#include <opennurbs_surface.h>

Inheritance diagram for ON_Surface:

Public Types
enum	ISO { not_iso = 0, x_iso = 1, y_iso = 2, W_iso = 3, S_iso = 4, E_iso = 5, N_iso = 6, iso_count = 7 }
	pure virtual class for surface objects More...

Public Types inherited from ON_Object
enum	UserDataConflictResolution : unsigned char { UserDataConflictResolution::destination_object = 0, UserDataConflictResolution::source_object = 1, UserDataConflictResolution::source_copycount_gt = 2, UserDataConflictResolution::source_copycount_ge = 3, UserDataConflictResolution::destination_copycount_gt = 4, UserDataConflictResolution::destination_copycount_ge = 5, UserDataConflictResolution::delete_item = 6 }

Public Member Functions
	ON_Surface ()

	ON_Surface (const ON_Surface &)

virtual	~ON_Surface ()

bool	AreaMassProperties (class ON_MassProperties &mp, bool bArea=true, bool bFirstMoments=true, bool bSecondMoments=true, bool bProductMoments=true, double rel_tol=1.0e-6, double abs_tol=1.0e-6) const

ON_Brep *	BrepForm (ON_Brep *brep=nullptr) const override

virtual ON_Mesh *	CreateMesh (const ON_MeshParameters &mp, ON_Mesh *mesh=nullptr) const
	surface interface More...

virtual ON_SurfaceTree *	CreateSurfaceTree () const

virtual int	Degree (int dir) const =0

void	DestroyRuntimeCache (bool bDelete=true) override
	virtual ON_Object::DestroyRuntimeCache override More...

void	DestroySurfaceTree ()

virtual ON_Interval	Domain (int dir) const =0

virtual ON_Surface *	DuplicateSurface () const

bool	Ev1Der (double u, double v, ON_3dPoint &point, ON_3dVector &du, ON_3dVector &dv, int quadrant=0, int *hint=0) const

bool	Ev2Der (double u, double v, ON_3dPoint &point, ON_3dVector &du, ON_3dVector &dv, ON_3dVector &duu, ON_3dVector &duv, ON_3dVector &dvv, int quadrant=0, int *hint=0) const

virtual bool	Evaluate (double u, double v, int num_der, int array_stride, double der_array, int quadrant=0, int hint=0) const =0
	work horse evaluator More...

bool	EvaluatePoint (const class ON_ObjRef &objref, ON_3dPoint &P) const override
	virtual ON_Geometry override More...

bool	EvNormal (double u, double v, ON_3dPoint &point, ON_3dVector &du, ON_3dVector &dv, ON_3dVector &normal, int=0, int *=0) const

bool	EvNormal (double u, double v, ON_3dPoint &point, ON_3dVector &normal, int quadrant=0, int *hint=0) const

bool	EvNormal (double u, double v, ON_3dVector &normal, int quadrant=0, int *hint=0) const

bool	EvPoint (double u, double v, ON_3dPoint &point, int quadrant=0, int *hint=0) const

virtual bool	Extend (int dir, const ON_Interval &domain)

bool	FrameAt (double u, double v, ON_Plane &frame) const

virtual bool	GetClosestPoint (const ON_3dPoint &P, double s, double t, double maximum_distance=0.0, const ON_Interval sdomain=0, const ON_Interval tdomain=0) const

bool	GetDomain (int dir, double t0, double t1) const

int	GetIsoPushupDirection (const ON_Curve &curve_2d, double tolerance, const ON_Interval curve_2d_subdomain, double c, ON_Interval *c3_dom) const

virtual bool	GetLocalClosestPoint (const ON_3dPoint &, double, double, double , double , const ON_Interval =nullptr, const ON_Interval =nullptr) const

virtual bool	GetNextDiscontinuity (int dir, ON::continuity c, double t0, double t1, double t, int hint=nullptr, int *dtype=nullptr, double cos_angle_tolerance=ON_DEFAULT_ANGLE_TOLERANCE_COSINE, double curvature_tolerance=ON_SQRT_EPSILON) const

virtual int	GetNurbForm (ON_NurbsSurface &nurbs_surface, double tolerance=0.0) const

virtual bool	GetNurbFormParameterFromSurfaceParameter (double surface_s, double surface_t, double nurbs_s, double nurbs_t) const

virtual bool	GetParameterTolerance (int dir, double t, double tminus, double tplus) const

bool	GetSilhouette (const ON_Interval udom, const ON_Interval vdom, const ON_SilhouetteParameters parameters, const ON_PlaneEquation clipping_planes, size_t clipping_plane_count, ON_ClassArray< ON_SIL_EVENT > &silhouettes, ON_ProgressReporter progress, ON_Terminator *terminator) const

virtual bool	GetSpanVector (int dir, double *span_vector) const =0

virtual bool	GetSpanVectorIndex (int dir, double t, int side, int span_vector_index, ON_Interval span_interval) const

ON_Curve *	GetSurfaceParameterFromNurbFormParameter (const ON_Curve &curve3d, const ON_Curve &ns_curve2dX, double fit_tolerance) const

virtual bool	GetSurfaceParameterFromNurbFormParameter (double nurbs_s, double nurbs_t, double surface_s, double surface_t) const

virtual bool	GetSurfaceSize (double width, double height) const

bool	HasBrepForm () const override

virtual int	HasNurbForm () const

int	IntersectPlane (ON_PlaneEquation plane_equation, ON_ClassArray< ON_SSX_EVENT > &x, double intersection_tolerance=0.0, double overlap_tolerance=0.0, double fitting_tolerance=0.0, const ON_Interval surface_udomain=0, const ON_Interval surface_vdomain=0) const

int	IntersectSurface (const ON_Surface surfaceB, ON_ClassArray< ON_SSX_EVENT > &x, double intersection_tolerance=0.0, double overlap_tolerance=0.0, double fitting_tolerance=0.0, const ON_Interval surfaceA_udomain=0, const ON_Interval surfaceA_vdomain=0, const ON_Interval surfaceB_udomain=0, const ON_Interval *surfaceB_vdomain=0) const

int	IsAtSeam (double s, double t) const

bool	IsAtSingularity (double s, double t, bool bExact=true) const

virtual bool	IsClosed (int) const

bool	IsCone (ON_Cone *cone=nullptr, double tolerance=ON_ZERO_TOLERANCE) const

virtual bool	IsContinuous (ON::continuity c, double s, double t, int *hint=nullptr, double point_tolerance=ON_ZERO_TOLERANCE, double d1_tolerance=ON_ZERO_TOLERANCE, double d2_tolerance=ON_ZERO_TOLERANCE, double cos_angle_tolerance=ON_DEFAULT_ANGLE_TOLERANCE_COSINE, double curvature_tolerance=ON_SQRT_EPSILON) const

bool	IsCylinder (ON_Cylinder *cylinder=nullptr, double tolerance=ON_ZERO_TOLERANCE) const

virtual ISO	IsIsoparametric (const ON_BoundingBox &bbox) const

virtual ISO	IsIsoparametric (const ON_Curve &curve, const ON_Interval *curve_domain=nullptr) const

virtual ON_Curve *	IsoCurve (int dir, double c) const

virtual bool	IsPeriodic (int) const

virtual bool	IsPlanar (ON_Plane *plane=nullptr, double tolerance=ON_ZERO_TOLERANCE) const

virtual bool	IsSingular (int) const

bool	IsSolid () const

bool	IsSphere (ON_Sphere *sphere=nullptr, double tolerance=ON_ZERO_TOLERANCE) const

bool	IsTorus (ON_Torus *torus=nullptr, double tolerance=ON_ZERO_TOLERANCE) const

ON_3dVector	NormalAt (double, double) const

ON_NurbsSurface *	NurbsSurface (ON_NurbsSurface pNurbsSurface=nullptr, double tolerance=0.0, const ON_Interval s_subdomain=nullptr, const ON_Interval *t_subdomain=nullptr) const

ON::object_type	ObjectType () const override
	override ON_Object::ObjectType() - returns ON::surface_object More...

virtual ON_Surface *	Offset (double offset_distance, double tolerance, double *max_deviation=nullptr) const

ON_Surface &	operator= (const ON_Surface &)

ON_3dPoint	PointAt (double, double) const
	simple evaluation interface - no error handling More...

virtual ON_Curve *	Pullback (const ON_Curve &curve_3d, double tolerance, const ON_Interval curve_3d_subdomain=nullptr, ON_3dPoint start_uv=ON_3dPoint::UnsetPoint, ON_3dPoint end_uv=ON_3dPoint::UnsetPoint, ON_FitResult rc=0) const

virtual ON_Curve *	Pushup (const ON_Curve &curve_2d, double tolerance, const ON_Interval curve_2d_subdomain=nullptr, ON_FitResult rc=0) const

virtual bool	Reverse (int)=0

virtual bool	SetDomain (int dir, double t0, double t1)

bool	SetDomain (int dir, ON_Interval domain)

unsigned int	SizeOf () const override
	virtual ON_Object::SizeOf override More...

virtual int	SpanCount (int dir) const =0
	number of smooth nonempty spans in the parameter direction More...

