag.

double	DeviationStepAlong (double u, double v, double angle, bool alongU, const MbVector3D &der, const MbVector3D &sec) const
	Step calculation by normal deviation.

Protected Member Functions inherited from MbSpaceItem
	MbSpaceItem ()
	Default constructor.

Protected Member Functions inherited from MbRefItem
	MbRefItem ()
	Constructor without parameters.

Protected Attributes inherited from MbElementarySurface
MbPlacement3D	position
	Local coordinate system.

double	umin
	Minimal value of first parameter.

double	vmin
	Minimal value of second parameter.

double	umax
	Maximal value of first parameter.

double	vmax
	Maximal value of second parameter.

Protected Attributes inherited from MbSurface
MbCube	cube
	Bounding box of surface. More...

Detailed Description

Toroidal surface.

A surface of torus is described by the radius of centers 'majorRadius' and the radius of tube 'minorRadius', which are set in the local coordinate system.
The first parameter of a surface is measured by an arc from the axis 'position.axisX' in direction of the axis 'position.axisY'. The first parameter of a surface u takes values on the segment: umin<=u<=umax. Values u=0 and u=2pi correspond to the point on the plane XZ of a local coordinate system. A surface may be closed in direction of the first parameter. If a surface is closed, then umax-umin=2pi, otherwise umax-umin<2pi.
The second parameter of a surface is measured by an arc from the plane XY of the surface local coordinate system in direction of the axis 'position.axisZ'. The second parameter of a surface v takes values on the segment: vmin<=v<=vmax. The values v=0 and v=2pi correspond to a point on the plane XY of the surface local coordinate system. A surface may be closed in direction of the second parameter if majorRadius>minorRadius. If a surface is closed, then vmax-vmin=2pi, otherwise vmax-vmin<2pi.
Radius-vector of line surface is described by the vector function
r(u,v) = position.origin + ((majorRadius + (minorRadius cos(v)) (cos(u) position.axisX + sin(u) position.axisY)) + (minorRadius sin(v) position.axisZ).
Radius of tube must be positive: minorRadius>0. Radius of centers must be not less than the radius of tube with the opposite sign: majorRadius>-minorRadius. If majorRadius<minorRadius, then the surface has a pole for the parameter v=arccos(majorRadius/minorRadius) and v=2pi-arccos(majorRadius/minorRadius).
The following inequalities must be satisfied for the parameters of surface boundary: umin<umax, vmin<vmax.
Local coordinate system 'position' can be both right and left. If the local coordinate system is right then the normal is directed outside the tube of a surface, if the local coordinate system is left then the normal is directed inside the tube of a surface.

Constructor & Destructor Documentation

◆ MbTorusSurface() [1/3]

MbTorusSurface::MbTorusSurface	(	double	initMajorR,
		double	initMinorR,
		const MbPlacement3D &	pl,
		double	vin,
		double	vax
	)

Constructor by major and minor radii, local coordinate system, minimal and maximal parameters by V.

Warning: This is used only in converters.

◆ MbTorusSurface() [2/3]

MbTorusSurface::MbTorusSurface	(	const MbCartPoint3D &	c0,
		const MbCartPoint3D &	c1,
		const MbCartPoint3D &	c2
	)

Constructor by three points.

The first point is the center of the surface local coordinate system.
A length of a vector directed from the first point to the second point is equal to the major radius,
its direction coincides with the direction of the axis X.
A length of a vector directed from the second point to the third point is equal to the minor radius,
The axis Z lies on the plane of the points and directed to the side of the vector from the first point to the third point.

◆ MbTorusSurface() [3/3]

MbTorusSurface::MbTorusSurface	(	const MbCartPoint3D &	c0,
		const MbCartPoint3D &	c1,
		const MbCartPoint3D &	c2,
		double	initMinorR
	)

Constructor by three points and minor radius.

Constructor by three points and minor radius.
The first point is the center of the toroidal surface local coordinate system.
A vector from the first point to the second point - direction of the axis Z. Major radius is equal to the length of the projection to the axis Z of the vector directed from the first point to the third point.

Member Function Documentation

◆ Duplicate()

MbSpaceItem& MbTorusSurface::Duplicate ( MbRegDuplicate * iReg = nullptr ) const

overridevirtual

Create a copy of the object.

