#include <opennurbs_bezier.h>

Inheritance diagram for ON_BezierSurface:

Public Member Functions
	ON_BezierSurface ()

	ON_BezierSurface (const ON_BezierSurface &)

	ON_BezierSurface (const ON_PolynomialSurface &)

	ON_BezierSurface (int dim, bool is_rat, int order0, int order1)

	~ON_BezierSurface ()

ON_BoundingBox	BoundingBox () const

bool	Create (int dim, bool is_rat, int order0, int order1)

double *	CV (int cv_index0, int cv_index1) const

int	CVSize () const

ON::point_style	CVStyle () const

int	Degree (int) const

void	Destroy ()

int	Dimension () const

ON_Interval	Domain (int) const

void	Dump (ON_TextLog &) const
	for debugging More...

void	EmergencyDestroy ()
	call if memory used by ON_NurbsCurve becomes invalid More...

bool	Evaluate (double, double, int, int, double *) const

bool	GetBBox (double , double , bool bGrowBox=false) const

bool	GetBoundingBox (ON_BoundingBox &bbox, int bGrowBox) const

bool	GetClosestPoint (ON_3dPoint P, double s, double t, double maximum_distance=0.0, const ON_Interval sub_domain0=0, const ON_Interval sub_domain1=0) const

bool	GetCV (int, int, ON::point_style, double *) const

bool	GetCV (int, int, ON_3dPoint &) const

bool	GetCV (int, int, ON_4dPoint &) const

bool	GetLocalClosestPoint (ON_3dPoint P, double s_seed, double t_seed, double s, double t, const ON_Interval sub_domain0=0, const ON_Interval sub_domain1=0) const

int	GetNurbForm (ON_NurbsSurface &) const

bool	GetSurfaceSize (double width, double height) const

ON_BezierCurve *	IsoCurve (int dir, double c, ON_BezierCurve *iso=nullptr) const
	returns the isocurve. More...

bool	IsRational () const
	true if NURBS curve is rational More...

bool	IsSingular (int) const

bool	IsValid () const

bool	Loft (const ON_ClassArray< ON_BezierCurve > &curve_list)

bool	Loft (int count, const ON_BezierCurve const curve_list)

bool	MakeNonRational ()

bool	MakeRational ()

bool	Morph (const ON_SpaceMorph &morph)

ON_BezierSurface &	operator= (const ON_BezierSurface &)

ON_BezierSurface &	operator= (const ON_PolynomialSurface &)

int	Order (int) const
	= IsRational() ? Dim()+1 : Dim() More...

ON_3dPoint	PointAt (double s, double t) const

bool	ReserveCVCapacity (int)
	Tools for managing CV and knot memory. More...

bool	Reverse (int)

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)

bool	SetCV (int, int, const ON_3dPoint &)

bool	SetCV (int, int, const ON_4dPoint &)

bool	SetCV (int, int, ON::point_style, const double *)

bool	SetWeight (int, int, double)

bool	Split (int, double, ON_BezierSurface &, ON_BezierSurface &) const

bool	Transform (const ON_Xform &)

bool	Translate (const ON_3dVector &translation_vector)

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

bool	Trim (int dir, const ON_Interval &domain)

double	Weight (int, int) const

bool	ZeroCVs ()
	zeros control vertices and, if rational, sets weights to 1 More...

Static Public Member Functions
static ON_BezierSurface *	InterpolateGrid (const double point_grid, int dim, int point_count0, int point_count1, size_t point_stride0, size_t point_stride1, ON_BezierSurface dest)
	Interpolate arectangular grid of points so that bez(i/(point_count0 - 1), i/(point_count1 - 1))) = point_grid[i][j]. The returned bezier has order (point_count0,point_count1). Be aware that interpolation of irregular grids can create surfaces with extreme oscillations. More...

static ON_BezierSurface *	InterpolateGrid (const ON_3dPoint point_grid, int point_count0, int point_count1, size_t point_stride0, size_t point_stride1, ON_BezierSurface dest)
	Interpolate arectangular grid of 3d points so that bez(i/(point_count0 - 1), i/(point_count1 - 1))) = point_grid[i][j] More...

static bool	MatchTangency (ON_SimpleArray< ON_BezierSurface * > &BezArray, ON_3dPoint P, ON_3dVector N, double *pMaxAngleDeviation)

Public Attributes
double *	m_cv

int	m_cv_capacity
	if 0, then destructor does not free m_cv More...

int	m_cv_stride [2]

int	m_dim
	Implementation. More...

int	m_is_rat
	0 = no, 1 = yes More...

int	m_order [2]
	order = degree+1 >= 2 More...

