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 Vertices <=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 Vertices 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.

Copyright (c) 1993-2022 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 Vertices <=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 returned 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 Vertices 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