virtual bool	Split (int dir, double c, ON_Surface &west_or_south_side, ON_Surface &east_or_north_side) const

const ON_SurfaceTree *	SurfaceTree () const

virtual bool	Transpose ()=0
	transpose surface parameterization (swap "s" and "t") More...

virtual bool	Trim (int dir, const ON_Interval &domain)

bool	VolumeMassProperties (class ON_MassProperties &mp, bool bVolume=true, bool bFirstMoments=true, bool bSecondMoments=true, bool bProductMoments=true, ON_3dPoint base_point=ON_3dPoint::UnsetPoint, double rel_tol=1.0e-6, double abs_tol=1.0e-6) const

Public Member Functions inherited from ON_Geometry
	ON_Geometry ()=default

	ON_Geometry (const ON_Geometry &)=default

	~ON_Geometry ()=default

ON_BoundingBox	BoundingBox () const

virtual void	ClearBoundingBox ()

virtual ON_COMPONENT_INDEX	ComponentIndex () const

virtual int	Dimension () const

virtual bool	GetBBox (double boxmin, double boxmax, bool bGrowBox=false) const

bool	GetBoundingBox (ON_3dPoint &bbox_min, ON_3dPoint &bbox_max, bool bGrowBox=false) const

bool	GetBoundingBox (ON_BoundingBox &bbox, bool bGrowBox=false) const

virtual bool	GetTightBoundingBox (class ON_BoundingBox &tight_bbox, bool bGrowBox=false, const class ON_Xform *xform=nullptr) const

virtual bool	IsDeformable () const

virtual bool	IsMorphable () const

bool	IsValid (class ON_TextLog *text_log=nullptr) const override

virtual bool	MakeDeformable ()

virtual bool	Morph (const class ON_SpaceMorph &morph)

ON_Geometry &	operator= (const ON_Geometry &)=default

bool	Rotate (double rotation_angle, const ON_3dVector &rotation_axis, const ON_3dPoint &rotation_center)

bool	Rotate (double sin_angle, double cos_angle, const ON_3dVector &rotation_axis, const ON_3dPoint &rotation_center)

bool	Scale (double scale_factor)

virtual bool	SwapCoordinates (int i, int j)

const ON_BoundingBox	TightBoundingBox () const

virtual bool	Transform (const ON_Xform &xform)

bool	Translate (const ON_3dVector &translation_vector)

Public Member Functions inherited from ON_Object
	ON_Object () ON_NOEXCEPT

	ON_Object (const ON_Object &)

virtual	~ON_Object ()

virtual ON_AggregateComponentStatus	AggregateComponentStatus () const

bool	AttachUserData (class ON_UserData *pUserData)

unsigned int	ClearAllComponentStates () const

virtual unsigned int	ClearComponentStates (ON_COMPONENT_INDEX component_index, ON_ComponentStatus states_to_clear) const

virtual unsigned int	ClearComponentStates (ON_ComponentStatus states_to_clear) const

void	CopyUserData (const ON_Object &source_object)

unsigned int	CopyUserData (const ON_Object &source_object, ON_UUID source_userdata_item_id, ON_Object::UserDataConflictResolution userdata_conflict_resolution)

virtual ON__UINT32	DataCRC (ON__UINT32 current_remainder) const

virtual bool	DeleteComponents (const ON_COMPONENT_INDEX *ci_list, size_t ci_count)

bool	DetachUserData (class ON_UserData *pUserData)

virtual void	Dump (ON_TextLog &) const

void	EmergencyDestroy ()

class ON_UserData *	FirstUserData () const

virtual unsigned int	GetComponentsWithSetStates (ON_ComponentStatus states_filter, bool bAllEqualStates, ON_SimpleArray< ON_COMPONENT_INDEX > &components) const

class ON_UserData *	GetUserData (const ON_UUID &userdata_uuid) const

bool	GetUserString (const wchar_t *key, ON_wString &string_value) const

int	GetUserStringKeys (ON_ClassArray< ON_wString > &user_string_keys) const

int	GetUserStrings (ON_ClassArray< ON_UserString > &user_strings) const

bool	IsCorrupt (bool bRepair, bool bSilentError, class ON_TextLog *text_log) const

bool	IsKindOf (const ON_ClassId *pClassId) const

virtual void	MarkAggregateComponentStatusAsNotCurrent () const

virtual void	MemoryRelocate ()

virtual ON_UUID	ModelObjectId () const

void	MoveUserData (ON_Object &source_object)

unsigned int	MoveUserData (ON_Object &source_object, ON_UUID source_userdata_item_id, ON_Object::UserDataConflictResolution userdata_conflict_resolution, bool bDeleteAllSourceItems)

ON_Object &	operator= (const ON_Object &)

void	PurgeUserData ()

virtual bool	Read (ON_BinaryArchive &binary_archive)

virtual unsigned int	SetComponentStates (ON_COMPONENT_INDEX component_index, ON_ComponentStatus states_to_set) const

virtual unsigned int	SetComponentStatus (ON_COMPONENT_INDEX component_index, ON_ComponentStatus status_to_copy) const

bool	SetUserString (const wchar_t key, const wchar_t string_value)

int	SetUserStrings (int count, const ON_UserString *user_strings, bool bReplace)

bool	ThisIsNullptr (bool bSilentError) const

void	TransformUserData (const class ON_Xform &xform)

virtual bool	UpdateReferencedComponents (const class ON_ComponentManifest &source_manifest, const class ON_ComponentManifest &destination_manifest, const class ON_ManifestMap &manifest_map)

int	UserStringCount () const

virtual bool	Write (ON_BinaryArchive &binary_archive) const

Static Public Member Functions
static class ON_NurbsSurface *	CreateCubicLoft (int curve_count, const ON_Curve const curve_list, double k, int is_closed=0, ON::cubic_loft_end_condition start_shape=ON::cubic_loft_ec_quadratic, ON::cubic_loft_end_condition end_shape=ON::cubic_loft_ec_quadratic, class ON_NurbsSurface *nurbs_surface=0)

static class ON_NurbsSurface *	CreateLinearLoft (int curve_count, const ON_Curve const curve_list, double k, int is_closed=0, class ON_NurbsSurface *nurbs_surface=0)

Protected Member Functions
ON_Curve *	PullbackCurveProxy (const ON_CurveProxy &curveproxy_3d, double tolerance, const ON_Interval curve_3d_subdomain, ON_3dPoint start_uv, ON_3dPoint end_uv, ON_FitResult rc) const
	Helper for ON_Surface::Pullback overrides that handles "real" curve issues. More...

ON_Curve *	PullbackPolyCurve (const ON_PolyCurve &polycurve_3d, double tolerance, const ON_Interval curve_3d_subdomain, ON_3dPoint start_uv, ON_3dPoint end_uv, ON_FitResult rc) const

ON_Curve *	PushupCurveProxy (const ON_CurveProxy &curveproxy_2d, double tolerance, const ON_Interval curve_2d_subdomain, ON_FitResult rc) const
	Helper for ON_Surface::Pushup overrides that handles "real" curve issues. More...

ON_Curve *	PushupPolyCurve (const ON_PolyCurve &polycurve_2d, double tolerance, const ON_Interval curve_2d_subdomain, ON_FitResult rc) const

Friends
ON_Curve *	TL_Surface_PullbackHelper (const ON_Surface &, const ON_Curve &, double, const ON_Interval , ON_3dPoint, ON_3dPoint, ON_FitResult )

ON_Curve *	TL_Surface_PushupHelper (const ON_Surface &, const ON_Curve &, double, const ON_Interval , ON_FitResult )

Additional Inherited Members
Static Public Attributes inherited from ON_Geometry
const static ON_Geometry	Unset

Member Enumeration Documentation

◆ ISO

enum ON_Surface::ISO

pure virtual class for surface objects

flags for isoparametric curves note: odd values are all "x" = constant and even values > 0 are all "y" = constant ON_BrepTrim::m_iso uses these flags

Enumerator
not_iso	curve is not an isoparameteric curve
x_iso	curve is a "x" = constant (vertical) isoparametric curve in the interior of the surface's domain
y_iso	curve is a "y" = constant (horizontal) isoparametric curve in the interior of the surface's domain
W_iso	curve is a "x" = constant isoparametric curve along the west side of the surface's domain
S_iso	curve is a "y" = constant isoparametric curve along the south side of the surface's domain
E_iso	curve is a "x" = constant isoparametric curve along the east side of the surface's domain
N_iso	curve is a "y" = constant isoparametric curve along the north side of the surface's domain
iso_count

Constructor & Destructor Documentation

◆ ON_Surface() [1/2]

ON_Surface::ON_Surface ( )

◆ ON_Surface() [2/2]

ON_Surface::ON_Surface ( const ON_Surface & )

◆ ~ON_Surface()

virtual ON_Surface::~ON_Surface ( )

virtual

Member Function Documentation

◆ AreaMassProperties()

bool ON_Surface::AreaMassProperties	(	class ON_MassProperties &	mp,
		bool	bArea = `true`,
		bool	bFirstMoments = `true`,
		bool	bSecondMoments = `true`,
		bool	bProductMoments = `true`,
		double	rel_tol = `1.0e-6`,
		double	abs_tol = `1.0e-6`
	)		const

Description: Calculate area mass properties of the surface. Parameters: mp - [out] bArea - [in] true to calculate area bFirstMoments - [in] true to calculate area first moments, area and area centroid. bSecondMoments - [in] true to calculate area second moments. bProductMoments - [in] true to calculate area product moments. Returns: True if successful.