Create a copy of an object using the registrator. Registrator is used to prevent multiple copy of the object. If the object contains references to the other objects, then nested objects are copied as well. It is allowed not to pass registrator into the function. Then new copy of object will be created. While copying of single object or set of not connected objects, it is allowed not to use registrator. Registrator should be used if it is required to copy several connected objects. It is possible, that objects connection is based on the references to common objects. Then, while copying without using of registrator, it is possible to obtain set of copies, that contain references to the different copies of the same nested object, that leads to loss of connection between copies.

Parameters

[in] iReg - Registrator.

Returns: A copy of the object.

Implements MbSpaceItem.

◆ IsSame()

bool MbTorusSurface::IsSame	(	const MbSpaceItem &	other,
		double	accuracy = `LENGTH_EPSILON`
	)		const

overridevirtual

Determine whether an object is equal.

Still considered objects of the same type, all data is the same (equal).

Parameters

[in]	item	- The object to compare.
[in]	accuracy	- The accuracy to compare.

Returns: Whether the objects are equal.

Implements MbSpaceItem.

◆ SetEqual()

bool MbTorusSurface::SetEqual ( const MbSpaceItem & item )

overridevirtual

Make objects equal if they are similar.

You can still make only a similar objects.

Parameters

[in] item - The object to initialize.

Returns: Object is changed.

Implements MbSpaceItem.

◆ Transform()

void MbTorusSurface::Transform	(	const MbMatrix3D &	matr,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Convert the object according to the matrix.

Convert the original object according to the matrix using the registrator. If object contains references to the other geometric objects, then nested objects are transformed according to the matrix. Registrator is needed to prevent multiple object copying. It is allowed to use function without registrator, if it is needed to transform single object. If it is needed to transform a set of connected objects, then one should use registrator to prevent repeating transformation of nested objects, because of the possible situation when several objects contain references to the same common objects, that require to be transformed.

Parameters

[in]	matr	- Transformation matrix.
[in]	iReg	- Registrator.

Reimplemented from MbElementarySurface.

◆ GetProperties()

void MbTorusSurface::GetProperties ( MbProperties & properties )

overridevirtual

Outstanding properties of the object.

Issue internal data (properties) of the object for viewing and modification.

Parameters

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

Implements MbSpaceItem.

◆ SetProperties()

void MbTorusSurface::SetProperties ( const MbProperties & properties )

overridevirtual

Change the properties of an object.

Changing the internal data (properties) of the object you are copying the corresponding values from the sent object.

Parameters

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

Implements MbSpaceItem.

◆ IsUClosed()

bool MbTorusSurface::IsUClosed ( ) const

overridevirtual

Determine whether a surface is closed in u-parameter direction.

Determine whether a surface is closed smoothly in u-parameter direction without regard to the boundary contour. It is always false for MbCurveBoundSurface. It is recommended to use IsUPeriodic.

Implements MbSurface.

◆ IsVClosed()

bool MbTorusSurface::IsVClosed ( ) const

overridevirtual

Determine whether a surface is closed in v-parameter direction.

Determine whether a surface is closed smoothly in v-parameter direction without regard to the boundary contour. It is always false for MbCurveBoundSurface. It is recommended to use IsVPeriodic.

Implements MbSurface.

◆ PointOn()

void MbTorusSurface::PointOn	(	double &	u,
		double &	v,
		MbCartPoint3D &	p
	)		const

overridevirtual

Calculate a point on the surface.

Correct parameters when getting out of rectangular domain bounds and Calculate a point on the surface.

Parameters

[in]	u	- First surface parameter.
[in]	v	- Second surface parameter.
[out]	p	- A point on the surface.

Implements MbSurface.

◆ _PointOn()

void MbTorusSurface::_PointOn	(	double	u,
		double	v,
		MbCartPoint3D &	p
	)		const

overridevirtual

Calculate a point on the surface.

Calculate a point on the surface including the outside area determination parameters.

Parameters

[in]	u	- First surface parameter.
[in]	v	- Second surface parameter.
[out]	p	- A point on the surface or on extended surface.

Reimplemented from MbSurface.

