Surface in three-dimensional space. More...

#include <surface.h>

Inheritance diagram for MbSurface:

Collaboration diagram for MbSurface:

Public Member Functions
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.

Functions for surface domain description.
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.

Functions for working at surface domain
Functions PointOn, Derive... correct parameters when getting out of rectangular domain bounds. Exceptions: MbPlane (plane) Functions PointOn, Derive... of plane don't correct parameters when getting out of rectangular domain bounds. MbSmoothSurface and its inheritors (fillet of chamfer surfaces) Functions PointOn and Derive... of smooth surfaces don't correct the first parameter when getting out of domain bounds.
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...

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.
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...

Functions of moving on surface
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.

Common functions of surface.
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) const
	Get fillet radius if the surface is a fillet surface.

virtual MbeParamDir	GetFilletDirection () const
	Direction of fillet surface.

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

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

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

void	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.

virtual void	GetParamsToUnit (double u, double v, double &uParam, double &vParam) const
	Get increment of parameters, 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	IsRectangular () const
	Determine whether derivatives with respect to u and v are orthogonal.

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 void	Transform (const MbMatrix3D &matr, MbRegTransform *iReg=nullptr)=0
	Convert the object according to the matrix. More...

virtual void	Move (const MbVector3D &to, MbRegTransform *iReg=nullptr)=0
	Move an object along a vector. More...

virtual void	Rotate (const MbAxis3D &axis, double angle, MbRegTransform *iReg=nullptr)=0
	Rotate an object around an axis at a given angle. 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

virtual void	GetBasisItems (RPArray< MbSpaceItem > &)
	Outstanding reference objects in a container sent.

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 Member Functions
	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
MbCube	cube
	Bounding box of surface. More...

Detailed Description

Surface in three-dimensional space.

The parent class for all surfaces in three-dimensional space. A surface is a vector function of two scalar parameters, taking values on the two-dimensional connected region. Surface represents a continuous mapping of two-dimensional connected region to three-dimensional space.
For all surfaces, except MbCurveBoundedSurface, the domain is a rectangle in two-dimensional parameter space.
A surface is used:
for spatial modeling,
for construction of solid faces in special cases.

Member Function Documentation

◆ DistanceToPoint()

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

overridevirtual

Determine the distance to the point.

Parameters

[in] point - Point.

Returns: Distance to point

Implements MbSpaceItem.

◆ AddYourGabaritTo()

void MbSurface::AddYourGabaritTo ( MbCube & cube ) const

overridevirtual

Expand sent bounding box (a.k.a. gabarit), so that it included the object.

Expand sent bounding box, so that it included the object.

Parameters

[in,out] cube - The bounding box to expand.

Implements MbSpaceItem.

◆ PrepareIntegralData()

virtual void MbSurface::PrepareIntegralData ( const bool forced ) const

virtual

Calculate temporary (mutable) data of an object.

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

Parameters

[in] forced - Forced recalculation.

◆ CalculateMesh()

void MbSurface::CalculateMesh	(	const MbStepData &	stepData,
		const MbFormNote &	note,
		MbMesh &	mesh
	)		const

overridevirtual

Build polygonal copy mesh.

Build a polygonal copy of the object that is represented by polygons or/and fasets.

Parameters

[in]	stepData	- Data for еру step calculation for polygonal object.
[in]	note	- Way for polygonal object constructing.
[in,out]	mesh	- The builded polygonal object.

Implements MbSpaceItem.

◆ IsUClosed()

virtual bool MbSurface::IsUClosed ( ) const

pure virtual

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.

Implemented in MbTorusSurface, MbSweptSurface, MbSplineSurface, MbSphereSurface, MbSmoothSurface, MbSectionSurface, MbPolySurface, MbPlane, MbOffsetSurface, MbMeshSurface, MbLoftedSurface, MbJoinSurface, MbGridSurface, MbGregorySurface, MbCylinderSurface, MbCurveBoundedSurface, MbCoverSurface, MbCornerSurface, MbCoonsPatchSurface, and MbConeSurface.

◆ IsVClosed()

virtual bool MbSurface::IsVClosed ( ) const

pure virtual

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.

Implemented in MbTorusSurface, MbSweptSurface, MbSplineSurface, MbSphereSurface, MbSmoothSurface, MbSectionSurface, MbPolySurface, MbPlane, MbOffsetSurface, MbMeshSurface, MbLoftedSurface, MbJoinSurface, MbGridSurface, MbGregorySurface, MbCylinderSurface, MbCurveBoundedSurface, MbCoverSurface, MbCornerSurface, MbCoonsPatchSurface, and MbConeSurface.

◆ IsUTouch()

virtual bool MbSurface::IsUTouch ( ) const

virtual

Determine whether a surface is closed in u-parameter direction regardless of the smoothness of the closure.

Determine whether a surface is actually closed in u-parameter direction regardless of the smoothness of the closure.