◆ BrepForm()

ON_Brep* ON_Surface::BrepForm ( ON_Brep * brep = nullptr ) const

overridevirtual

Description: Overrides virtual ON_Geometry::HasBrepForm.
Uses ON_Brep::Create( ON_Surface&* ) to create a brep form. The surface is copied for use in the returned brep. Parameters: brep - [in] if not nullptr, brep is used to store the brep form of the surface. Result: Returns a pointer to on ON_Brep or nullptr. If the brep parameter is not nullptr, then brep is returned if the surface has a brep form and nullptr is returned if the geometry does not have a brep form. Remarks: The caller is responsible for managing the brep memory.

Reimplemented from ON_Geometry.

◆ CreateCubicLoft()

static class ON_NurbsSurface* ON_Surface::CreateCubicLoft	(	int	curve_count,
		const ON_Curve const	curve_list,
		double	k,
		int	is_closed = `0`,
		ON::cubic_loft_end_condition	start_shape = `ON::cubic_loft_ec_quadratic`,
		ON::cubic_loft_end_condition	end_shape = `ON::cubic_loft_ec_quadratic`,
		class ON_NurbsSurface *	nurbs_surface = `0`
	)

static

Description: Create a cubic nurbs surface that interpolates a list of curves.

Parameters: curve_count - [in] >= 2 number of curves

curve_list - [in] array of pointers to curves. These curves define the location of the The returned surface's "v" parameter

k - in or k = ON_UNSET_VALUE k determines how the surface's m_knot[0] values are calculated. Most frequently, 0.0, 0.5, or 1.0 should be used. 0.0: uniform 0.5: sqrt(chord length) 1.0: chord length In general, when k >= 0.0, then spacing is pow(d,k), where d is the average distance between the curves defining the span. ON_UNSET_VALUE: the intepolation knot vector is explicitly specified. The knots in the interpolated direction are specified. You must understand the mathematics of NURBS surfaces to use this option. To specify an explicit knot vector for the interpolation, the nurbs_suface parameter must be non-null, nurbs_surface->m_order[0] must be 4. The value of nurbs_surface->m_cv_count[0] must be set as described in the is_closed parameter section. The array nurbs_surface->m_knot[0][] must have length nurbs_surface->m_cv_count[0]+2, and the values in nurbs_surface->m_knot[0][2, ..., nurbs_surface->m_cv_count[0]-1] must be strictly increasing. is_closed - [in] 0: open curve_count must be at least 2. The resulting nurbs_surface will have m_cv_count[0] = curve_count+2. 1: closed curve_count must be at least 3. Do not include a duplicate of the start curve as the last curve in the list. The resulting nurbs_surface will have m_cv_count[0] = curve_count+3. 2: periodic curve_count must be at least 3. The resulting nurbs_surface will have m_cv_count[0] = curve_count+3.

start_shape - [in] end_shape - [in] The start_shape and end_shape parameters determine the starting and ending shape of the lofted surface.

Simple shapes: The simple end conditions calculate the rows of free control points based on the locations of the input curves and do not require additional input information. ON::cubic_loft_ec_quadratic: quadratic ON::cubic_loft_ec_linear: linear ON::cubic_loft_ec_cubic: cubic ON::cubic_loft_ec_natural: natural (zero 2nd derivative)

Explicit shapes: ON::cubic_loft_ec_unit_tangent: unit tangent is specified ON::cubic_loft_ec_1st_derivative: first derivative is specified ON::cubic_loft_ec_2nd_derivative: second derivative is specified ON::cubic_loft_ec_free_cv: free control vertex is specified

In order to specify explicit end conditions, curve_count must be at least 3, is_closed must be 0 or 1, the nurbs_surface parameter must be non-null, the nurbs_surface control points must be allocated, nurbs_surface->m_cv_count[0] must be set as described under the is_closed parameter, and the input curves must have nurbs curve formats that are compatible with the number of control points nurbs_surface->m_cv_count[1] and knots in nurbs_surface->m_knot[1]. The values of the starting shape points are specified in nurbs_surface->CV(1,...) and the values of ending shape points are specified in nurbs_surface->CV(curve_count,...). A good way to specify explicit shapes is to call CreateCubicLoft() with ON::cubic_loft_ec_quadratic as the condition parameters, modify the returned surface's end condition CVs as desired, and then call CreateCubicLoft() with the explicit end condition option. This way you will be sure to have a properly initialized nurbs_surface.

nurbs_surface - [in] If not null, the result will returned in this ON_NurbsSurface. Typically, this parameter is used when you want to store the result in an ON_NurbsSurface that is on the stack. This parameter is also used when you want to specify the interpolation knots or end conditions.

Returns: If successful, a pointer to the surface is returned. If the input nurbs_surface parameter was null, then this surface is on the heap and will need to be deleted to avoid memory leaks. If the input is not valid, null is returned, even when nurbs_surface is not null.

Example:

/ EXAMPLE 1: Loft a surface through a list of curves ON_SimpleArray< const ON_Curve* > curve_list = ....; ON_NurbsSurface* srf = ON_Surface::CreateCubicLoft( curve_list.Count(), curve_list, 0.5 ///< sqrt(chord length) spacing );

/ EXAMPLE 2: Create adjacent surfaces with an identical shared edge. / First make two curve lists with / curve_listA.Count() == curve_listB.Count() and / curve_listA[i]->PointAtEnd() == curve_listB[i]->PointAtStart() ON_SimpleArray< const ON_Curve* > curve_listA = ....; ON_SimpleArray< const ON_Curve* > curve_listB = ....; curve_count = curve_listA.Count(); ON_NurbsSurface* srfA = 0; ON_NurbsSurface* srfB = 0; if ( curve_count == curve_listB.Count() ) { srfA = ON_Surface::CreateCubicLoft( curve_count, curve_listA.Array(), 1.0 ///< chord length spacing ); if (0 != srfA) { srfB = new ON_NurbsSurface(); int knot_count0 = srfA->KnotCount(0); srfB->ReserveKnotCapacity(0,knot_count0); memcpy(srfB->m_knot[0],srfA->m_knot[0],knot_count0*sizeof(srfB->m_knot[0][0])) if ( 0 == ON_Surface::CreateCubicLoft( curve_count, curve_listB.Array(), ON_UNSET_VALUE, ///< knots specified in srfB->m_knot[0] 0, ///< open loft ON::cubic_loft_ec_quadratic, ON::cubic_loft_ec_quadratic, srfB ) ) { / clean up to prevent memory leaks delete srfB; srfB = 0; } } }

◆ CreateLinearLoft()

static class ON_NurbsSurface* ON_Surface::CreateLinearLoft	(	int	curve_count,
		const ON_Curve const	curve_list,
		double	k,
		int	is_closed = `0`,
		class ON_NurbsSurface *	nurbs_surface = `0`
	)

static

Description: Create a linear nurbs surface that interpolates a list of curves.

Parameters: curve_count - [in] >= 2 number of curves

curve_list - [in] array of pointers to curves. These curves define the location of the The returned surface's "v" parameter

k - in or k = ON_UNSET_VALUE k determines how the surface's m_knot[0] values are calculated. Most frequently, 0.0, or 1.0 should be used. 0.0: uniform 0.5: sqrt(chord length) 1.0: chord length In general, when k >= 0.0, then spacing is pow(d,k), where d is the average distance between the curves defining the span. ON_UNSET_VALUE: the intepolation knot vector is explicitly specified. The knots in the interpolated direction are specified. You must understand the mathematics of NURBS surfaces to use this option. To specify an explicit knot vector for the interpolation, the nurbs_suface parameter must be non-null, nurbs_surface->m_order[0] must be 2. The value of nurbs_surface->m_cv_count[0] must be set as described in the is_closed parameter section. The array nurbs_surface->m_knot[0][] must have length nurbs_surface->m_cv_count[0], and the values in nurbs_surface->m_knot[0][] must be strictly increasing. is_closed - [in] 0: open curve_count must be at least 2. The resulting nurbs_surface will have m_cv_count[0] = curve_count. 1: closed curve_count must be at least 3. Do not include a duplicate of the start curve as the last curve in the list. The resulting nurbs_surface will have m_cv_count[0] = curve_count+1.

nurbs_surface - [in] If not null, the result will returned in this ON_NurbsSurface. Typically, this parameter is used when you want to store the result in an ON_NurbsSurface that is on the stack. This parameter is also used when you want to specify the interpolation knots.

Returns: If successful, a pointer to the surface is returned. If the input nurbs_surface parameter was null, then this surface is on the heap and will need to be deleted to avoid memory leaks. If the input is not valid, null is returned, even when nurbs_surface is not null.