Constructor & Destructor Documentation

◆ ON_BezierSurface() [1/4]

ON_BezierSurface::ON_BezierSurface ( )

◆ ON_BezierSurface() [2/4]

ON_BezierSurface::ON_BezierSurface	(	int	dim,
		bool	is_rat,
		int	order0,
		int	order1
	)

◆ ~ON_BezierSurface()

ON_BezierSurface::~ON_BezierSurface ( )

◆ ON_BezierSurface() [3/4]

ON_BezierSurface::ON_BezierSurface ( const ON_BezierSurface & )

◆ ON_BezierSurface() [4/4]

ON_BezierSurface::ON_BezierSurface ( const ON_PolynomialSurface & )

Member Function Documentation

◆ BoundingBox()

ON_BoundingBox ON_BezierSurface::BoundingBox ( ) const

◆ Create()

bool ON_BezierSurface::Create	(	int	dim,
		bool	is_rat,
		int	order0,
		int	order1
	)

◆ CV()

double* ON_BezierSurface::CV	(	int	cv_index0,
		int	cv_index1
	)		const

Description: Expert user function to get a pointer to control vertex memory. If you are not an expert user, please use ON_BezierSurface::GetCV( ON_3dPoint& ) or ON_BezierSurface::GetCV( ON_4dPoint& ). Parameters: cv_index0 - [in] (0 <= cv_index0 < m_order[0]) cv_index1 - [in] (0 <= cv_index1 < m_order[1]) Returns: Pointer to control vertex. Remarks: If the Bezier surface is rational, the format of the returned array is a homogeneos rational point with length m_dim+1. If the Bezier surface is not rational, the format of the returned array is a nonrational euclidean point with length m_dim. See Also ON_BezierSurface::CVStyle ON_BezierSurface::GetCV ON_BezierSurface::Weight

◆ CVSize()

int ON_BezierSurface::CVSize ( ) const

number of doubles per control vertex

◆ CVStyle()

ON::point_style ON_BezierSurface::CVStyle ( ) const

Description: Returns the style of control vertices in the m_cv array. Returns: @untitled table ON::not_rational m_is_rat is false ON::homogeneous_rational m_is_rat is true

◆ Degree()

int ON_BezierSurface::Degree ( int ) const

◆ Destroy()

void ON_BezierSurface::Destroy ( )

◆ Dimension()

int ON_BezierSurface::Dimension ( ) const

◆ Domain()

ON_Interval ON_BezierSurface::Domain ( int ) const

◆ Dump()

void ON_BezierSurface::Dump ( ON_TextLog & ) const

for debugging

◆ EmergencyDestroy()

void ON_BezierSurface::EmergencyDestroy ( )

call if memory used by ON_NurbsCurve becomes invalid

◆ Evaluate()

bool ON_BezierSurface::Evaluate	(	double	,
		double	,
		int	,
		int	,
		double *
	)		const

◆ GetBBox()

bool ON_BezierSurface::GetBBox	(	double *	,
		double *	,
		bool	bGrowBox = `false`
	)		const

Parameters

bGrowBox true means grow box

◆ GetBoundingBox()

bool ON_BezierSurface::GetBoundingBox	(	ON_BoundingBox &	bbox,
		int	bGrowBox
	)		const

◆ GetClosestPoint()

bool ON_BezierSurface::GetClosestPoint	(	ON_3dPoint	P,
		double *	s,
		double *	t,
		double	maximum_distance = `0.0`,
		const ON_Interval *	sub_domain0 = `0`,
		const ON_Interval *	sub_domain1 = `0`
	)		const

Description: Get the parameters of the point on the bezier surface that is closest to the point P. Parameters: P - [in] s - [out] t - [out] Closest point parameters. maximum_distance - [in] If maximum_distance > 0.0, then an answer is returned only if the distance from the bezier surface to P is <= maximum_distance. If maximum_distance <= 0.0, then maximum_distance is ignored. sub_domain0 - [in] If not nullptr, the search is confined to "s" parameters in the intersection of the sub_domain0 interval and (0,1). sub_domain1 - [in] If not nullptr, the search is confined to "t" parameters in the intersection of the sub_domain1 interval and (0,1). Returns: True if a point is found. See Also: ON_SurfaceTreeNode::GetClosestPoint Remarks: This function is not efficient if you will be finding multiple closest points to the same bezier. To efficiently find multiple closest points, make a surface tree and use it. See the ON_BezierSurface::GetClosestPoint code for an example.