Reimplemented in MbSplineSurface, MbMeshSurface, MbGregorySurface, and MbCurveBoundedSurface.

◆ IsVTouch()

virtual bool MbSurface::IsVTouch ( ) const

virtual

Determine whether a surface is closed in v-parameter direction regardless of the smoothness of the closure.

Determine whether a surface is actually closed in v-parameter direction regardless of the smoothness of the closure.

Reimplemented in MbSplineSurface, MbMeshSurface, MbGregorySurface, and MbCurveBoundedSurface.

◆ IsUPeriodic()

virtual bool MbSurface::IsUPeriodic ( ) const

virtual

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

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

Reimplemented in MbSplineSurface, MbMeshSurface, MbGregorySurface, and MbCurveBoundedSurface.

◆ IsVPeriodic()

virtual bool MbSurface::IsVPeriodic ( ) const

virtual

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

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

Reimplemented in MbSplineSurface, MbMeshSurface, MbGregorySurface, and MbCurveBoundedSurface.

◆ GetPeriod()

virtual double MbSurface::GetPeriod ( ptrdiff_t i ) const

virtual

Return period.

Period is calculated for smoothly closed surface in one of its parameters. If a surface is not closed in this parameter then 0 is returned.

Parameters

[in] i - Shows direction: 0 - period in u, 1 - period in v.

◆ Periodicity()

virtual size_t MbSurface::Periodicity ( ) const

virtual

Determine periodicity.

Whether a surface is periodic.

Returns: 0 - it is not periodic
1 - it is periodic in U
2 - it is periodic in V
3 - it is periodic in U and V

◆ GetLimitPoint() [1/3]

virtual void MbSurface::GetLimitPoint	(	ptrdiff_t	number,
		MbCartPoint3D &	pnt
	)		const

virtual

Calculate the boundary point.

Calculate one of the points where parameters take the maximum or the minimum values.

Parameters

[in]	number	- A number of a boundary point. 1 corresponds to the point (umin, vmin) 2 corresponds to the point (umax, vmin) 3 corresponds to the point (umax, vmax) 4 corresponds to the point (umin, vmax)
[in,out]	pnt	- A calculated point.

Reimplemented in MbPlane, MbGridSurface, and MbCurveBoundedSurface.

◆ GetLimitPoint() [2/3]

virtual void MbSurface::GetLimitPoint	(	ptrdiff_t	number,
		MbCartPoint &	pnt
	)		const

virtual

Calculate the boundary two-dimensional point.

Calculate one of the points where parameters take the maximum or the minimum values.

Parameters

[in]	number	- A number of a boundary point. 1 corresponds to the point (umin, vmin) 2 corresponds to the point (umax, vmin) 3 corresponds to the point (umax, vmax) 4 corresponds to the point (umin, vmax)
[in,out]	pnt	- A calculated point.

Reimplemented in MbPlane, MbGridSurface, and MbCurveBoundedSurface.

◆ GetLimitPoint() [3/3]

MbCartPoint3D MbSurface::GetLimitPoint ( ptrdiff_t number ) const

Calculate the boundary point.

Calculate one of the points where parameters take the maximum or the minimum values.

Parameters

[in] number - A number of a boundary point.
1 corresponds to the point (umin, vmin)
2 corresponds to the point (umax, vmin)
3 corresponds to the point (umax, vmax)
4 corresponds to the point (umin, vmax)

Returns: A calculated point. Get the boundary three-dimensional point.

◆ CurvatureU()

virtual double MbSurface::CurvatureU	(	double	u,
		double	v
	)		const

virtual

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 in MbTorusSurface, MbSpiralSurface, MbSphereSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbOffsetSurface, MbExtrusionSurface, MbExpansionSurface, MbEvolutionSurface, MbCylinderSurface, MbCurveBoundedSurface, and MbConeSurface.

◆ CurvatureV()

virtual double MbSurface::CurvatureV	(	double	u,
		double	v
	)		const

virtual

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 in MbTorusSurface, MbSphereSurface, MbSectorSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbOffsetSurface, MbFilletSurface, MbExtrusionSurface, MbExpansionSurface, MbCylinderSurface, MbCurveBoundedSurface, MbConeSurface, and MbChamferSurface.

◆ NormalCurvatureU()

double MbSurface::NormalCurvatureU	(	double	u,
		double	v
	)		const

Calculate a normal curvature of line along the direction of u.

Normal curvature of the coordinate line is calculated along the direction of u.

Parameters

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

Returns: Curvature.

◆ NormalCurvatureV()

double MbSurface::NormalCurvatureV	(	double	u,
		double	v
	)		const

Calculate a normal curvature of line along the direction of v.

Normal curvature of the coordinate line is calculated along the direction of v.

Parameters

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

Returns: Curvature.