Example:

/ EXAMPLE 1: Loft a surface through a list of curves ON_SimpleArray< const ON_Curve* > curve_list = ....; ON_NurbsSurface* srf = ON_Surface::CreateLinearLoft( curve_list.Count(), curve_list, 1.0 ///< chord length spacing );

◆ CreateMesh()

virtual ON_Mesh* ON_Surface::CreateMesh	(	const ON_MeshParameters &	mp,
		ON_Mesh *	mesh = `nullptr`
	)		const

virtual

surface interface

Description: Computes a polygon mesh approximation of the surface.
Parameters: mp - [in] meshing parameters mesh - [in] if not nullptr, the surface mesh will be put into this mesh. Returns: A polygon mesh of the surface. Remarks: This virtual function works in the openNURBS that is part of the Rhino SDK. The source code for this functionality is not provided in the free openNURBS toolkit.

Reimplemented in ON_BrepFace, ON_NurbsSurface, ON_Extrusion, ON_SumSurface, ON_RevSurface, ON_SurfaceProxy, and ON_PlaneSurface.

◆ CreateSurfaceTree()

virtual ON_SurfaceTree* ON_Surface::CreateSurfaceTree ( ) const

virtual

◆ Degree()

virtual int ON_Surface::Degree ( int dir ) const

pure virtual

Parameters

dir	returns maximum algebraic degree of any span ( or a good estimate if curve spans are not algebraic ) 0 gets first parameter's domain, 1 gets second parameter's domain

Implemented in ON_NurbsSurface, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ DestroyRuntimeCache()

void ON_Surface::DestroyRuntimeCache ( bool bDelete = true )

overridevirtual

virtual ON_Object::DestroyRuntimeCache override

Reimplemented from ON_Object.

Reimplemented in ON_SurfaceProxy.

◆ DestroySurfaceTree()

void ON_Surface::DestroySurfaceTree ( )

If the geometry surface is modified in any way, then call DestroySurfaceTree().

◆ Domain()

virtual ON_Interval ON_Surface::Domain ( int dir ) const

pure virtual

Parameters

dir	0 gets first parameter's domain, 1 gets second parameter's domain

Implemented in ON_NurbsSurface, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ DuplicateSurface()

virtual ON_Surface* ON_Surface::DuplicateSurface ( ) const

virtual

Description: Get a duplicate of the surface. Returns: A duplicate of the surface.
Remarks: The caller must delete the returned surface. For non-ON_SurfaceProxy objects, this simply duplicates the surface using ON_Object::Duplicate. For ON_SurfaceProxy objects, this duplicates the actual proxy surface geometry and, if necessary, transposes the result to that the returned surfaces's parameterization and locus match the proxy surface's.

Reimplemented in ON_SurfaceProxy.

◆ Ev1Der()

bool ON_Surface::Ev1Der	(	double	u,
		double	v,
		ON_3dPoint &	point,
		ON_3dVector &	du,
		ON_3dVector &	dv,
		int	quadrant = `0`,
		int *	hint = `0`
	)		const

Parameters

u	returns false if unable to evaluate
v	evaluation parameters (s,t)
point	returns value of surface
du	first partial derivatives (Ds)
dv	(Dt)
quadrant	optional - determines which side to evaluate from 0 = default 1 from NE quadrant 2 from NW quadrant 3 from SW quadrant 4 from SE quadrant
hint	optional - evaluation hint (int[2]) used to speed repeated evaluations

◆ Ev2Der()

bool ON_Surface::Ev2Der	(	double	u,
		double	v,
		ON_3dPoint &	point,
		ON_3dVector &	du,
		ON_3dVector &	dv,
		ON_3dVector &	duu,
		ON_3dVector &	duv,
		ON_3dVector &	dvv,
		int	quadrant = `0`,
		int *	hint = `0`
	)		const

Parameters

u	returns false if unable to evaluate
v	evaluation parameters (s,t)
point	returns value of surface
du	first partial derivatives (Ds)
dv	(Dt)
duu	second partial derivatives (Dss)
duv	(Dst)
dvv	(Dtt)
quadrant	optional - determines which side to evaluate from 0 = default 1 from NE quadrant 2 from NW quadrant 3 from SW quadrant 4 from SE quadrant
hint	optional - evaluation hint (int[2]) used to speed repeated evaluations

◆ Evaluate()

virtual bool ON_Surface::Evaluate	(	double	u,
		double	v,
		int	num_der,
		int	array_stride,
		double *	der_array,
		int	quadrant = `0`,
		int *	hint = `0`
	)		const

pure virtual

work horse evaluator

Parameters

u	returns false if unable to evaluate
v	evaluation parameters
num_der	number of derivatives (>=0)
array_stride	array stride (>=Dimension())
der_array	array of length stride(ndir+1)(ndir+2)/2
quadrant	optional - determines which quadrant to evaluate from 0 = default 1 from NE quadrant 2 from NW quadrant 3 from SW quadrant 4 from SE quadrant
hint	optional - evaluation hint (int[2]) used to speed repeated evaluations

Implemented in ON_NurbsSurface, ON_RevSurface, ON_SumSurface, ON_PlaneSurface, ON_SurfaceProxy, ON_OffsetSurface, and ON_Extrusion.

◆ EvaluatePoint()

bool ON_Surface::EvaluatePoint	(	const class ON_ObjRef &	objref,
		ON_3dPoint &	P
	)		const

overridevirtual

virtual ON_Geometry override

Reimplemented from ON_Geometry.

◆ EvNormal() [1/3]

bool ON_Surface::EvNormal	(	double	u,
		double	v,
		ON_3dPoint &	point,
		ON_3dVector &	du,
		ON_3dVector &	dv,
		ON_3dVector &	normal,
		int	= `0`,
		int *	= `0`
	)		const

Parameters

u	returns false if unable to evaluate
v	evaluation parameters (s,t)
point	returns value of surface
du	first partial derivatives (Ds)
dv	(Dt)
normal	unit normal

◆ EvNormal() [2/3]

bool ON_Surface::EvNormal	(	double	u,
		double	v,
		ON_3dPoint &	point,
		ON_3dVector &	normal,
		int	quadrant = `0`,
		int *	hint = `0`
	)		const

Parameters

u	returns false if unable to evaluate
v	evaluation parameters (s,t)
point	returns value of surface
normal	unit normal
quadrant	optional - determines which side to evaluate from 0 = default 1 from NE quadrant 2 from NW quadrant 3 from SW quadrant 4 from SE quadrant
hint	optional - evaluation hint (int[2]) used to speed repeated evaluations

◆ EvNormal() [3/3]

bool ON_Surface::EvNormal	(	double	u,
		double	v,
		ON_3dVector &	normal,
		int	quadrant = `0`,
		int *	hint = `0`
	)		const

Parameters

u	returns false if unable to evaluate
v	evaluation parameters (s,t)
normal	unit normal
quadrant	optional - determines which side to evaluate from 0 = default 1 from NE quadrant 2 from NW quadrant 3 from SW quadrant 4 from SE quadrant
hint	optional - evaluation hint (int[2]) used to speed repeated evaluations

◆ EvPoint()

bool ON_Surface::EvPoint	(	double	u,
		double	v,
		ON_3dPoint &	point,
		int	quadrant = `0`,
		int *	hint = `0`
	)		const

Parameters

u	returns false if unable to evaluate
v	evaluation parameters
point	returns value of surface
quadrant	optional - determines which side to evaluate from 0 = default 1 from NE quadrant 2 from NW quadrant 3 from SW quadrant 4 from SE quadrant
hint	optional - evaluation hint (int[2]) used to speed repeated evaluations

◆ Extend()

virtual bool ON_Surface::Extend	(	int	dir,
		const ON_Interval &	domain
	)

virtual

Description: Pure virtual function. Default returns false. Where possible, analytically extends surface to include domain. Parameters: dir - [in] 0 new Domain(0) will include domain. (the first surface parameter). 1 new Domain(1) will include domain. (the second surface parameter). domain - [in] if domain is not included in surface domain, surface will be extended so that its domain includes domain.
Will not work if surface is closed in direction dir. Original surface is identical to the restriction of the resulting surface to the original surface domain, Returns: true if successful.

Reimplemented in ON_NurbsSurface, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, and ON_Extrusion.

◆ FrameAt()

bool ON_Surface::FrameAt	(	double	u,
		double	v,
		ON_Plane &	frame
	)		const

◆ GetClosestPoint()

virtual bool ON_Surface::GetClosestPoint	(	const ON_3dPoint &	P,
		double *	s,
		double *	t,
		double	maximum_distance = `0.0`,
		const ON_Interval *	sdomain = `0`,
		const ON_Interval *	tdomain = `0`
	)		const

virtual

Description: Get the parameters of the point on the surface that is closest to P. Parameters: P - [in] test point s - [out] t - [out] (*s,*t) = parameters of the surface point that is closest to P. maximum_distance = 0.0 - [in] optional upper bound on the distance from P to the surface. If you are only interested in finding a point Q on the surface when P.DistanceTo(Q) < maximum_distance, then set maximum_distance to that value. sdomain = 0 - [in] optional domain restriction tdomain = 0 - [in] optional domain restriction Returns: True if successful. If false, the values of *s and *t are undefined. See Also: ON_Surface::GetLocalClosestPoint.

