ON_3dSimplex Class Reference

A Simplex in 3d. More...

#include <opennurbs_convex_poly.h>

Public Member Functions
	ON_3dSimplex ()
	An empty simplex. More...
	ON_3dSimplex (const ON_3dPoint &a)
	0-simplex in 3d More...
	ON_3dSimplex (const ON_3dPoint &a, const ON_3dPoint &b)
	1-simplex More...
	ON_3dSimplex (const ON_3dPoint &a, const ON_3dPoint &b, const ON_3dPoint &c)
	2-simplex More...
	ON_3dSimplex (const ON_3dPoint &a, const ON_3dPoint &b, const ON_3dPoint &c, const ON_3dPoint &d)
	3-simplex More...
	ON_3dSimplex (const ON_3dSimplex &rhs)=default
	~ON_3dSimplex ()=default
bool	AddVertex (const ON_3dPoint &)
ON_BoundingBox	BoundingBox () const
int	Count () const
	Number of Verticies <=4. More...
ON_3dVector	Edge (int e0, int e1) const
ON_3dPoint	Evaluate (const double *b) const
ON_3dPoint	Evaluate (const ON_4dPoint &b) const
ON_3dVector	FaceNormal (int noti=0) const
ON_3dVector	FaceUnitNormal (int noti=0) const
bool	GetBoundingBox (ON_BoundingBox &bbox, int bGrowBox=false) const
bool	GetClosestPoint (const ON_3dPoint &P0, ON_4dPoint &Bary, double maximum_distance=ON_DBL_MAX) const
bool	GetClosestPointToOrigin (ON_4dPoint &Bary) const
bool	GetTightBoundingBox (ON_BoundingBox &tight_bbox, bool bGrowBox=false, const ON_Xform *xform=nullptr) const
bool	IsValid (double eps) const
	true if the Verticies are affinely independent More...
double	MaximumCoordinate () const
ON_3dSimplex &	operator= (const ON_3dSimplex &rhs)=default
const ON_3dPoint &	operator[] (int i) const
ON_3dPoint &	operator[] (int)
	Returns a Vertex or a reference to one when 0<=i<Count() More...
bool	RemoveVertex (int i)
bool	Rotate (double angle_in_radians, const ON_3dVector &axis_of_rotation, const ON_3dPoint &center_of_rotation)
bool	Rotate (double sin_angle, double cos_angle, const ON_3dVector &axis_of_rotation, const ON_3dPoint &center_of_rotation)
	rotate line about a point and axis More...
bool	SetVertex (int i, ON_3dPoint P)
double	SignedVolume () const
	returns ON_UNSET_VALUE if Count()<4 else the signed volume More...
bool	Transform (const ON_Xform &xform)
bool	Translate (const ON_3dVector &delta)
ON_3dPoint &	Vertex (int i)
ON_3dPoint	Vertex (int i) const
double	Volume () const

Detailed Description

A Simplex in 3d.

NoKeywords

/ / Copyright (c) 1993-2012 Robert McNeel & Associates. All rights reserved. / OpenNURBS, Rhinoceros, and Rhino3D are registered trademarks of Robert / McNeel & Associates. / / THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT EXPRESS OR IMPLIED WARRANTY. / ALL IMPLIED WARRANTIES OF FITNESS FOR ANY PARTICULAR PURPOSE AND OF / MERCHANTABILITY ARE HEREBY DISCLAIMED. /
/ For complete openNURBS copyright information see http://www.opennurbs.org. / //////////////////////////////////////////////////////////////

Constructor & Destructor Documentation

ON_3dSimplex() [1/6]

ON_3dSimplex::ON_3dSimplex

(

)

An empty simplex.

ON_3dSimplex() [2/6]

ON_3dSimplex::ON_3dSimplex ( const ON_3dPoint &  a )

explicit

0-simplex in 3d

ON_3dSimplex() [3/6]

ON_3dSimplex::ON_3dSimplex	(	const ON_3dPoint &	a,
		const ON_3dPoint &	b
	)

1-simplex

ON_3dSimplex() [4/6]

ON_3dSimplex::ON_3dSimplex	(	const ON_3dPoint &	a,
		const ON_3dPoint &	b,
		const ON_3dPoint &	c
	)

2-simplex

ON_3dSimplex() [5/6]

ON_3dSimplex::ON_3dSimplex	(	const ON_3dPoint &	a,
		const ON_3dPoint &	b,
		const ON_3dPoint &	c,
		const ON_3dPoint &	d
	)

3-simplex

ON_3dSimplex() [6/6]

ON_3dSimplex::ON_3dSimplex ( const ON_3dSimplex &  rhs )

default

~ON_3dSimplex()

ON_3dSimplex::~ON_3dSimplex ( )

default

Member Function Documentation

AddVertex()

bool ON_3dSimplex::AddVertex

(

const ON_3dPoint &

)

append new vertex at end

BoundingBox()

ON_BoundingBox ON_3dSimplex::BoundingBox

(

)

const

Description: Get Simplex's 3d axis aligned bounding box. Returns: 3d bounding box.

Count()

int ON_3dSimplex::Count

(

)

const

Number of Verticies <=4.