◆ NormalCurvature()

double MbSurface::NormalCurvature	(	double	u,
		double	v,
		double	du,
		double	dv
	)		const

Calculate a normal curvature of surface.

Normal curvature of surface is calculated along the line (du, dv).

Parameters

[in]	u	- Parameter.
[in]	v	- Parameter.
[in]	du	- Sets the direction of line a normal curvature is calculated along.
[in]	dv	- Sets the direction of line a normal curvature is calculated along.

Returns: Curvature.

◆ MeanGaussCurvature()

bool MbSurface::MeanGaussCurvature	(	double	u,
		double	v,
		double &	mean,
		double &	gauss
	)		const

Calculate the mean and the Gaussian curvature.

The mean and the Gaussian curvature.

Parameters

[in]	u	- Parameter.
[in]	v	- Parameter.
[out]	mean	- Mean curvature.
[out]	gauss	- Gaussian curvature.

Returns: True if the operation succeeded
otherwise false.

◆ MainCurvatures()

bool MbSurface::MainCurvatures	(	double	u,
		double	v,
		double &	c1,
		double &	c2,
		double &	du,
		double &	dv
	)		const

Calculate the mean and the Gaussian curvature.

The mean and the Gaussian curvature.

Parameters

[in]	u	- First surface parameter.
[in]	v	- Second surface parameter.
[out]	c1	- First surface curvature.
[out]	c2	- Second surface curvature.
[out]	du	- du and dv are the components of the curvature vector.
[out]	dv	- du and dv are the components of the curvature vector.

Returns: True if the calculation succeeded
otherwise false.

◆ GetRadius()

virtual double MbSurface::GetRadius ( ) const

virtual

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 in MbTorusSurface, MbSplineSurface, MbSphereSurface, MbFilletSurface, MbExtrusionSurface, MbCylinderSurface, MbCurveBoundedSurface, and MbConeSurface.

◆ ChangeCarrier()

virtual void MbSurface::ChangeCarrier	(	const MbSpaceItem &	item,
		MbSpaceItem &	init
	)

virtual

Changing of carrier.

It is used for union of coplanar faces.

Reimplemented in MbSpiralSurface, MbSectorSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbOffsetSurface, MbMeshSurface, MbLoftedSurface, MbFilletSurface, MbExtrusionSurface, MbExpansionSurface, MbEvolutionSurface, MbElevationSurface, MbCurveBoundedSurface, MbCoverSurface, MbCornerSurface, MbCoonsPatchSurface, and MbChamferSurface.

◆ ChangeCarrierBorne()

virtual bool MbSurface::ChangeCarrierBorne	(	const MbSurface &	item,
		MbSurface &	init,
		const MbMatrix &	matr
	)

virtual

Changing of carrier elements.

It is used for union of coplanar faces. The surfaces 'item' and 'init' must be similar.

Parameters

[in]	item	- Changed surface
[in]	init	- New surface
[in]	matr	- Transition matrix from 'item' to 'init'

Returns: True if the operation succeeded
otherwise false.

Reimplemented in MbOffsetSurface, MbFilletSurface, MbCurveBoundedSurface, and MbChamferSurface.

◆ IsSpinePeriodic()

virtual bool MbSurface::IsSpinePeriodic ( ) const

virtual

Periodicity of the guide.

Returns: True if a surface has a guide and it is periodic.

Reimplemented in MbEvolutionSurface.

◆ NurbsSurface() [1/3]

MbSplineSurface* MbSurface::NurbsSurface ( bool bmatch = false ) const

Construct a NURBS copy of a 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

[in] bmatch - true, if it is required to keep one-to-one correspondence of parametric regions in mapping.

◆ NurbsSurface() [2/3]

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

virtual

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 in MbTorusSurface, MbSpiralSurface, MbSphereSurface, MbSectorSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbOffsetSurface, MbLoftedSurface, MbFilletSurface, MbExtrusionSurface, MbExplorationSurface, MbExpansionSurface, MbExactionSurface, MbEvolutionSurface, MbElevationSurface, MbCylinderSurface, MbConeSurface, MbChamferSurface, MbSplineSurface, MbPlane, MbJoinSurface, and MbCurveBoundedSurface.

◆ NurbsSurface() [3/3]

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

virtual

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 in MbTorusSurface, MbSplineSurface, MbSphereSurface, MbSmoothSurface, MbSectorSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbJoinSurface, MbFilletSurface, MbExtrusionSurface, MbExpansionSurface, MbCylinderSurface, MbCurveBoundedSurface, and MbConeSurface.

◆ NurbsParam()

bool MbSurface::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.

Prepare parameters for the transformation to NURBS surface. The number of points along the chosen direction if defined by the variable tParam.