Reimplemented in ON_RevSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ GetDomain()

bool ON_Surface::GetDomain	(	int	dir,
		double *	t0,
		double *	t1
	)		const

Parameters

dir	0 gets first parameter, 1 gets second parameter

◆ GetIsoPushupDirection()

int ON_Surface::GetIsoPushupDirection	(	const ON_Curve &	curve_2d,
		double	tolerance,
		const ON_Interval *	curve_2d_subdomain,
		double *	c,
		ON_Interval *	c3_dom
	)		const

Description: Helper for ON_Surface::Pushup() to determine if an iso-curve can be used. Parameters: curve_2d - [in] tolerance - [in] curve_2d_subdomain - [in] Pass null if entire curve_2d is being used. c - [out] Pass null if you don't need this value returned. c3_dom - [out] Pass null if you don't want this returned. c3_dom will be decreasing if curve_2d is going opposite the surface's parameterization. If -1 is returned, then the input value of c2_dom is not changed. Returns: 0 or 1: The 3d curve returned by IsoCurve( dir, c ) will be a pushup tolerance. The starting parameter of the 3d curve is c3_dom[0] and the ending parameter of the 3d curve is at c3_dom[1].
Note that c3_dom will be decreasing when curve_2d is oriented opposite to the direction of the surface's paramterization. -1: if a pushup cannot be used.

◆ GetLocalClosestPoint()

virtual bool ON_Surface::GetLocalClosestPoint	(	const ON_3dPoint &	,
		double	,
		double	,
		double *	,
		double *	,
		const ON_Interval *	= `nullptr`,
		const ON_Interval *	= `nullptr`
	)		const

virtual

Find parameters of the point on a surface that is locally closest to the test_point. The search for a local close point starts at seed parameters. If a sub_domain parameter is not nullptr, then the search is restricted to the specified portion of the surface.

true if returned if the search is successful. false is returned if the search fails.

Reimplemented in ON_RevSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ GetNextDiscontinuity()

virtual bool ON_Surface::GetNextDiscontinuity	(	int	dir,
		ON::continuity	c,
		double	t0,
		double	t1,
		double *	t,
		int *	hint = `nullptr`,
		int *	dtype = `nullptr`,
		double	cos_angle_tolerance = `ON_DEFAULT_ANGLE_TOLERANCE_COSINE`,
		double	curvature_tolerance = `ON_SQRT_EPSILON`
	)		const

virtual

Description: Search for a derivatitive, tangent, or curvature discontinuity. Parameters: dir - [in] If 0, then "u" parameter is checked. If 1, then the "v" parameter is checked. c - [in] type of continity to test for. t0 - [in] Search begins at t0. If there is a discontinuity at t0, it will be ignored. This makes it possible to repeatedly call GetNextDiscontinuity and step through the discontinuities. t1 - [in] (t0 != t1) If there is a discontinuity at t1 is will be ignored unless c is a locus discontinuity type and t1 is at the start or end of the curve. t - [out] if a discontinuity is found, then *t reports the parameter at the discontinuity. hint - [in/out] if GetNextDiscontinuity will be called repeatedly, passing a "hint" with initial value *hint=0 will increase the speed of the search.
dtype - [out] if not nullptr, *dtype reports the kind of discontinuity found at *t. A value of 1 means the first derivative or unit tangent was discontinuous. A value of 2 means the second derivative or curvature was discontinuous. A value of 0 means the curve is not closed, a locus discontinuity test was applied, and t1 is at the start of end of the curve. cos_angle_tolerance - [in] default = cos(1 degree) Used only when c is ON::continuity::G1_continuous or ON::continuity::G2_continuous. If the cosine of the angle between two tangent vectors is <= cos_angle_tolerance, then a G1 discontinuity is reported. curvature_tolerance - [in] (default = ON_SQRT_EPSILON) Used only when c is ON::continuity::G2_continuous. If K0 and K1 are curvatures evaluated from above and below and |K0 - K1| > curvature_tolerance, then a curvature discontinuity is reported. Returns: Parametric continuity tests c = (C0_continuous, ..., G2_continuous):

true if a parametric discontinuity was found strictly between t0 and t1. Note well that all curves are parametrically continuous at the ends of their domains.

Locus continuity tests c = (C0_locus_continuous, ...,G2_locus_continuous):

true if a locus discontinuity was found strictly between t0 and t1 or at t1 is the at the end of a curve. Note well that all open curves (IsClosed()=false) are locus discontinuous at the ends of their domains. All closed curves (IsClosed()=true) are at least C0_locus_continuous at the ends of their domains.

Reimplemented in ON_NurbsSurface, ON_RevSurface, ON_SumSurface, ON_Extrusion, ON_PlaneSurface, and ON_SurfaceProxy.

◆ GetNurbForm()

virtual int ON_Surface::GetNurbForm	(	ON_NurbsSurface &	nurbs_surface,
		double	tolerance = `0.0`
	)		const

virtual

Description: Get a NURBS surface representation of this surface. Parameters: nurbs_surface - [out] NURBS representation returned here tolerance - [in] tolerance to use when creating NURBS representation. s_subdomain - [in] if not nullptr, then the NURBS representation for this portion of the surface is returned. t_subdomain - [in] if not nullptr, then the NURBS representation for this portion of the surface is returned. Returns: 0 unable to create NURBS representation with desired accuracy. 1 success - returned NURBS parameterization matches the surface's to wthe desired accuracy 2 success - returned NURBS point locus matches the surface's to the desired accuracy and the domain of the NURBS surface is correct. On However, This surface's parameterization and the NURBS surface parameterization may not match to the desired accuracy. This situation happens when getting NURBS representations of surfaces that have a transendental parameterization like spheres, cylinders, and cones. Remarks: This is a low-level virtual function. If you do not need the parameterization information provided by the return code, then ON_Surface::NurbsSurface may be easier to use. See Also: ON_Surface::NurbsSurface

Reimplemented in ON_Extrusion, ON_NurbsSurface, ON_PlaneSurface, ON_RevSurface, ON_SurfaceProxy, and ON_SumSurface.

◆ GetNurbFormParameterFromSurfaceParameter()

virtual bool ON_Surface::GetNurbFormParameterFromSurfaceParameter	(	double	surface_s,
		double	surface_t,
		double *	nurbs_s,
		double *	nurbs_t
	)		const

virtual

Reimplemented in ON_RevSurface, ON_SurfaceProxy, ON_SumSurface, and ON_Extrusion.

◆ GetParameterTolerance()

virtual bool ON_Surface::GetParameterTolerance	(	int	dir,
		double	t,
		double *	tminus,
		double *	tplus
	)		const

virtual

Parameters

dir	returns tminus < tplus: parameters tminus <= s <= tplus 0 gets first parameter, 1 gets second parameter
t	t = parameter in domain
tminus	tminus
tplus	tplus

Reimplemented in ON_NurbsSurface, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ GetSilhouette()

bool ON_Surface::GetSilhouette	(	const ON_Interval *	udom,
		const ON_Interval *	vdom,
		const ON_SilhouetteParameters	parameters,
		const ON_PlaneEquation *	clipping_planes,
		size_t	clipping_plane_count,
		ON_ClassArray< ON_SIL_EVENT > &	silhouettes,
		ON_ProgressReporter *	progress,
		ON_Terminator *	terminator
	)		const

◆ GetSpanVector()

virtual bool ON_Surface::GetSpanVector	(	int	dir,
		double *	span_vector
	)		const

pure virtual

Parameters

dir	span "knots" 0 gets first parameter's domain, 1 gets second parameter's domain
span_vector	array of length SpanCount() + 1

Implemented in ON_NurbsSurface, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ GetSpanVectorIndex()

virtual bool ON_Surface::GetSpanVectorIndex	(	int	dir,
		double	t,
		int	side,
		int *	span_vector_index,
		ON_Interval *	span_interval
	)		const

virtual

If t is in the domain of the surface, GetSpanVectorIndex() returns the span vector index "i" such that span_vector[i] <= t <= span_vector[i+1]. The "side" parameter determines which span is selected when t is at the end of a span.

Parameters

	dir	0 gets first parameter's domain, 1 gets second parameter's domain
[in]	t	[IN] t = evaluation parameter
[in]	side	[IN] side 0 = default, -1 = from below, +1 = from above
[out]	span_vector_index	[OUT] span vector index
[out]	span_interval	[OUT] domain of the span containing "t"

Reimplemented in ON_Extrusion.

◆ GetSurfaceParameterFromNurbFormParameter() [1/2]

ON_Curve* ON_Surface::GetSurfaceParameterFromNurbFormParameter	(	const ON_Curve &	curve3d,
		const ON_Curve &	ns_curve2dX,
		double	fit_tolerance
	)		const

Description: Transform a parameter space curve from the surface tree (Nurbs) parameter space to the surface's innate parameter space. Requires a curve on the surface, and a parameter space curve defined in terms of the surface tree's parameter space, we transform this into the surfaces innate parameter space. Parameters: Srf - [in] Surface curve3d - [in] 3d intersection curve ns_curve2dX -[in] Curve in surface tree parameter space

fit_tolerance - [in] tolerance

Returns: A curve in the the surface's parameter space or nullptr if unsecessfull.