◆ GetCV() [1/3]

bool ON_BezierSurface::GetCV	(	int	,
		int	,
		ON::point_style	,
		double *
	)		const

◆ GetCV() [2/3]

bool ON_BezierSurface::GetCV	(	int	,
		int	,
		ON_3dPoint &
	)		const

◆ GetCV() [3/3]

bool ON_BezierSurface::GetCV	(	int	,
		int	,
		ON_4dPoint &
	)		const

◆ GetLocalClosestPoint()

bool ON_BezierSurface::GetLocalClosestPoint	(	ON_3dPoint	P,
		double	s_seed,
		double	t_seed,
		double *	s,
		double *	t,
		const ON_Interval *	sub_domain0 = `0`,
		const ON_Interval *	sub_domain1 = `0`
	)		const

Description: Get the parameter of the point on the bezier surface that is locally closest to the point P when the search begins at (s_seed,t_seed). Parameters: P - [in] s_seed - [in] t_seed - [in] Parameters where the search begins. s - [out] t - [out] Closest point parameter. sub_domain0 - [in] If not nullptr, the search is confined to "s" parameters in the intersection of the sub_domain0 interval and (0,1). sub_domain1 - [in] If not nullptr, the search is confined to "t" parameters in the intersection of the sub_domain1 interval and (0,1). Returns: True if a point is found.

◆ GetNurbForm()

int ON_BezierSurface::GetNurbForm ( ON_NurbsSurface & ) const

Returns: 0 = failure. 1 = success.

◆ GetSurfaceSize()

bool ON_BezierSurface::GetSurfaceSize	(	double *	width,
		double *	height
	)		const

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) Returns: true if successful.

◆ InterpolateGrid() [1/2]

static ON_BezierSurface* ON_BezierSurface::InterpolateGrid	(	const double *	point_grid,
		int	dim,
		int	point_count0,
		int	point_count1,
		size_t	point_stride0,
		size_t	point_stride1,
		ON_BezierSurface *	dest
	)

static

Interpolate arectangular grid of points so that bez(i/(point_count0 - 1), i/(point_count1 - 1))) = point_grid[i][j]. The returned bezier has order (point_count0,point_count1). Be aware that interpolation of irregular grids can create surfaces with extreme oscillations.

Parameters

point_grid	Grid points
dim	dimension of grid points and returned bezier surface (dim >= 1)
point_count0	Number of grid points in the "i" direction.
point_count1	Number of grid points in the "j" direction.
point_stride0	"i" direction stride in doubles.
point_stride1	"j" direction stride in doubles.
dest	If dest is not nullptr, then the bezier will be created in this instance. Otherwise new ON_BezierSurface(dim,0,point_count0,point_count1) will be used to allocate a bezier.

Returns: If the input is valid, a bezier surface is returned such that bez(i/(point_count0 - 1), i/(point_count1 - 1))) = point_grid[i][j]. Otherwise nullptr is returned.

◆ InterpolateGrid() [2/2]

static ON_BezierSurface* ON_BezierSurface::InterpolateGrid	(	const ON_3dPoint *	point_grid,
		int	point_count0,
		int	point_count1,
		size_t	point_stride0,
		size_t	point_stride1,
		ON_BezierSurface *	dest
	)

static

Interpolate arectangular grid of 3d points so that bez(i/(point_count0 - 1), i/(point_count1 - 1))) = point_grid[i][j]

Parameters

point_grid	Grid points
point_count0	Number of grid points "i" direction.

///

Parameters

point_count1	Number of grid points in the "j" direction.
point_stride0	"i" direction stride in ON_3dPoints.
point_stride1	"j" direction stride in ON_3dPoints.
dest	If dest is not nullptr, then the bezier will be created in this instance. Otherwise new ON_BezierSurface(dim,0,point_count0,point_count1) will be used to allocate a bezier.

Returns

◆ IsoCurve()

ON_BezierCurve* ON_BezierSurface::IsoCurve	(	int	dir,
		double	c,
		ON_BezierCurve *	iso = `nullptr`
	)		const

returns the isocurve.