Parameters

[in]	tParam	- Parameters for the transformation of a surface to NURBS with respect to one of parameters.
[in]	uParam	- Which parameter is considered: true - prepares an approximation with respect to u. false - prepares an approximation with respect to v.
[in]	op1	- Minimal value of the second parameter.
[in]	op2	- Maximal value of the second parameter.
[out]	isClosedNurbs	- True - the approximating surface is closed in the chosen direction.
[out]	epsilon	- At the output - parametric tolerance in the given direction.
[out]	params	- A filled array of splitting parameters along the chosen direction.

Returns: True if the operation succeeded.

◆ CheckApproxPointParamsOpen()

void MbSurface::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.

Chose points on a surface for NURBS approximation along the parameter in the case of unclosed in the chosen direction surface. If a surface is approximated with the given knot vector, then splitting parameters are checked in order to leave at least one splitting point between the elements of a knot vector. If necessary, the list of splitting points is complemented. If a knot vector is not set (empty), then the knot vector is calculated according to the order, the number of knots and the proposed splitting.

Parameters

[in]	isU	- Which parameter is considered: true - prepares an approximation with respect to u. false - prepares an approximation with respect to v.
[in]	par	- A value of second parameter.
[in]	degree	- An order of NURBS surface by a chosen direction.
[in]	pCount	- A number of knots of NURBS surface by a chosen direction.
[in,out]	tList	- A splitting parameters of NURBS surface by a chosen direction. They are calculated in the NurbsParam function.
[in,out]	aKnots	- A knot vector of NURBS surface.

◆ CheckApproxPointParamsClosed()

void MbSurface::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.

Chose points on a surface for NURBS approximation along the parameter in a case of closed in the chosen direction surface. If a surface is approximated with the given knot vector then splitting parameters are checked in order to leave at least one splitting point between the elements of a knot vector. If necessary, the list of splitting points is complemented. If a knot vector is not set (empty) then the knot vector is calculated according to the order, the number of knots and the proposed splitting.

Parameters

[in]	isU	- Which parameter is considered: true - prepares an approximation with respect to u. false - prepares an approximation with respect to v.
[in]	par	- A value of second parameter.
[in]	degree	- An order of NURBS surface by a chosen direction.
[in]	pCount	- A number of knots of NURBS surface by a chosen direction.
[in,out]	tList	- A splitting parameters of NURBS surface by a chosen direction. They are calculated in the NurbsParam function.
[in,out]	aKnots	- A knot vector of NURBS surface.

◆ Offset()

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

virtual

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 in MbTorusSurface, MbSpiralSurface, MbSphereSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbOffsetSurface, MbMeshSurface, MbLoftedSurface, MbJoinSurface, MbFilletSurface, MbExtrusionSurface, MbExplorationSurface, MbExactionSurface, MbEvolutionSurface, MbElevationSurface, MbCylinderSurface, MbCurveBoundedSurface, MbConeSurface, MbChannelSurface, and MbChamferSurface.

◆ CurveU()

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

virtual

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 in MbCoverSurface, MbCornerSurface, MbTorusSurface, MbSplineSurface, MbSpiralSurface, MbSphereSurface, MbSectorSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbMeshSurface, MbLoftedSurface, MbExtrusionSurface, MbExplorationSurface, MbExpansionSurface, MbExactionSurface, MbEvolutionSurface, MbCylinderSurface, MbCurveBoundedSurface, MbCoonsPatchSurface, and MbConeSurface.

◆ CurveV()

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

virtual

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 in MbChamferSurface, MbCoverSurface, MbCornerSurface, MbTorusSurface, MbSplineSurface, MbSpiralSurface, MbSphereSurface, MbSectorSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbMeshSurface, MbLoftedSurface, MbFilletSurface, MbExtrusionSurface, MbExplorationSurface, MbExpansionSurface, MbExactionSurface, MbEvolutionSurface, MbElevationSurface, MbCylinderSurface, MbCurveBoundedSurface, MbCoonsPatchSurface, and MbConeSurface.

◆ CurveUV()

virtual MbCurve3D* MbSurface::CurveUV	(	const MbLineSegment &	segm,
		bool	bApprox = `true`
	)		const

virtual

Construct spatial copy of line by parametric line.

Parameters

[in]	segm	- A segment in parametric plane of surface, a spatial copy of which is required to construct.
[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.

Reimplemented in MbRuledSurface, MbPlane, MbCylinderSurface, MbCurveBoundedSurface, and MbConeSurface.

◆ PointRelative()

virtual MbeItemLocation MbSurface::PointRelative	(	const MbCartPoint3D &	pnt,
		double	eps = `ANGLE_REGION`
	)		const

virtual

Get point location relative to the surface.

Parameters

[in]	pnt	- The investigated point.
[in]	eps	- Tolerance of getting a point onto a surface.

Returns: Iloc_InItem = 1 - point is located over the surface (from the side of normal vector)
iloc_OnItem = 0 - point is located on the surface,
iloc_OutOfItem = -1 - point is located under the surface.

Reimplemented in MbPlane.