◆ Explore()

void MbTorusSurface::Explore	(	double &	u,
		double &	v,
		bool	ext,
		MbCartPoint3D &	pnt,
		MbVector3D &	uDer,
		MbVector3D &	vDer,
		MbVector3D *	uuDer,
		MbVector3D *	vvDer,
		MbVector3D *	uvDer,
		MbVector3D *	nor
	)		const

overridevirtual

Calculate point and derivatives of object for given parameters.

Values of point and derivatives are calculated on parameters area and on extended surface.

Parameters

[in]	u	- Parameter.
[in]	v	- Parameter.
[in]	ext	- On parameters area (false), on extended surface (true).
[out]	pnt	- Point.
[out]	uDer	- Derivative with respect to u.
[out]	vDer	- Derivative with respect to v.
[out]	uuDer	- Second derivative with respect to u, if not nullptr.
[out]	vvDer	- Second derivative with respect to v, if not nullptr.
[out]	uvDer	- Second derivative with respect to u and v, if not nullptr.

Reimplemented from MbSurface.

◆ _PointNormal()

void MbTorusSurface::_PointNormal	(	double	u,
		double	v,
		MbCartPoint3D &	pnt,
		MbVector3D &	deru,
		MbVector3D &	derv,
		MbVector3D &	norm,
		MbVector3D &	noru,
		MbVector3D &	norv,
		MbVector3D &	deruu,
		MbVector3D &	dervv,
		MbVector3D &	deruv
	)		const

overridevirtual

Calculate all derivatives at point.

Values of point and derivatives are calculated an extended surface.

Parameters

[in]	u	- Parameter.
[in]	v	- Parameter.
[out]	pnt	- Point.
[out]	deru	- Derivative with respect to u.
[out]	derv	- Derivative with respect to v.
[out]	norm	- Normal.
[out]	noru	- Derivative of normal vector with respect to u.
[out]	norv	- Derivative of normal vector with respect to v.
[out]	deruu	- Second derivative with respect to u.
[out]	dervv	- Second derivative with respect to v.
[out]	deruv	- Second derivative with respect to u and v.

Reimplemented from MbSurface.

◆ StepU()

double MbTorusSurface::StepU	(	double	u,
		double	v,
		double	sag
	)		const

overridevirtual

Calculate parameter step.

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

Parameters

[in]	u	- A parameter defining a point on the surface.
[in]	v	- A parameter defining a point on the surface.
[in]	sag	- Maximum feasible sag value.

Returns: A sag value by parameter at given point.

Reimplemented from MbSurface.

◆ StepV()

double MbTorusSurface::StepV	(	double	u,
		double	v,
		double	sag
	)		const

overridevirtual

Calculate parameter step.

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

Parameters

[in]	u	- A parameter defining a point on the surface.
[in]	v	- A parameter defining a point on the surface.
[in]	sag	- Maximum feasible sag value.

Returns: A sag value by parameter at given point.

Reimplemented from MbSurface.

◆ DeviationStepU()

double MbTorusSurface::DeviationStepU	(	double	u,
		double	v,
		double	angle
	)		const

overridevirtual

Calculate parameter step.

Calculate parameter step for the surface approximation by the deviation angle of the tangent vector along a line with a constant value of u. A step of surface approximation along a curve is chosen in such way, that angular deviation of the tangent to the curve at the next point does not exceed the given value ang.

Parameters

[in]	u	- A parameter defining a point on the surface.
[in]	v	- A parameter defining a point on the surface.
[in]	ang	- The maximum feasible deviation angle of tangent.

Returns: A sag value by parameter at given point.

Reimplemented from MbSurface.

◆ DeviationStepV()

double MbTorusSurface::DeviationStepV	(	double	u,
		double	v,
		double	angle
	)		const

overridevirtual

Calculate parameter step.

Calculate parameter step for the surface approximation by the deviation angle of the tangent vector along a line with a constant value of v. A step of surface approximation along a curve is chosen in such way, that angular deviation of the tangent to the curve at the next point does not exceed the given value ang.

Parameters

[in]	u	- A parameter defining a point on the surface.
[in]	v	- A parameter defining a point on the surface.
[in]	ang	- The maximum feasible deviation angle of tangent.