Parameters

dir	0 first parameter varies and second parameter is constant
c	e.g., point on IsoCurve(0,c) at t is srf(t,c) 1 first parameter is constant and second parameter varies e.g., point on IsoCurve(1,c) at t is srf(c,t) value of constant parameter
iso	When nullptr result is constructed on the heap.

◆ IsRational()

bool ON_BezierSurface::IsRational ( ) const

true if NURBS curve is rational

◆ IsSingular()

bool ON_BezierSurface::IsSingular ( int ) const

◆ IsValid()

bool ON_BezierSurface::IsValid ( ) const

◆ Loft() [1/2]

bool ON_BezierSurface::Loft ( const ON_ClassArray< ON_BezierCurve > & curve_list )

Description: Loft a bezier surface through a list of bezier curves. Parameters: curve_list - [in] list of curves that have the same degree. Returns: True if successful.

◆ Loft() [2/2]

bool ON_BezierSurface::Loft	(	int	count,
		const ON_BezierCurve const	curve_list
	)

Description: Loft a bezier surface through a list of bezier curves. Parameters: curve_count - [in] number of curves in curve_list curve_list - [in] array of pointers to curves that have the same degree. Returns: True if successful.

◆ MakeNonRational()

bool ON_BezierSurface::MakeNonRational ( )

◆ MakeRational()

bool ON_BezierSurface::MakeRational ( )

◆ MatchTangency()

static bool ON_BezierSurface::MatchTangency	(	ON_SimpleArray< ON_BezierSurface * > &	BezArray,
		ON_3dPoint	P,
		ON_3dVector	N,
		double *	pMaxAngleDeviation
	)

static

Description: Given a set of bicubic bezier surfaces that share a vertex P, and form a complete ring around V, with common edges having identical control points, adjust the control points at and adjacent to V so that the normals at V are all N, and the angle between normals along common edges is minimized. Parameters: BezArray - [in, out] The input bezier surfaces. The do not have to be in order around the common vertex. They will be adjusted in place. P - [in] The desired location of the common vertex N - [in] The desired normal at the vertex. pMaxAngleDeviation - [out] max angle between normals along a shared edge (degrees). Returns: true if successful. false if the input beziers do not meet the criterion or if there are other failures. Note: Since only the control points at or adjacent to the vertex are changed, The normals and locations along the edges opposite the vertex do not change.

◆ Morph()

bool ON_BezierSurface::Morph ( const ON_SpaceMorph & morph )

◆ operator=() [1/2]

ON_BezierSurface& ON_BezierSurface::operator= ( const ON_BezierSurface & )

◆ operator=() [2/2]

ON_BezierSurface& ON_BezierSurface::operator= ( const ON_PolynomialSurface & )

◆ Order()

int ON_BezierSurface::Order ( int ) const

= IsRational() ? Dim()+1 : Dim()

◆ PointAt()

ON_3dPoint ON_BezierSurface::PointAt	(	double	s,
		double	t
	)		const

◆ ReserveCVCapacity()

bool ON_BezierSurface::ReserveCVCapacity ( int )

Tools for managing CV and knot memory.

◆ Reverse()

bool ON_BezierSurface::Reverse ( int )

reverse parameterizatrion Domain changes from [a,b] to [-b,-a]

◆ Rotate() [1/2]

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

Description: Rotates the bezier surface about the specified axis. A positive rotation angle results in a counter-clockwise rotation about the axis (right hand rule). Parameters: rotation_angle - [in] angle of rotation in radians rotation_axis - [in] direction of the axis of rotation rotation_center - [in] point on the axis of rotation Returns: true if bezier surface successfully rotated Remarks: Uses ON_BezierSurface::Transform() function to calculate the result.

◆ Rotate() [2/2]

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

Description: Rotates the bezier surface about the specified axis. A positive rotation angle results in a counter-clockwise rotation about the axis (right hand rule). Parameters: sin_angle - [in] sine of rotation angle cos_angle - [in] sine of rotation angle rotation_axis - [in] direction of the axis of rotation rotation_center - [in] point on the axis of rotation Returns: true if bezier surface successfully rotated Remarks: Uses ON_BezierSurface::Transform() function to calculate the result.

◆ Scale()

bool ON_BezierSurface::Scale ( double scale_factor )

Description: Scales the bezier surface by the specified facotor. The scale is centered at the origin. Parameters: scale_factor - [in] scale factor Returns: true if bezier surface successfully scaled Remarks: Uses ON_BezierSurface::Transform() function to calculate the result.