◆ PointClassification()

virtual MbeItemLocation MbSurface::PointClassification	(	const MbCartPoint &	pnt,
		bool	ignoreClosed = `false`
	)		const

virtual

A point is located inside the region on a surface.

Investigated two-dimensional point in the parametric plane of a surface.

Parameters

[in]	pnt	- The investigated point.
[in]	ignoreClosed	- Whether to consider the surface closedness. If true, then the closedness is not considered.

Returns: Iloc_InItem - point is inside surface region.
iloc_OnItem - point belongs to surface boundary.
iloc_OutOfItem - point is outside surface region.

Reimplemented in MbGridSurface, and MbCurveBoundedSurface.

◆ DistanceToBorder()

virtual double MbSurface::DistanceToBorder	(	const MbCartPoint &	point,
		double &	epsilon
	)		const

virtual

Calculate the parametric distance to the nearest boundary.

The calculated distance is positive if the point is inside, and is negative if it is outside.

Parameters

[in]	point	- The investigated point.
[in]	epsilon	- Tolerance of getting a point onto a surface.

Returns: Returns the distance to the boundary.

Reimplemented in MbGridSurface, and MbCurveBoundedSurface.

◆ CurveClassification()

virtual size_t MbSurface::CurveClassification	(	const MbCurve &	curve,
		SArray< double > &	tcurv,
		SArray< MbVector > &	dir
	)		const

virtual

Determine points of intersections between the curve and the surface contours.

Determine points of intersections between the curve and the surface boundaries in order to find parts of the curve inside the surface region and vectors for their translation to the surface region. Translation vector is defined for each intersection point. If it is impossible to find a translation vector, then the vector with null size is saved into the array. It can be non-null if a surface is closed at least in one of directions. In this case the translation vector allows to move a part of a curve by a certain number of periods in such way that the found point of intersection between the curve and the boundary is located inside the surface region and the derivative of a curve at this point is directed inside the surface. Using the translation vector a curve can be moved by a certain number of periods. I.e. metrically the curve will not change.

Parameters

[in]	curve	- A given curve.
[in,out]	tcurv	- A set of curve parameters corresponding to the intersection points.
[in,out]	dir	- A set of translation vectors.

Returns: The number of intersections.

Reimplemented in MbGridSurface, and MbCurveBoundedSurface.

◆ SurfaceBorderIntersection()

size_t MbSurface::SurfaceBorderIntersection	(	const MbCurve &	curve,
		SArray< double > &	tcurv,
		SArray< MbVector > &	dir
	)		const

Determine points of intersections between the curve and the surface contours.

Determine points of intersections between the curve and the surface boundaries in order to find parts of a curve inside the surface region and vectors for their translation to the surface region. Translation vector is defined for each intersection point. If it is impossible to find a translation vector then the vector with null size is saved into the array. It can be non-null if a surface is closed at least in one of directions. In this case the translation vector allows to move a part of a curve by a certain number of periods in such way that the found point of intersection between the curve and the boundary is located inside the surface region and the derivative of a curve at this point is directed inside the surface. Using the translation vector a curve can be moved by a certain number of periods. I.e. metrically the curve will not change.

Parameters

[in]	curve	- A given curve.
[in,out]	tcurv	- A set of curve parameters corresponding to the intersection points.
[in,out]	dir	- A set of translation vectors.

Returns: The number of intersections.

◆ NearPointProjection()

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

virtual

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 in MbSplineSurface, MbSpiralSurface, MbMeshSurface, MbLoftedSurface, MbRuledSurface, MbRevolutionSurface, MbOffsetSurface, MbGridSurface, MbFilletSurface, MbExtrusionSurface, MbElementarySurface, and MbCurveBoundedSurface.

◆ DirectPointProjection()

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

virtual

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 in MbSplineSurface, MbOffsetSurface, MbMeshSurface, MbLoftedSurface, MbTorusSurface, MbSphereSurface, MbRevolutionSurface, MbGridSurface, MbCylinderSurface, MbCurveBoundedSurface, MbConeSurface, and MbPlane.

◆ NearDirectPointProjection()

virtual bool MbSurface::NearDirectPointProjection	(	const MbCartPoint3D &	pnt,
		const MbVector3D &	vect,
		double &	u,
		double &	v,
		bool	ext,
		MbRect2D *	uvRange = `nullptr`,
		bool	onlyPositiveDirection = `false`
	)		const

virtual

Find the nearest point projection to the surface in the vector direction.

Calculate the nearest point 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.
[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 curve.
[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 in MbPlane.

◆ CurveIntersection()

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

virtual

Determine points of intersection between a surface and a curve.

Parameters

[in]	curv	- A given curve.
[in]	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 in MbTorusSurface, MbSphereSurface, MbRuledSurface, MbGridSurface, MbExtrusionSurface, MbCylinderSurface, MbCurveBoundedSurface, MbConeSurface, and MbPlane.