Parameters

curve3d	3d intersection curve
ns_curve2dX	2d curve in surface tree (i.e. nurbs_surface)
fit_tolerance	parameter space distance_tolerance for fitting

◆ GetSurfaceParameterFromNurbFormParameter() [2/2]

virtual bool ON_Surface::GetSurfaceParameterFromNurbFormParameter	(	double	nurbs_s,
		double	nurbs_t,
		double *	surface_s,
		double *	surface_t
	)		const

virtual

Reimplemented in ON_RevSurface, ON_SurfaceProxy, ON_SumSurface, and ON_Extrusion.

◆ GetSurfaceSize()

virtual bool ON_Surface::GetSurfaceSize	(	double *	width,
		double *	height
	)		const

virtual

Description: Get an estimate of the size of the rectangle that would be created if the 3d surface where flattened into a rectangle. Parameters: width - [out] (corresponds to the first surface parameter) height - [out] (corresponds to the first surface parameter) Example:

/ Reparameterize a surface to minimize distortion / in the map from parameter space to 3d. ON_Surface* surf = ...; double width, height; if ( surf->GetSurfaceSize( &width, &height ) ) { srf->SetDomain( 0, ON_Interval( 0.0, width ) ); srf->SetDomain( 1, ON_Interval( 0.0, height ) ); }

Returns: true if successful.

Reimplemented in ON_NurbsSurface, ON_Extrusion, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, and ON_SurfaceProxy.

◆ HasBrepForm()

bool ON_Surface::HasBrepForm ( ) const

overridevirtual

virtual ON_Geometry functions Description: Overrides virtual ON_Geometry::HasBrepForm and returns true. Result: Returns true. See Also: ON_Brep::Create( ON_Surface&* )

Reimplemented from ON_Geometry.

◆ HasNurbForm()

virtual int ON_Surface::HasNurbForm ( ) const

virtual

Description: Is there a NURBS surface representation of this surface. Parameters: Returns: 0 unable to create NURBS representation with desired accuracy. 1 success - NURBS parameterization matches the surface's 2 success - NURBS point locus matches the surface's and the domain of the NURBS surface is correct.
However, This surface's parameterization and the NURBS surface parameterization may not match. This situation happens when getting NURBS representations of surfaces that have a transendental parameterization like spheres, cylinders, and cones. Remarks: This is a low-level virtual function. See Also: ON_Surface::GetNurbForm ON_Surface::NurbsSurface

Reimplemented in ON_NurbsSurface, ON_PlaneSurface, ON_RevSurface, ON_SurfaceProxy, ON_SumSurface, and ON_Extrusion.

◆ IntersectPlane()

int ON_Surface::IntersectPlane	(	ON_PlaneEquation	plane_equation,
		ON_ClassArray< ON_SSX_EVENT > &	x,
		double	intersection_tolerance = `0.0`,
		double	overlap_tolerance = `0.0`,
		double	fitting_tolerance = `0.0`,
		const ON_Interval *	surface_udomain = `0`,
		const ON_Interval *	surface_vdomain = `0`
	)		const

Description: Intersect this surface with an infinite plane.

Parameters: plane_equation - [in]

x - [out] Intersection events are appended to this array.

intersection_tolerance - [in] If the input intersection_tolerance <= 0.0, then 0.001 is used.

overlap_tolerance - [in] If positive, then overlap_tolerance must be >= intersection_tolerance and is used to test for overlapping regions. If the input overlap_tolerance <= 0.0, then 2*intersection_tolerance is used.

fitting_tolerance - [in] If fitting_tolerance is > 0 and >= intersection_tolerance, then the intersection curves are fit to this tolerance. If input fitting_tolerance <= 0.0 or < intersection_tolerance, then intersection_tolerance is used.

surface_udomain - [in] optional restriction on surfaceA u domain surface_vdomain - [in] optional restriction on surfaceA v domain

Returns: Number of intersection events appended to x.

◆ IntersectSurface()

int ON_Surface::IntersectSurface	(	const ON_Surface *	surfaceB,
		ON_ClassArray< ON_SSX_EVENT > &	x,
		double	intersection_tolerance = `0.0`,
		double	overlap_tolerance = `0.0`,
		double	fitting_tolerance = `0.0`,
		const ON_Interval *	surfaceA_udomain = `0`,
		const ON_Interval *	surfaceA_vdomain = `0`,
		const ON_Interval *	surfaceB_udomain = `0`,
		const ON_Interval *	surfaceB_vdomain = `0`
	)		const

Description: Intersect this surface with surfaceB.

Parameters: surfaceB - [in]

x - [out] Intersection events are appended to this array.

intersection_tolerance - [in] If the input intersection_tolerance <= 0.0, then 0.001 is used.

overlap_tolerance - [in] If positive, then overlap_tolerance must be >= intersection_tolerance and is used to test for overlapping regions. If the input overlap_tolerance <= 0.0, then 2*intersection_tolerance is used.

fitting_tolerance - [in] If fitting_tolerance is > 0 and >= intersection_tolerance, then the intersection curves are fit to this tolerance. If input fitting_tolerance <= 0.0 or < intersection_tolerance, then intersection_tolerance is used.

surfaceA_udomain - [in] optional restriction on surfaceA u domain surfaceA_vdomain - [in] optional restriction on surfaceA v domain

surfaceB_udomain - [in] optional restriction on surfaceB u domain surfaceB_vdomain - [in] optional restriction on surfaceB v domain Returns: Number of intersection events appended to x.

◆ IsAtSeam()

int ON_Surface::IsAtSeam	(	double	s,
		double	t
	)		const

Description: Test if a surface parameter value is at a seam. Parameters: s - [in] surface parameter to test t - [in] surface parameter to test Returns: 0 if not a seam, 1 if s == Domain(0)[i] and srf(s, t) == srf(Domain(0)[1-i], t) 2 if t == Domain(1)[i] and srf(s, t) == srf(s, Domain(1)[1-i]) 3 if 1 and 2 are true.

◆ IsAtSingularity()

bool ON_Surface::IsAtSingularity	(	double	s,
		double	t,
		bool	bExact = `true`
	)		const

Description: Test if a surface parameter value is at a singularity. Parameters: s - [in] surface parameter to test t - [in] surface parameter to test bExact - [in] if true, test if s,t is exactly at a singularity if false, test if close enough to cause numerical problems. Returns: true if surface is singular at (s,t)

◆ IsClosed()

virtual bool ON_Surface::IsClosed ( int ) const

virtual

Reimplemented in ON_NurbsSurface, ON_RevSurface, ON_Extrusion, ON_SumSurface, ON_PlaneSurface, and ON_SurfaceProxy.

◆ IsCone()

bool ON_Surface::IsCone	(	ON_Cone *	cone = `nullptr`,
		double	tolerance = `ON_ZERO_TOLERANCE`
	)		const

Description: Determine if the surface is a portion of a cone. Parameters: cone - [out] if not nullptr and true is returned, then the cone definition is returned. tolerance - [in] tolerance to use when checking Returns: True if the surface is a portion of a cone.

◆ IsContinuous()

virtual bool ON_Surface::IsContinuous	(	ON::continuity	c,
		double	s,
		double	t,
		int *	hint = `nullptr`,
		double	point_tolerance = `ON_ZERO_TOLERANCE`,
		double	d1_tolerance = `ON_ZERO_TOLERANCE`,
		double	d2_tolerance = `ON_ZERO_TOLERANCE`,
		double	cos_angle_tolerance = `ON_DEFAULT_ANGLE_TOLERANCE_COSINE`,
		double	curvature_tolerance = `ON_SQRT_EPSILON`
	)		const

virtual

Description: Test continuity at a surface parameter value. Parameters: c - [in] continuity to test for s - [in] surface parameter to test t - [in] surface parameter to test hint - [in] evaluation hint point_tolerance - [in] if the distance between two points is greater than point_tolerance, then the surface is not C0. d1_tolerance - [in] if the difference between two first derivatives is greater than d1_tolerance, then the surface is not C1. d2_tolerance - [in] if the difference between two second derivatives is greater than d2_tolerance, then the surface is not C2. cos_angle_tolerance - [in] default = cos(1 degree) Used only when c is ON::continuity::G1_continuous or ON::continuity::G2_continuous. If the cosine of the angle between two normal vectors is <= cos_angle_tolerance, then a G1 discontinuity is reported. curvature_tolerance - [in] (default = ON_SQRT_EPSILON) Used only when c is ON::continuity::G2_continuous. If K0 and K1 are curvatures evaluated from above and below and |K0 - K1| > curvature_tolerance, then a curvature discontinuity is reported. Returns: true if the surface has at least the c type continuity at the parameter t.

Reimplemented in ON_NurbsSurface, ON_RevSurface, ON_SumSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ IsCylinder()

bool ON_Surface::IsCylinder	(	ON_Cylinder *	cylinder = `nullptr`,
		double	tolerance = `ON_ZERO_TOLERANCE`
	)		const

Description: Determine if the surface is a portion of a cylinder. Parameters: cylinder - [out] if not nullptr and true is returned, then the cylinder definition is returned. tolerance - [in] tolerance to use when checking Returns: True if the surface is a portion of a cylinder.