◆ SetCV() [1/3]

bool ON_BezierSurface::SetCV	(	int	,
		int	,
		const ON_3dPoint &
	)

◆ SetCV() [2/3]

bool ON_BezierSurface::SetCV	(	int	,
		int	,
		const ON_4dPoint &
	)

◆ SetCV() [3/3]

bool ON_BezierSurface::SetCV	(	int	,
		int	,
		ON::point_style	,
		const double *
	)

◆ SetWeight()

bool ON_BezierSurface::SetWeight	(	int	,
		int	,
		double
	)

◆ Split()

bool ON_BezierSurface::Split	(	int	,
		double	,
		ON_BezierSurface &	,
		ON_BezierSurface &
	)		const

◆ Transform()

bool ON_BezierSurface::Transform ( const ON_Xform & )

◆ Translate()

bool ON_BezierSurface::Translate ( const ON_3dVector & translation_vector )

Description: Translates the bezier surface along the specified vector. Parameters: translation_vector - [in] translation vector Returns: true if bezier surface successfully translated Remarks: Uses ON_BezierSurface::Transform() function to calculate the result.

◆ Transpose()

bool ON_BezierSurface::Transpose ( )

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

◆ Trim()

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

◆ Weight()

double ON_BezierSurface::Weight	(	int	,
		int
	)		const

◆ ZeroCVs()

bool ON_BezierSurface::ZeroCVs ( )

zeros control vertices and, if rational, sets weights to 1

Member Data Documentation

◆ m_cv

double* ON_BezierSurface::m_cv

◆ m_cv_capacity

int ON_BezierSurface::m_cv_capacity

if 0, then destructor does not free m_cv

◆ m_cv_stride

int ON_BezierSurface::m_cv_stride[2]

◆ m_dim

int ON_BezierSurface::m_dim

Implementation.

NOTE: These members are left "public" so that expert users may efficiently create bezier curves using the default constructor and borrow the knot and CV arrays from their native NURBS representation. No technical support will be provided for users who access these members directly. If you can't get your stuff to work, then use the constructor with the arguments and the SetKnot() and SetCV() functions to fill in the arrays. >= 1

◆ m_is_rat

int ON_BezierSurface::m_is_rat

0 = no, 1 = yes

◆ m_order

int ON_BezierSurface::m_order[2]

order = degree+1 >= 2

Public Member Functions

Static Public Member Functions

Public Attributes

Constructor & Destructor Documentation

◆ ON_BezierSurface() [1/4]

◆ ON_BezierSurface() [2/4]

◆ ~ON_BezierSurface()

◆ ON_BezierSurface() [3/4]

◆ ON_BezierSurface() [4/4]

Member Function Documentation

◆ BoundingBox()

◆ Create()

◆ CV()

◆ CVSize()

◆ CVStyle()

◆ Degree()

◆ Destroy()

◆ Dimension()

◆ Domain()

◆ Dump()

◆ EmergencyDestroy()

◆ Evaluate()

◆ GetBBox()

◆ GetBoundingBox()

◆ GetClosestPoint()

◆ GetCV() [1/3]

◆ GetCV() [2/3]

◆ GetCV() [3/3]

◆ GetLocalClosestPoint()

◆ GetNurbForm()

◆ GetSurfaceSize()

◆ InterpolateGrid() [1/2]

◆ InterpolateGrid() [2/2]

◆ IsoCurve()

◆ IsRational()

◆ IsSingular()

◆ IsValid()

◆ Loft() [1/2]

◆ Loft() [2/2]

◆ MakeNonRational()

◆ MakeRational()

◆ MatchTangency()

◆ Morph()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ Order()

◆ PointAt()

◆ ReserveCVCapacity()

◆ Reverse()

◆ Rotate() [1/2]

◆ Rotate() [2/2]

◆ Scale()

◆ SetCV() [1/3]

◆ SetCV() [2/3]

◆ SetCV() [3/3]

◆ SetWeight()

◆ Split()

◆ Transform()

◆ Translate()

◆ Transpose()

◆ Trim()

◆ Weight()

◆ ZeroCVs()

Member Data Documentation

◆ m_cv

◆ m_cv_capacity

◆ m_cv_stride

◆ m_dim

◆ m_is_rat

◆ m_order