Edge()

ON_3dVector ON_3dSimplex::Edge	(	int	e0,
		int	e1
	)		const

Edge vector from Vertex(e0) to Vertex(e1)

Evaluate() [1/2]

ON_3dPoint ON_3dSimplex::Evaluate

(

const double *

b

)

const

Description: Evaluate a point in a Simplex from a barycentric coordinate b. Returns: The point b[0] * Vertex[0] + ... + b[Count()-1] * Vertex[Count()-1] Notes: If b[0] + ... + b[Count()-1] = 1 and b[i]>=0 for i=0 to Count()-1 then the returned point is on the simplex

Evaluate() [2/2]

ON_3dPoint ON_3dSimplex::Evaluate

(

const ON_4dPoint &

b

)

const

FaceNormal()

ON_3dVector ON_3dSimplex::FaceNormal

(

int

noti = 0

)

const

FaceNormal(noti) is the oriented face normal obtained by omitting vertex noti. FaceNormal returns ON_UNSET_VALUE if Count()<3 or Count()==4 noti not 0,1,2 or 3. FaceUnitNormal returns ON_UNSET_VALUE if Count()<3 or Count()==4 noti not 0,1,2 or 3 or if FaceNormal(noti)=Zero_Vector

FaceUnitNormal()

ON_3dVector ON_3dSimplex::FaceUnitNormal

(

int

noti = 0

)

const

GetBoundingBox()

bool ON_3dSimplex::GetBoundingBox	(	ON_BoundingBox &	bbox,
		int	bGrowBox = false
	)		const

Description: Get simplexes 3d axis aligned bounding box or the union of the input box with the object's bounding box. Parameters: bbox - [in/out] 3d axis aligned bounding box bGrowBox - [in] (default=false) If true, then the union of the input bbox and the object's bounding box is returned in bbox. If false, the object's bounding box is returned in bbox. Returns: true if object has bounding box and calculation was successful.

GetClosestPoint()

bool ON_3dSimplex::GetClosestPoint	(	const ON_3dPoint &	P0,
		ON_4dPoint &	Bary,
		double	maximum_distance = ON_DBL_MAX
	)		const

Description: Find Closest Point to this simplex from a base point P0 or the Origin. If true is retuned then Evaluate(Bary) is the closest point on the Simplex. maximum_distance - optional upperbound on closest point. If maximum_distance>=0 is specified and Dist(P0, Simplex)>maximum_distance then false is returned.

GetClosestPointToOrigin()

bool ON_3dSimplex::GetClosestPointToOrigin

(

ON_4dPoint &

Bary

)

const

GetTightBoundingBox()

bool ON_3dSimplex::GetTightBoundingBox	(	ON_BoundingBox &	tight_bbox,
		bool	bGrowBox = false,
		const ON_Xform *	xform = nullptr
	)		const

Description: Get tight bounding box with respect to a given frame Parameters: tight_bbox - [in/out] tight bounding box bGrowBox -[in] (default=false) If true and the input tight_bbox is valid, then returned tight_bbox is the union of the input tight_bbox and the line's tight bounding box. xform -[in] (default=nullptr) If not nullptr, the tight bounding box of the transformed triangle is calculated. The triangle is not modified. Returns: True if a valid tight_bbox is returned.

IsValid()

bool ON_3dSimplex::IsValid

(

double

eps

)

const

true if the Verticies are affinely independent

MaximumCoordinate()

double ON_3dSimplex::MaximumCoordinate

(

)

const

Maximum absolute value of vertex coordinates

operator=()

ON_3dSimplex& ON_3dSimplex::operator= ( const ON_3dSimplex &  rhs )

default

operator[]() [1/2]

const ON_3dPoint& ON_3dSimplex::operator[]

(

int

i

)

const

operator[]() [2/2]

ON_3dPoint& ON_3dSimplex::operator[]

(

int

)

Returns a Vertex or a reference to one when 0<=i<Count()

RemoveVertex()

bool ON_3dSimplex::RemoveVertex

(

int

i

)

If 0<=i<Count() modify this simplex by removing Vertex[i], specifically,
Vertex[k] is fixed for k<i , and Vertex[k] <- Vertex[k+1] for i<= k= Count()-2

Rotate() [1/2]

bool ON_3dSimplex::Rotate	(	double	angle_in_radians,
		const ON_3dVector &	axis_of_rotation,
		const ON_3dPoint &	center_of_rotation
	)

Rotate() [2/2]

bool ON_3dSimplex::Rotate	(	double	sin_angle,
		double	cos_angle,
		const ON_3dVector &	axis_of_rotation,
		const ON_3dPoint &	center_of_rotation
	)

rotate line about a point and axis

SetVertex()

bool ON_3dSimplex::SetVertex	(	int	i,
		ON_3dPoint	P
	)

Modify a vertex. i<Count()

SignedVolume()

double ON_3dSimplex::SignedVolume

(

)

const

returns ON_UNSET_VALUE if Count()<4 else the signed volume

Transform()

bool ON_3dSimplex::Transform

(

const ON_Xform &

xform

)

Translate()

bool ON_3dSimplex::Translate

(

const ON_3dVector &

delta

)

Vertex() [1/2]

ON_3dPoint& ON_3dSimplex::Vertex

(

int

i

)

Vertex() [2/2]

ON_3dPoint ON_3dSimplex::Vertex

(

int

i

)

const

Volume()

double ON_3dSimplex::Volume

(

)

const

Count() Volume() returns 0 0.0 1 0.0 2 length >=0 3 area >=0 4 volume >=0