Returns: A sag value by parameter at given point.

Reimplemented from MbSurface.

◆ MetricStepU()

double MbTorusSurface::MetricStepU	(	double	u,
		double	v,
		double	length
	)		const

overridevirtual

Calculate parameter step.

Calculate the parameter step for approximation of a surface by the given metric length of a step along a line with a constant value of u.

Parameters

[in]	u	- A parameter defining a point on the surface.
[in]	v	- A parameter defining a point on the surface.
[in]	len	- The given metric length.

Returns: A sag value by parameter at given point.

Reimplemented from MbSurface.

◆ MetricStepV()

double MbTorusSurface::MetricStepV	(	double	u,
		double	v,
		double	length
	)		const

overridevirtual

Calculate parameter step.

Calculate the parameter step for approximation of a surface by the given metric length of a step along a line with a constant value of v.

Parameters

[in]	u	- A parameter defining a point on the surface.
[in]	v	- A parameter defining a point on the surface.
[in]	len	- The given metric length.

Returns: A sag value by parameter at given point.

Reimplemented from MbSurface.

◆ CurvatureU()

double MbTorusSurface::CurvatureU	(	double	u,
		double	v
	)		const

overridevirtual

Calculate line curvature along the direction of u.

There is calculated a line curvature along the direction of u when v = const.

Parameters

[in]	u	- Parameter.
[in]	v	- Parameter.

Returns: Curvature.

Reimplemented from MbSurface.

◆ CurvatureV()

double MbTorusSurface::CurvatureV	(	double	u,
		double	v
	)		const

overridevirtual

Calculate line curvature along the direction of v.

There is calculated a line curvature along the direction of v when u = const.

Parameters

[in]	u	- Parameter.
[in]	v	- Parameter.

Returns: Curvature.

Reimplemented from MbSurface.

◆ NurbsSurface() [1/2]

MbSplineSurface* MbTorusSurface::NurbsSurface	(	double	u1,
		double	u2,
		double	v1,
		double	v2,
		bool	bmatch = `false`
	)		const

overridevirtual

Construct a NURBS copy of trimmed surface.

An obtained surface is always unclosed in u and in v. The exception is the NURBS surface itself. If the surface does not require recalculation, then a copy of it is returned. Parameters u1, u2, v1 and v2 are the bounds of surface trimming.

Parameters

[in]	u1	- Minimum parameter in U.
[in]	u2	- Maximum parameter in U.
[in]	v1	- Minimum parameter in V.
[in]	v2	- Maximum parameter in V.
[in]	bmatch	- true, if it is required to keep one-to-one correspondence of parametric regions in mapping.

Reimplemented from MbSurface.

◆ NurbsSurface() [2/2]

MbSurface* MbTorusSurface::NurbsSurface	(	const MbNurbsParameters &	uParam,
		const MbNurbsParameters &	vParam
	)		const

overridevirtual

Construct a NURBS copy of a surface.

Constructs a NURBS surface which approximates a given surface with the given parameters in each direction. 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]	uParam	- Parameters of construction in u direction.
[in]	vParam	- Parameters of construction in v direction.

Returns: The constructed NURBS surface or nullptr in a case of failure.

Reimplemented from MbSurface.

◆ Offset()

MbSurface* MbTorusSurface::Offset	(	double	d,
		bool	same
	)		const

overridevirtual

Create an offset surface.

Parameters

[in]	d	- Distance by the normal vector from the base surface to the offset surface.
[in]	same	- A flag showing whether to use the current surface or its copy in offset surface.

Reimplemented from MbSurface.

◆ CurveU()

MbCurve3D* MbTorusSurface::CurveU	(	double	v,
		MbRect1D *	pRgn,
		bool	bApprox = `true`
	)		const

overridevirtual

Construct spatial copy of the line v = const.

Parameters

[in]	v	- Parameter in V direction.
[in]	pRgn	- A range of u-parameters.
[in]	bApprox	- If false, then it returns null only in a case when the exact curve has been successfully created. If true, then it returns null in a case when the curve is not degenerate.

Returns: Constructed curve.

Reimplemented from MbSurface.

