An elementary surface. More...

#include <surf_elementary_surface.h>

Inheritance diagram for MbElementarySurface:

Collaboration diagram for MbElementarySurface:

Public Member Functions
Common functions of a geometric object
MbeSpaceType	Type () const override
	Get the group object type.

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

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.

Common functions of surface
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.

Functions of elementary surfaces
virtual bool	GetPointProjection (const MbCartPoint3D &p, bool init, double &u, double &v, bool ext, MbRect2D *uvRange=nullptr) const =0
	The nearest point projection onto the surface. More...

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

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 double	GetUMin () const =0
	Get the minimum value of u.

virtual double	GetVMin () const =0
	Get the minimum value of v.

virtual double	GetUMax () const =0
	Get the maximum value of u.

virtual double	GetVMax () const =0
	Get the maximum value of v.

virtual bool	IsUClosed () const =0
	Determine whether a surface is closed in u-parameter direction. More...

virtual bool	IsVClosed () const =0
	Determine whether a surface is closed in v-parameter direction. More...

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

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

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.

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

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

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

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

virtual void	PointOn (double &u, double &v, MbCartPoint3D &p) const =0
	Calculate a point on the surface. More...

virtual void	DeriveU (double &u, double &v, MbVector3D &) const =0
	Calculate first derivative with respect to u.

virtual void	DeriveV (double &u, double &v, MbVector3D &) const =0
	Calculate first derivative with respect to v.

virtual void	DeriveUU (double &u, double &v, MbVector3D &) const =0
	Calculate second derivative with respect to u.

virtual void	DeriveVV (double &u, double &v, MbVector3D &) const =0
	Calculate second derivative with respect to v.

virtual void	DeriveUV (double &u, double &v, MbVector3D &) const =0
	Calculate second derivative.

virtual void	DeriveUUU (double &u, double &v, MbVector3D &) const =0
	Calculate third derivative.

virtual void	DeriveUUV (double &u, double &v, MbVector3D &) const =0
	Calculate third derivative.

virtual void	DeriveUVV (double &u, double &v, MbVector3D &) const =0
	Calculate third derivative.

virtual void	DeriveVVV (double &u, double &v, MbVector3D &) const =0
	Calculate third derivative.

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

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

virtual void	NormalV (double &u, double &v, MbVector3D &) const
	Calculate derivative of normal with respect to 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	_PointOn (double u, double v, MbCartPoint3D &p) const
	Calculate a point on the surface. More...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

virtual void	_NormalVV (double u, double v, MbVector3D &) const
	Calculate second derivative of normal vector 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).

virtual void	Explore (double &u, double &v, bool ext, MbCartPoint3D &pnt, MbVector3D &uDer, MbVector3D &vDer, MbVector3D uuDer, MbVector3D vvDer, MbVector3D uvDer, MbVector3D nor) const
	Calculate point and derivatives of object for given parameters. More...

virtual 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
	Calculate all derivatives at point. More...

virtual double	StepU (double u, double v, double sag) const
	Calculate parameter step. More...

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

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

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

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

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

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

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

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

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...

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

virtual double	CurvatureV (double u, double v) const
	Calculate line curvature along the direction of v. 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 double	GetRadius () const
	Get the physical radius of the object or null if it impossible. More...

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

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

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

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

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

virtual MbSplineSurface *	NurbsSurface (double u1, double u2, double v1, double v2, bool bmatch=false) const
	Construct a NURBS copy of trimmed surface. More...

virtual MbSurface *	NurbsSurface (const MbNurbsParameters &uParam, const MbNurbsParameters &vParam) 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 MbSurface *	Offset (double d, bool same) const
	Create an offset surface. More...

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

virtual MbCurve3D *	CurveV (double u, MbRect1D *pRgn, bool bApprox=true) const
	Construct spatial copy of the line u = const. 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 void	DirectPointProjection (const MbCartPoint3D &pnt, const MbVector3D &vect, SArray< MbCartPoint > &uv, bool ext, MbRect2D *uvRange=nullptr) const
	Find all a point projection onto the surface along a vector in either of two directions. More...

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	CurveTangentNewton (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 tangency between a surface and a curve. For internal use only.

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

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

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

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

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

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

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

virtual void	IncludePoint (double u, double v)
	Include a point into domain. 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.

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

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

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

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

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.

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

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

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...

virtual void	GetTesselation (const MbStepData &stepData, double u1, double u2, double v1, double v2, SArray< double > &uu, SArray< double > &vv) const
	Determine a splitting of parametric region of a surface by verticals and horizontals. 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 bool	IsShift (const MbSpaceItem &obj, MbVector3D &dir, bool &isSame, double accuracy=LENGTH_EPSILON) const
	Determine whether the object is a translation. More...