◆ IsSimilarToSurface()

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

virtual

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 in MbTorusSurface, MbSplineSurface, MbSpiralSurface, MbSphereSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbOffsetSurface, MbFilletSurface, MbExtrusionSurface, MbExpansionSurface, MbExactionSurface, MbEvolutionSurface, MbCylinderSurface, MbCurveBoundedSurface, MbCoverSurface, MbConeSurface, and MbChamferSurface.

◆ ProjectCurveOnSimilarSurface() [1/2]

virtual bool MbSurface::ProjectCurveOnSimilarSurface	(	const MbCurve3D &	spaceCurve,
		const MbCurve &	curve,
		const MbSurface &	surfNew,
		MbCurve *&	curveNew
	)		const

virtual

Construction of projection of a surface curve on coincident surface.

A projection of surface intersection curve is constructed on a given surface. It is implied that the given surface is similar to one of surfaces of the intersection curve but this fact is not checked.

Parameters

[in]	spaceCurve	- A given intersection curve.
[in]	curve	- A two-dimensional curve on a surface.
[in]	surfNew	- New surface.
[out]	curveNew	- An obtained two-dimensional curve on new surface.

Returns: True - if the operation succeeded.

Reimplemented in MbSphereSurface, and MbCurveBoundedSurface.

◆ ProjectCurveOnSimilarSurface() [2/2]

bool MbSurface::ProjectCurveOnSimilarSurface	(	const MbCurve3D &	spaceCurve,
		const MbCurve &	curve,
		const MbSurface &	surfNew,
		SPtr< MbCurve > &	curveNew
	)		const

Construction of projection of a surface curve on coincident surface.

A projection of surface intersection curve is constructed on a given surface. It is implied that the given surface is similar to one of surfaces of the intersection curve but this fact is not checked.

Parameters

[in]	spaceCurve	- A given intersection curve.
[in]	curve	- A two-dimensional curve on a surface.
[in]	surfNew	- New surface.
[out]	curveNew	- An obtained two-dimensional curve on new surface.

Returns: True - if the operation succeeded.

◆ GetMatrixToSurface()

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

virtual

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 in MbTorusSurface, MbSplineSurface, MbSpiralSurface, MbSphereSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbOffsetSurface, MbFilletSurface, MbExtrusionSurface, MbExpansionSurface, MbExactionSurface, MbEvolutionSurface, MbCylinderSurface, MbCurveBoundedSurface, MbCoverSurface, MbConeSurface, and MbChamferSurface.

◆ DistanceToCurve()

virtual double MbSurface::DistanceToCurve	(	const MbCurve3D &	curve,
		double &	u,
		double &	v,
		double &	t,
		bool	tCalc = `false`
	)		const

virtual

Calculate the nearest distance to a curve.

Calculation of the minimum distance between a curve and a surface. Determination of the points on a surface and a curve where the minimum distance is reached.

Parameters

[in]	curve	- A given curve.
[out]	u	- Coordinate of the calculated point on surface.
[out]	v	- Coordinate of the calculated point on surface.
[in,out]	t	- Input - an initial approximation to the required point on a curve. Output - a parameter of the calculated point on a curve.
[in]	tCalc	- A flag showing whether to use t as initial approximation.

Returns: The minimum distance between a curve and a surface.

◆ DistanceToSurface()

virtual double MbSurface::DistanceToSurface	(	const MbSurface &	surf1,
		double &	u0,
		double &	v0,
		double &	u1,
		double &	v1
	)		const

virtual

Calculate the nearest distance to a surface.

Calculating of minimum distance between two surfaces. Determination of the points on surfaces where the minimum distance is reached.

Parameters

[in]	surf1	- A given surface.
[out]	u0	- Coordinate of the calculated point on the current surface.
[out]	v0	- Coordinate of the calculated point on the current surface.
[out]	u1	- Coordinate of the calculated point on the given surface.
[out]	v1	- Coordinate of the calculated point on the given surface.

Returns: Minimal distance between surfaces.

◆ GetUPairs()

virtual size_t MbSurface::GetUPairs	(	double	v,
		SArray< double > &	u
	)		const

virtual

Calculate U-pairs by V.

Calculate significant u-parameters of a surface with the given parameter v. In a case of general form - minimal and maximal values of u-parameter.

Parameters

[in]	v	- Given parameters.
[out]	u	- A set of values of u.

Returns: The number of calculated values of u.

Reimplemented in MbGridSurface, and MbCurveBoundedSurface.

◆ GetVPairs()

virtual size_t MbSurface::GetVPairs	(	double	u,
		SArray< double > &	v
	)		const

virtual

Calculate V-pairs by U.

Calculate significant v-parameters of a surface with the given parameter u. In case of a surface of general form - minimal and maximal values of v-parameter.

Parameters

[in]	u	- Given parameters.
[out]	v	- A set of values of v.

Returns: The number of calculated values of v.