◆ CurveV()

MbCurve3D* MbTorusSurface::CurveV	(	double	u,
		MbRect1D *	pRgn,
		bool	bApprox = `true`
	)		const

overridevirtual

Construct spatial copy of the line u = const.

Parameters

[in]	u	- Parameter in U direction.
[in]	pRgn	- A range of v-parameters.
[in]	bApprox	- If false, then it returns null only in a case when the exact curve has been successfully created. If true, then it returns null in a case when the curve is not degenerate.

Returns: Constructed curve.

Reimplemented from MbSurface.

◆ DirectPointProjection()

void MbTorusSurface::DirectPointProjection	(	const MbCartPoint3D &	pnt,
		const MbVector3D &	vect,
		SArray< MbCartPoint > &	uv,
		bool	ext,
		MbRect2D *	uvRange = `nullptr`
	)		const

overridevirtual

Find all a point projection onto the surface along a vector in either of two directions.

Calculate all points of intersection with the ray outgoing from the given point 'p' by the direction 'vect'. If the range of parameters changing 'uvRange' is set, then it is required to find a projection in the given range. A range of parameters may not belong to the domain of a surface.

Parameters

[in]	pnt	- A given point.
[in]	vect	- A direction vector.
[out]	uv	- A set of projection points in the area of surface definition.
[in]	ext	- A flag defining whether to seek projection on the extension of the surface.
[in]	uvRange	- A range of surface parameters changing in which the solution should be found.

Reimplemented from MbSurface.

◆ CurveIntersection()

void MbTorusSurface::CurveIntersection	(	const MbCurve3D &	curv,
		SArray< MbCartPoint > &	uv,
		SArray< double > &	tt,
		bool	ext0,
		bool	ext,
		bool	touchInclude = `false`
	)		const

overridevirtual

Determine points of intersection between a surface and a curve.

Parameters

[in]	curv	- A given curve.
[in,out]	uv	- A set of intersection points on the surface.
[in,out]	tt	- A set of intersection points on the curve.
[in]	ext0	- A flag defining whether to seek intersections on extended surface (if it is true, then seek).
[in]	ext	- A flag defining whether to seek intersections on extended curve (if it is true, then seek).
[in]	touchInclude	- Whether to consider tangency as intersection. If true, then consider.

Reimplemented from MbSurface.

◆ IsSimilarToSurface()

bool MbTorusSurface::IsSimilarToSurface	(	const MbSurface &	surf,
		VERSION	version,
		double	precision = `METRIC_PRECISION`
	)		const

overridevirtual

Define whether the surfaces are similar for merge.

Surfaces are similar for merge if they coincide geometrically or one surface transits to another.

Parameters

[in]	surf	- A given surface.
[in]	version	- Version of operation.
[in]	precision	- Precision of calculation.

Returns: True - if surfaces are similar.

Reimplemented from MbSurface.

◆ GetMatrixToSurface()

bool MbTorusSurface::GetMatrixToSurface	(	const MbSurface &	surf,
		MbMatrix &	matr,
		VERSION	version,
		double	precision = `METRIC_PRECISION`
	)		const

overridevirtual

Get two-dimensional matrix of transformation from its parametric region to the parametric region of 'surf'.

Calculation of matrix of transformation from one parametric region to another. it is performed for the surfaces which are similar for merge.

Parameters

[in]	surf	- A given surface.
[out]	matr	- A transformation matrix.
[in]	version	- Version of operation.
[in]	precision	- Precision of calculation.

Returns: True - matrix is calculated.

Reimplemented from MbSurface.

◆ GetFilletRadius()

double MbTorusSurface::GetFilletRadius	(	const MbCartPoint3D &	p,
		double	accuracy = `METRIC_REGION`
	)		const

overridevirtual

Get fillet radius if the surface is a fillet surface with the set accuracy.

Get fillet radius if the surface is a fillet surface with the set accuracy. Accuracy is used to compare surface slices to an arc to find rotation axis.

Parameters

[in]	p	- Point near which the radius is searched. Used when the radius is variable.
[in]	accuracy	- Accuracy.

Returns: Fillet radius if possible or 0.

Reimplemented from MbSurface.

◆ Salient()

ThreeStates MbTorusSurface::Salient ( ) const

overridevirtual

Determine whether the surface is convex.