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).

virtual MbeSpaceType	IsA () const =0
	Get the type of the object.

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

virtual MbSpaceItem &	Duplicate (MbRegDuplicate *iReg=nullptr) const =0
	Create a copy of the object. More...

virtual bool	IsSame (const MbSpaceItem &other, double accuracy=LENGTH_EPSILON) const =0
	Determine whether an object is equal. More...

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

virtual bool	SetEqual (const MbSpaceItem &item)=0
	Make objects equal if they are similar. More...

virtual void	GetProperties (MbProperties &properties)=0
	Outstanding properties of the object. More...

virtual void	SetProperties (const MbProperties &properties)=0
	Change the properties of an object. 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.

Protected Attributes
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...

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.

Detailed Description

An elementary surface.

Parent class for surfaces: MbConeSurface, MbCylinderSurface, MbPlane, MbSphereSurface, MbTorusSurface. Elementary surface is described by analytical expression in local coordinate system. Analytical expression of radius-vector of surface has canonical form in local coordinate system.
Local coordinate system 'position' can be both right and left.

Member Function Documentation

◆ Transform()

void MbElementarySurface::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.

Implements MbSpaceItem.

Reimplemented in MbTorusSurface, MbSphereSurface, and MbPlane.

◆ Move()

void MbElementarySurface::Move	(	const MbVector3D &	to,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Move an object along a vector.

Move an object along a geometric vector using the registrator. If object contains references to the other geometric objects then the move operation is applied to the nested objects. Registrator is needed to prevent multiple copying of the object. It is allowed to use function without registrator, if it is needed to transform a 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 moved.

Parameters

[in]	to	- Shift vector.
[in]	iReg	- Registrator.

Implements MbSpaceItem.

◆ Rotate()

void MbElementarySurface::Rotate	(	const MbAxis3D &	axis,
		double	angle,
		MbRegTransform *	iReg = `nullptr`
	)

overridevirtual

Rotate an object around an axis at a given angle.

Rotate an object around an axis at a given angle with the registrator. If object contains references to the other geometric objects then the rotation operation is applied to the nested objects. Registrator is needed to prevent multiple copying of the object. It is allowed to use function without registrator, if it is needed to transform a 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 rotated.

Parameters

[in]	axis	- The axis of rotation.
[in]	angle	- Rotation.
[in]	iReg	- Registrator.

Implements MbSpaceItem.

◆ DistanceToPoint()

double MbElementarySurface::DistanceToPoint ( const MbCartPoint3D & point ) const

overridevirtual

Determine the distance to the point.

Parameters

[in] point - Point.

Returns: Distance to point

Implements MbSpaceItem.

Reimplemented in MbPlane.

◆ NearPointProjection()

bool MbElementarySurface::NearPointProjection	(	const MbCartPoint3D &	pnt,
		double &	u,
		double &	v,
		bool	ext,
		MbRect2D *	uvRange = `nullptr`
	)		const

overridevirtual

Find the projection of a point onto the surface.

Find the nearest point projection to the surface or its extension by the given initial approximation. 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. The Newton method is used.

Parameters

[in]	pnt	- A given point.
[in,out]	u	- Input - initial approximation, output - parameter of a surface, corresponding to the nearest projection.
[in,out]	v	- Input - initial approximation, output - parameter of a surface, corresponding to the nearest projection.
[in]	ext	- A flag defining whether to seek projection on the extension of the surface.
[in]	uvRange	- A range of parameters changing in which the solution should be found.

Returns: True - if there is found a projection which satisfies to all input conditions.

Reimplemented from MbSurface.

◆ GetPointProjection()

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

pure virtual

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

Implemented in MbTorusSurface, MbSphereSurface, MbPlane, MbCylinderSurface, and MbConeSurface.

◆ AddTesselation()

void MbElementarySurface::AddTesselation	(	double	step,
		size_t	maxCount,
		double	w1,
		double	w2,
		SArray< double > &	ww
	)		const

Add parameters to the array with given step.

Add parameters from w1 to w2 to the array with given step.

Parameters

[in]	step	- Step
[in]	maxCount	- Maximum count of cell.
[out]	ww	- Container with parameters

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

surf_elementary_surface.h

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ Transform()

◆ Move()

◆ Rotate()

◆ DistanceToPoint()

◆ NearPointProjection()

◆ GetPointProjection()

◆ AddTesselation()