Reimplemented in MbGridSurface, and MbCurveBoundedSurface.

◆ GetIsoclinal()

virtual void MbSurface::GetIsoclinal	(	const MbVector3D &	nor,
		SArray< MbCartPoint > &	uv
	)		const

virtual

Find all isoclines of a surface.

Find the points on a surface where the tangent plane is parallel to a plane having a normal nor.

Parameters

[in]	nor	- A vector which defines a plane.
[out]	uv	- A set of parameters of points for the required tangent.

◆ CopyGabarit()

void MbSurface::CopyGabarit	(	const MbSurface &	s,
		const MbVector3D *	to = `nullptr`
	)

inline

Copy the bounding box from the copy.

Copy from the copy ready estimates which were not calculated in the original.

Warning: A check of identity between a copy and an original is not performed for the time saving!

Parameters

[in] s - A surface-copy.

◆ CalculateRect()

void MbSurface::CalculateRect	(	const MbPlacement3D &	place,
		MbRect &	rect
	)		const

Calculate the rectangular bounding box of a surface in the given plane.

Get the rectangular bounding box of surfaces in the XAOY plane of the placement.

Parameters

[in]	place	- The given placement.
[out]	rect	- Calculated rectangle.

◆ MakeContour()

virtual MbContour& MbSurface::MakeContour ( bool sense ) const

virtual

Return the bounding two-dimensional contour.

The function creates new two-dimensional bounding contour. The object should be deleted after using.

Parameters

[in] sense - Whether the contour direction coincides with the counterclockwise traverse direction.

Returns: Bounding contour.

Reimplemented in MbGridSurface, and MbCurveBoundedSurface.

◆ MakeSegment()

virtual MbCurve& MbSurface::MakeSegment	(	size_t	i,
		bool	sense
	)		const

virtual

Return a segment of the bounding two-dimensional contour.

The function creates a segment of bounding contour according to the parameter i.
i = 0 - A segment of boundary where v = vmin
i = 1 - A segment of boundary where u = umax
i = 2 - A segment of boundary where v = vmax
i = 3 - A segment of boundary where u = umin
The object should be deleted after using.

Parameters

[in]	i	- An index of segment.
[in]	sense	- Whether the contour direction coincides with the counterclockwise traverse direction.

Returns: A boundary curve.

Reimplemented in MbGridSurface, and MbCurveBoundedSurface.

◆ MakeCurve()

MbCurve& MbSurface::MakeCurve	(	size_t	number1,
		size_t	number2
	)		const

Return a segment of the bounding two-dimensional contour.

The function finds the boundary points of a surface using the function GetLimitPoint and constructs a segment from the point with the number 'number1' to the points with the number 'number2'. The object should be deleted after using.

Parameters

[in]	number1	- A number of a boundary surface.
[in]	number2	- A number of a boundary surface.

Returns: A boundary curve.

◆ CalculatePolygon()

void MbSurface::CalculatePolygon	(	double	minPar,
		double	maxPar,
		double	constPar,
		MbeParamDir	dir,
		const MbStepData &	stepData,
		MbPolygon3D &	polygon
	)		const

Calculate polygon by u or v.

In the function the surface curve is constructed - a segment along the chosen direction and after that a curve approximating polygon is calculated.

Parameters

[in]	minPar	- Minimal value of parameter in the chosen direction.
[in]	maxPar	- Maximal value of parameter in the chosen direction.
[in]	constPar	- A value of second parameter.
[in]	dir	- A chosen direction. dir == pd_DirU - calculation is performed by u-parameter, v = const. dir == pd_DirU - calculation is performed by v-parameter, u = const.
[in]	sag	- A sag value, defining the tolerance of approximation.
[out]	polygon	- Calculated polygon.

◆ CalculateSurfaceWire()

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

virtual

Calculate mesh.

In the function the mesh calculation for surface drawing is performed.

Parameters

[in]	sag	- A sag value, defining the tolerance..
[in]	beg	- A number of the the first knot which gets into the mesh by each direction. For the construction of mesh of the whole surface beg == 0.
[out]	mesh	- A calculated mesh.
[in]	uMeshCount	- The number of u-mesh lines.
[in]	vMeshCount	- The number of v-mesh lines.

Reimplemented in MbGridSurface, MbCurveBoundedSurface, and MbCornerSurface.

◆ GetTesselation()

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

virtual

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 in MbTorusSurface, MbSplineSurface, MbSpiralSurface, MbSphereSurface, MbSectorSurface, MbSectionSurface, MbRuledSurface, MbRevolutionSurface, MbPlane, MbOffsetSurface, MbLoftedSurface, MbGridSurface, MbFilletSurface, MbExtrusionSurface, MbExplorationSurface, MbExpansionSurface, MbEvolutionSurface, MbCylinderSurface, MbCurveBoundedSurface, and MbConeSurface.

◆ AddTesselation()

void MbSurface::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.