Returns: ts_positive - the surface is convex, ts_negative - the surface is concave, ts_neutral - impossible to determine.

Reimplemented from MbSurface.

◆ GetTesselation()

void MbTorusSurface::GetTesselation	(	const MbStepData &	stepData,
		double	u1,
		double	u2,
		double	v1,
		double	v2,
		SArray< double > &	uu,
		SArray< double > &	vv
	)		const

overridevirtual

Determine a splitting of parametric region of a surface by verticals and horizontals.

Determine a splitting of parametric region of a surface by verticals and horizontals during triangulation.

Parameters

[in]	stepData	- Data for step calculation during triangulation.
[in]	u1	- Minimal value of u-parameter in the region of surface splitting.
[in]	u2	- Maximal value of u-parameter in the region of surface splitting.
[in]	v1	- Minimal value of v-parameter in the region of surface splitting.
[in]	v2	- Maximal value of v-parameter in the region of surface splitting.
[out]	uu	- A set of parameters of splitting by u.
[out]	vv	- A set of parameters of splitting by v.

Reimplemented from MbSurface.

◆ IsShift()

bool MbTorusSurface::IsShift	(	const MbSpaceItem &	obj,
		MbVector3D &	dir,
		bool &	isSame,
		double	accuracy = `LENGTH_EPSILON`
	)		const

overridevirtual

Determine whether the object is a translation.

Determine whether the object is a translation of a given object.

Parameters

[in]	obj	- A pattern object.
[out]	dir	- A translation vector if the object is translation.
[out]	isSame	- True at the output if the current surface and the pattern object are identical.

Returns: True - if a surface is translation

Reimplemented from MbSurface.

◆ GetRadius()

double MbTorusSurface::GetRadius ( ) const

overridevirtual

Get the physical radius of the object or null if it impossible.

Method returns maximum physical radius by one of the parametric direction if the corresponding parametric curve is the arc, method returns zero otherwise.

Reimplemented from MbSurface.

◆ GetPointProjection()

bool MbTorusSurface::GetPointProjection	(	const MbCartPoint3D &	p,
		bool	init,
		double &	u,
		double &	v,
		bool	ext,
		MbRect2D *	uvRange = `nullptr`
	)		const

overridevirtual

The nearest point projection onto the surface.

Parameters

[in]	p	- Projecting point
[in]	init	- If true, then input parameters u and v are considered to be initial approximations
[in,out]	u	- Parameter of projection onto the surface
[in,out]	v	- Parameter of projection onto the surface
[in]	ext	- Attribute of search at the extension of a surface
[in]	uvRange	- Region of search the projection

Returns: True if the operation succeeded

Implements MbElementarySurface.

◆ GetVPoles()

bool MbTorusSurface::GetVPoles	(	double &	poleVMin,
		double &	poleVMax
	)		const

Define position of the poles.

Parameters

[out] poleVMin,poleVMax - Values of the poles.

Returns: True if the poles are found.

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

surf_torus_surface.h

Public Member Functions

Functions of toroidal surface

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ MbTorusSurface() [1/3]

◆ MbTorusSurface() [2/3]

◆ MbTorusSurface() [3/3]

Member Function Documentation

◆ Duplicate()

◆ IsSame()

◆ SetEqual()

◆ Transform()

◆ GetProperties()

◆ SetProperties()

◆ IsUClosed()

◆ IsVClosed()

◆ PointOn()

◆ _PointOn()

◆ Explore()

◆ _PointNormal()

◆ StepU()

◆ StepV()

◆ DeviationStepU()

◆ DeviationStepV()

◆ MetricStepU()

◆ MetricStepV()

◆ CurvatureU()

◆ CurvatureV()

◆ NurbsSurface() [1/2]

◆ NurbsSurface() [2/2]

◆ Offset()

◆ CurveU()

◆ CurveV()

◆ DirectPointProjection()

◆ CurveIntersection()

◆ IsSimilarToSurface()

◆ GetMatrixToSurface()

◆ GetFilletRadius()

◆ Salient()

◆ GetTesselation()

◆ IsShift()

◆ GetRadius()

◆ GetPointProjection()

◆ GetVPoles()