◆ IsIsoparametric() [1/2]

virtual ISO ON_Surface::IsIsoparametric ( const ON_BoundingBox & bbox ) const

virtual

Description: Test a 2d bounding box to see if it is iso parameteric in the surface's parameter space. Parameters: bbox - [in] bounding box to test Returns: Isoparametric status of the bounding box. Remarks: Because it may transpose domains, ON_SurfaceProxy overrides this function. All other surface classes just use the base class implementation.

Reimplemented in ON_Extrusion, and ON_SurfaceProxy.

◆ IsIsoparametric() [2/2]

virtual ISO ON_Surface::IsIsoparametric	(	const ON_Curve &	curve,
		const ON_Interval *	curve_domain = `nullptr`
	)		const

virtual

Description: Test a 2d curve to see if it is iso parameteric in the surface's parameter space. Parameters: curve - [in] curve to test curve_domain = [in] optional sub domain of the curve Returns: Isoparametric status of the curve. Remarks: Because it may transpose domains, ON_SurfaceProxy overrides this function. All other surface classes just use the base class implementation.

Reimplemented in ON_Extrusion, and ON_SurfaceProxy.

◆ IsoCurve()

virtual ON_Curve* ON_Surface::IsoCurve	(	int	dir,
		double	c
	)		const

virtual

Description: Get isoparametric curve. Parameters: dir - [in] 0 first parameter varies and second parameter is constant e.g., point on IsoCurve(0,c) at t is srf(t,c) This is a horizontal line from left to right 1 first parameter is constant and second parameter varies e.g., point on IsoCurve(1,c) at t is srf(c,t This is a vertical line from bottom to top

c - [in] value of constant parameter Returns: Isoparametric curve. Remarks: In this function "dir" indicates which direction the resulting curve runs. 0: horizontal, 1: vertical In the other ON_Surface functions that take a "dir" argument, "dir" indicates if "c" is a "u" or "v" parameter.

Reimplemented in ON_SumSurface, ON_NurbsSurface, ON_RevSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ IsPeriodic()

virtual bool ON_Surface::IsPeriodic ( int ) const

virtual

Reimplemented in ON_NurbsSurface, ON_RevSurface, ON_Extrusion, ON_SumSurface, ON_PlaneSurface, and ON_SurfaceProxy.

◆ IsPlanar()

virtual bool ON_Surface::IsPlanar	(	ON_Plane *	plane = `nullptr`,
		double	tolerance = `ON_ZERO_TOLERANCE`
	)		const

virtual

Description: Test a surface to see if it is planar. Parameters: plane - [out] if not nullptr and true is returned, the plane parameters are filled in. tolerance - [in] tolerance to use when checking Returns: true if there is a plane such that the maximum distance from the surface to the plane is <= tolerance.

Reimplemented in ON_NurbsSurface, ON_RevSurface, ON_Extrusion, ON_SumSurface, ON_PlaneSurface, and ON_SurfaceProxy.

◆ IsSingular()

virtual bool ON_Surface::IsSingular ( int ) const

virtual

Reimplemented in ON_NurbsSurface, ON_RevSurface, ON_SumSurface, ON_PlaneSurface, and ON_SurfaceProxy.

◆ IsSolid()

bool ON_Surface::IsSolid ( ) const

Returns: True if the surface defines a solid, like a sphere or torus. False if the surface does not define a solid, like a plane or cone.

◆ IsSphere()

bool ON_Surface::IsSphere	(	ON_Sphere *	sphere = `nullptr`,
		double	tolerance = `ON_ZERO_TOLERANCE`
	)		const

Description: Determine if the surface is a portion of a sphere. Parameters: sphere - [out] if not nullptr and true is returned, then the sphere definition is returned. tolerance - [in] tolerance to use when checking Returns: True if the surface is a portion of a sphere.

◆ IsTorus()

bool ON_Surface::IsTorus	(	ON_Torus *	torus = `nullptr`,
		double	tolerance = `ON_ZERO_TOLERANCE`
	)		const

Description: Determine if the surface is a portion of a torus. Parameters: torus - [out] if not nullptr and true is returned, then the torus definition is returned. tolerance - [in] tolerance to use when checking Returns: True if the surface is a portion of a torus.

◆ NormalAt()

ON_3dVector ON_Surface::NormalAt	(	double	,
		double
	)		const

◆ NurbsSurface()

ON_NurbsSurface* ON_Surface::NurbsSurface	(	ON_NurbsSurface *	pNurbsSurface = `nullptr`,
		double	tolerance = `0.0`,
		const ON_Interval *	s_subdomain = `nullptr`,
		const ON_Interval *	t_subdomain = `nullptr`
	)		const

Description: Get a NURBS surface representation of this surface. Parameters: pNurbsSurface - [in/out] if not nullptr, this pNurbsSurface will be used to store the NURBS representation of the surface and will be returned. tolerance - [in] tolerance to use when creating NURBS surface representation. s_subdomain - [in] if not nullptr, then the NURBS representation for this portion of the surface is returned. t_subdomain - [in] if not nullptr, then the NURBS representation for this portion of the surface is returned. Returns: nullptr or a NURBS representation of the surface. Remarks: See ON_Surface::GetNurbForm for important details about the NURBS surface parameterization. See Also: ON_Surface::GetNurbForm

◆ ObjectType()

ON::object_type ON_Surface::ObjectType ( ) const

overridevirtual

override ON_Object::ObjectType() - returns ON::surface_object

Reimplemented from ON_Object.

◆ Offset()

virtual ON_Surface* ON_Surface::Offset	(	double	offset_distance,
		double	tolerance,
		double *	max_deviation = `nullptr`
	)		const

virtual

Description: Offset surface. Parameters: offset_distance - [in] offset distance tolerance - [in] Some surfaces do not have an exact offset that can be represented using the same class of surface definition. In that case, the tolerance specifies the desired accuracy. max_deviation - [out] If this parameter is not nullptr, the maximum deviation from the returned offset to the true offset is returned here. This deviation is zero except for cases where an exact offset cannot be computed using the same class of surface definition. Returns: Offset surface.

Reimplemented in ON_PlaneSurface, ON_SurfaceProxy, and ON_NurbsSurface.

◆ operator=()

ON_Surface& ON_Surface::operator= ( const ON_Surface & )

◆ PointAt()

ON_3dPoint ON_Surface::PointAt	(	double	,
		double
	)		const

simple evaluation interface - no error handling

◆ Pullback()

virtual ON_Curve* ON_Surface::Pullback	(	const ON_Curve &	curve_3d,
		double	tolerance,
		const ON_Interval *	curve_3d_subdomain = `nullptr`,
		ON_3dPoint	start_uv = `ON_3dPoint::UnsetPoint`,
		ON_3dPoint	end_uv = `ON_3dPoint::UnsetPoint`,
		ON_FitResult *	rc = `0`
	)		const

virtual

Description: Pull a 3d curve back to the surface's parameter space. Parameters: curve_3d - [in] a 3d curve tolerance - [in] the maximum acceptable 3d distance between from surface(curve_2d(t)) to the locus of points on the surface that are closest to curve_3d. curve_3d_subdomain - [in] optional subdomain for curve_3d start_uv - [in] optional starting point (if known) end_uv - [in] optional ending point (if known) rc - [out] if not 0 on input, points to an ON_FitResult with the following value - ON_FitResult::in_tolerance if result is in tolerance ON_FitResult::not_in_tolerance if result is not in tolerance ON_FitResult::unknown if no result or it could not be determined if the result was in tolerance. Returns: 2d curve. See Also: ON_Surface::IsoCurve ON_Surface::Pushup

Reimplemented in ON_Extrusion, ON_PlaneSurface, and ON_SurfaceProxy.

◆ PullbackCurveProxy()

ON_Curve* ON_Surface::PullbackCurveProxy	(	const ON_CurveProxy &	curveproxy_3d,
		double	tolerance,
		const ON_Interval *	curve_3d_subdomain,
		ON_3dPoint	start_uv,
		ON_3dPoint	end_uv,
		ON_FitResult *	rc
	)		const

protected

Helper for ON_Surface::Pullback overrides that handles "real" curve issues.

◆ PullbackPolyCurve()

ON_Curve* ON_Surface::PullbackPolyCurve	(	const ON_PolyCurve &	polycurve_3d,
		double	tolerance,
		const ON_Interval *	curve_3d_subdomain,
		ON_3dPoint	start_uv,
		ON_3dPoint	end_uv,
		ON_FitResult *	rc
	)		const

protected

◆ Pushup()

virtual ON_Curve* ON_Surface::Pushup	(	const ON_Curve &	curve_2d,
		double	tolerance,
		const ON_Interval *	curve_2d_subdomain = `nullptr`,
		ON_FitResult *	rc = `0`
	)		const

virtual

Description: Compute a 3d curve that is the composite of a 2d curve and the surface map. Parameters: curve_2d - [in] a 2d curve whose image is in the surface's domain. tolerance - [in] the maximum acceptable distance from the returned 3d curve to the image of curve_2d on the surface. curve_2d_subdomain - [in] optional subdomain for curve_2d rc - [out] if not 0 on input, points to an ON_FitResult with the following value - ON_FitResult::in_tolerance if result is in tolerance ON_FitResult::not_in_tolerance if result is not in tolerance ON_FitResult::unknown if no result or it could not be determined if the result was in tolerance. Returns: 3d curve. See Also: ON_Surface::IsoCurve ON_Surface::Pullback

Reimplemented in ON_Extrusion, ON_PlaneSurface, and ON_SurfaceProxy.