Determine a splitting of parametric region of a surface by verticals and horizontals. Add parameters into an array in the direction dir. If the arrays uu and vv are not empty then their elements are deleted. i.e. a clarification of mesh in a given direction is performed.

Parameters

[in]	stepData	- Data for step calculation during triangulation.
[in]	dir	- A chosen direction. dir == pd_DirU - calculation is performed by u-parameter, v = const. dir == pd_DirU - calculation is performed by v-parameter, u = const.
[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.

◆ CalculateSurfaceGrid()

virtual void MbSurface::CalculateSurfaceGrid	(	const MbStepData &	stepData,
		bool	sense,
		MbGrid &	grid
	)		const

virtual

Approximate a surface by triangular plates.

Parameters

[in]	stepData	- Data for step calculation during triangulation.
[in]	sense	- It determines the coincidence of normals of surfaces and triangles.
[out]	grid	- The result of splitting.

Reimplemented in MbGridSurface, and MbCurveBoundedSurface.

◆ IsShift()

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

virtual

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

◆ CheckSurfParams()

virtual void MbSurface::CheckSurfParams	(	double &	u,
		double &	v
	)		const

virtual

Check parameters. Analogue of the global function _CheckParams, optimized for caches usage.

Check parameters and move them inside domain if parameter is out of pole.

Parameters

[in]	surface	- Surface.
[in]	u	- First parameter.
[in]	v	- Second parameter.

Reimplemented in MbSplineSurface, MbOffsetSurface, MbMeshSurface, and MbLoftedSurface.

◆ GetControlPlacement()

bool MbSurface::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.

Construct a local coordinate system of a surface with origin at the middle point of surface parametric limits.

Parameters

[out]	place	- Local coordinate system.
[in]	sameSense	- Normal's relative orientation.

Returns: True - if construction has been successfully.

◆ GetMatrix()

bool MbSurface::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.

The new range of parameters is set for a surface. A surface doesn't change geometrically. The function searches a matrix of transformation for the two-dimensional curves on a surface for the transition from old parameterization to new parameterization.

Parameters

[in]	xMin	- The new minimum value of u.
[in]	xMax	- The new maximum value of u.
[in]	yMin	- The new minimum value of v.
[in]	yMax	- The new maximum value of v.
[in]	matr	- A transformation matrix.

Member Data Documentation

◆ cube

MbCube MbSurface::cube

mutableprotected

Bounding box of surface.

Bounding box of surface is calculated only at the request. Bounding box of surface is undefined after object constructor and after object modifications.

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

surface.h

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Function Documentation

◆ DistanceToPoint()

◆ AddYourGabaritTo()

◆ PrepareIntegralData()

◆ CalculateMesh()

◆ IsUClosed()

◆ IsVClosed()

◆ IsUTouch()

◆ IsVTouch()

◆ IsUPeriodic()

◆ IsVPeriodic()

◆ GetPeriod()

◆ Periodicity()

◆ GetLimitPoint() [1/3]

◆ GetLimitPoint() [2/3]

◆ GetLimitPoint() [3/3]

◆ CurvatureU()

◆ CurvatureV()

◆ NormalCurvatureU()

◆ NormalCurvatureV()

◆ NormalCurvature()

◆ MeanGaussCurvature()

◆ MainCurvatures()

◆ GetRadius()

◆ ChangeCarrier()

◆ ChangeCarrierBorne()

◆ IsSpinePeriodic()

◆ NurbsSurface() [1/3]

◆ NurbsSurface() [2/3]

◆ NurbsSurface() [3/3]

◆ NurbsParam()

◆ CheckApproxPointParamsOpen()

◆ CheckApproxPointParamsClosed()

◆ Offset()

◆ CurveU()

◆ CurveV()

◆ CurveUV()

◆ PointRelative()

◆ PointClassification()

◆ DistanceToBorder()

◆ CurveClassification()

◆ SurfaceBorderIntersection()

◆ NearPointProjection()

◆ DirectPointProjection()

◆ NearDirectPointProjection()

◆ CurveIntersection()

◆ IsSimilarToSurface()

◆ ProjectCurveOnSimilarSurface() [1/2]

◆ ProjectCurveOnSimilarSurface() [2/2]

◆ GetMatrixToSurface()

◆ DistanceToCurve()

◆ DistanceToSurface()

◆ GetUPairs()

◆ GetVPairs()

◆ GetIsoclinal()

◆ CopyGabarit()

◆ CalculateRect()

◆ MakeContour()

◆ MakeSegment()

◆ MakeCurve()

◆ CalculatePolygon()

◆ CalculateSurfaceWire()

◆ GetTesselation()

◆ AddTesselation()

◆ CalculateSurfaceGrid()

◆ IsShift()

◆ CheckSurfParams()

◆ GetControlPlacement()

◆ GetMatrix()

Member Data Documentation

◆ cube