◆ PushupCurveProxy()

ON_Curve* ON_Surface::PushupCurveProxy	(	const ON_CurveProxy &	curveproxy_2d,
		double	tolerance,
		const ON_Interval *	curve_2d_subdomain,
		ON_FitResult *	rc
	)		const

protected

Helper for ON_Surface::Pushup overrides that handles "real" curve issues.

◆ PushupPolyCurve()

ON_Curve* ON_Surface::PushupPolyCurve	(	const ON_PolyCurve &	polycurve_2d,
		double	tolerance,
		const ON_Interval *	curve_2d_subdomain,
		ON_FitResult *	rc
	)		const

protected

Helper for ON_Surface::Pushup overrides that does a segment-by-segment pushup.

◆ Reverse()

virtual bool ON_Surface::Reverse ( int )

pure virtual

Implemented in ON_NurbsSurface, ON_RevSurface, ON_SumSurface, ON_PlaneSurface, ON_SurfaceProxy, ON_BrepFace, and ON_Extrusion.

◆ SetDomain() [1/2]

virtual bool ON_Surface::SetDomain	(	int	dir,
		double	t0,
		double	t1
	)

virtual

Parameters

dir	0 sets first parameter's domain, 1 gets second parameter's domain

Reimplemented in ON_BrepFace, ON_NurbsSurface, ON_Extrusion, ON_SumSurface, ON_RevSurface, and ON_PlaneSurface.

◆ SetDomain() [2/2]

bool ON_Surface::SetDomain	(	int	dir,
		ON_Interval	domain
	)

Parameters

dir	0 sets first parameter's domain, 1 gets second parameter's domain

◆ SizeOf()

unsigned int ON_Surface::SizeOf ( ) const

overridevirtual

virtual ON_Object::SizeOf override

Reimplemented from ON_Object.

Reimplemented in ON_SurfaceProxy.

◆ SpanCount()

virtual int ON_Surface::SpanCount ( int dir ) const

pure virtual

number of smooth nonempty spans in the parameter direction

Parameters

dir	0 gets first parameter's domain, 1 gets second parameter's domain

Implemented in ON_NurbsSurface, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ Split()

virtual bool ON_Surface::Split	(	int	dir,
		double	c,
		ON_Surface *&	west_or_south_side,
		ON_Surface *&	east_or_north_side
	)		const

virtual

Description: Splits (divides) the surface into two parts at the specified parameter.

Parameters: dir - [in] 0 The surface is split vertically. The "west" side is returned in "west_or_south_side" and the "east" side is returned in "east_or_north_side". 1 The surface is split horizontally. The "south" side is returned in "west_or_south_side" and the "north" side is returned in "east_or_north_side". c - [in] value of constant parameter in interval returned by Domain(dir) west_or_south_side - [out] west/south portion of surface returned here east_or_north_side - [out] east/north portion of surface returned here

Example:

    ON_NurbsSurface srf = ...;
    int dir = 1;
    ON_NurbsSurface* south_side = 0;
    ON_NurbsSurface* north_side = 0;
    srf.Split( dir, srf.Domain(dir).Mid() south_side, north_side );

Reimplemented in ON_NurbsSurface, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, and ON_Extrusion.

◆ SurfaceTree()

const ON_SurfaceTree* ON_Surface::SurfaceTree ( ) const

◆ Transpose()

virtual bool ON_Surface::Transpose ( )

pure virtual

transpose surface parameterization (swap "s" and "t")

Implemented in ON_BrepFace, ON_NurbsSurface, ON_RevSurface, ON_SumSurface, ON_PlaneSurface, ON_SurfaceProxy, and ON_Extrusion.

◆ Trim()

virtual bool ON_Surface::Trim	(	int	dir,
		const ON_Interval &	domain
	)

virtual

Description: Removes the portions of the surface outside of the specified interval.

Parameters: dir - [in] 0 The domain specifies an sub-interval of Domain(0) (the first surface parameter). 1 The domain specifies an sub-interval of Domain(1) (the second surface parameter). domain - [in] interval of the surface to keep. If dir is 0, then the portions of the surface with parameters (s,t) satisfying s < Domain(0).Min() or s > Domain(0).Max() are trimmed away. If dir is 1, then the portions of the surface with parameters (s,t) satisfying t < Domain(1).Min() or t > Domain(1).Max() are trimmed away.

Reimplemented in ON_NurbsSurface, ON_SumSurface, ON_RevSurface, ON_PlaneSurface, and ON_Extrusion.

◆ VolumeMassProperties()

bool ON_Surface::VolumeMassProperties	(	class ON_MassProperties &	mp,
		bool	bVolume = `true`,
		bool	bFirstMoments = `true`,
		bool	bSecondMoments = `true`,
		bool	bProductMoments = `true`,
		ON_3dPoint	base_point = `ON_3dPoint::UnsetPoint`,
		double	rel_tol = `1.0e-6`,
		double	abs_tol = `1.0e-6`
	)		const

Description: Calculate volume mass properties of the surface. Parameters: mp - [out] bVolume - [in] true to calculate volume bFirstMoments - [in] true to calculate volume first moments, volume, and volume centroid. bSecondMoments - [in] true to calculate volume second moments. bProductMoments - [in] true to calculate volume product moments. base_point - [in] If the surface is closed, then pass ON_UNSET_VALUE.

This parameter is for expert users who are computing a volume whose boundary is defined by several non-closed breps, surfaces, and meshes.

When computing the volume, volume centroid, or volume first moments of a volume whose boundary is defined by several breps, surfaces, and meshes, pass the same base_point to each call to VolumeMassProperties.

When computing the volume second moments or volume product moments of a volume whose boundary is defined by several breps, surfaces, and meshes, you MUST pass the entire volume's centroid as the base_point and the input mp parameter must contain the results of a previous call to VolumeMassProperties(mp,true,true,false,false,base_point). In particular, in this case, you need to make two sets of calls; use first set to calculate the volume centroid and the second set calculate the second moments and product moments. Returns: True if successful.

Friends And Related Function Documentation

◆ TL_Surface_PullbackHelper

ON_Curve* TL_Surface_PullbackHelper	(	const ON_Surface &	,
		const ON_Curve &	,
		double	,
		const ON_Interval *	,
		ON_3dPoint	,
		ON_3dPoint	,
		ON_FitResult *
	)

friend

◆ TL_Surface_PushupHelper

ON_Curve* TL_Surface_PushupHelper	(	const ON_Surface &	,
		const ON_Curve &	,
		double	,
		const ON_Interval *	,
		ON_FitResult *
	)

friend

Helper for ON_Surface::Pullback overrides that does a segment-by-segment pullback.

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Friends

Additional Inherited Members

Member Enumeration Documentation

◆ ISO

Constructor & Destructor Documentation

◆ ON_Surface() [1/2]

◆ ON_Surface() [2/2]

◆ ~ON_Surface()

Member Function Documentation

◆ AreaMassProperties()

◆ BrepForm()

◆ CreateCubicLoft()

◆ CreateLinearLoft()

◆ CreateMesh()

◆ CreateSurfaceTree()

◆ Degree()

◆ DestroyRuntimeCache()

◆ DestroySurfaceTree()

◆ Domain()

◆ DuplicateSurface()

◆ Ev1Der()

◆ Ev2Der()

◆ Evaluate()

◆ EvaluatePoint()

◆ EvNormal() [1/3]

◆ EvNormal() [2/3]

◆ EvNormal() [3/3]

◆ EvPoint()

◆ Extend()

◆ FrameAt()

◆ GetClosestPoint()

◆ GetDomain()

◆ GetIsoPushupDirection()

◆ GetLocalClosestPoint()

◆ GetNextDiscontinuity()

◆ GetNurbForm()

◆ GetNurbFormParameterFromSurfaceParameter()

◆ GetParameterTolerance()

◆ GetSilhouette()

◆ GetSpanVector()

◆ GetSpanVectorIndex()

◆ GetSurfaceParameterFromNurbFormParameter() [1/2]

◆ GetSurfaceParameterFromNurbFormParameter() [2/2]

◆ GetSurfaceSize()

◆ HasBrepForm()

◆ HasNurbForm()

◆ IntersectPlane()

◆ IntersectSurface()

◆ IsAtSeam()

◆ IsAtSingularity()

◆ IsClosed()

◆ IsCone()

◆ IsContinuous()

◆ IsCylinder()

◆ IsIsoparametric() [1/2]

◆ IsIsoparametric() [2/2]

◆ IsoCurve()

◆ IsPeriodic()

◆ IsPlanar()

◆ IsSingular()

◆ IsSolid()

◆ IsSphere()

◆ IsTorus()

◆ NormalAt()

◆ NurbsSurface()

◆ ObjectType()

◆ Offset()

◆ operator=()

◆ PointAt()

◆ Pullback()

◆ PullbackCurveProxy()

◆ PullbackPolyCurve()

◆ Pushup()

◆ PushupCurveProxy()

◆ PushupPolyCurve()

◆ Reverse()