Classes
class	PlaneT

class	QuadricT

Typedefs
typedef PlaneT< float >	Planef

typedef PlaneT< double >	Planed

typedef QuadricT< float >	Quadricf
	Quadric using floats.

typedef QuadricT< double >	Quadricd
	Quadric using double.

Functions
template<typename Scalar >
bool	edgeConvexPolygonIntersection (std::vector< VectorT< Scalar, 3 > > _polygon_points, VectorT< Scalar, 3 > _v0, VectorT< Scalar, 3 > _v1, VectorT< Scalar, 3 > &_result)
	Get intersection point of a ray and a convex polygon. More...

template<class Vec >
Vec::value_type	distPointTriangleSquared (const Vec &_p, const Vec &_v0, const Vec &_v1, const Vec &_v2, Vec &_nearestPoint, bool _stable)

template<typename Scalar >
bool	rotationOfTwoVectors (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, VectorT< Scalar, 3 > &_axis, Scalar &_angle, bool _degree=true)
	Get rotation axis and signed angle of rotation between two vectors. More...

template<typename Scalar >
bool	circumCenter (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2, const VectorT< Scalar, 3 > &_v3, VectorT< Scalar, 3 > &_result)
	return circumcenter of tetrahedron (_v0,_v1,_v2,_v3)

template<typename Scalar >
VectorT< Scalar, 3 >	perpendicular (const VectorT< Scalar, 3 > &_v)
	find a vector that's perpendicular to _v More...

template<typename Scalar >
bool	lineIntersection (const VectorT< Scalar, 2 > &_v0, const VectorT< Scalar, 2 > &_v1, const VectorT< Scalar, 2 > &_v2, const VectorT< Scalar, 2 > &_v3, Scalar &_t1, Scalar &_t2)
	intersect two line segments (_v0,_v1) and (_v2,_v3)

template<typename Vec >
bool	triangleIntersection (const Vec &_o, const Vec &_dir, const Vec &_v0, const Vec &_v1, const Vec &_v2, typename Vec::value_type &_t, typename Vec::value_type &_u, typename Vec::value_type &_v)
	Intersect a ray and a triangle. More...

template<typename Vec >
bool	axisAlignedBBIntersection (const Vec &_o, const Vec &_dir, const Vec &_bbmin, const Vec &_bbmax, typename Vec::value_type &_t0, typename Vec::value_type &_t1)
	Intersect a ray and an axis aligned bounding box. More...

template<typename Scalar >
Scalar	circumRadiusSquared (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2, const VectorT< Scalar, 3 > &_v3)
	return squared radius of circumcircle of tetrahedron (_v0,_v1,_v2,_v3)

template<typename Scalar >
Scalar	circumRadius (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2, const VectorT< Scalar, 3 > &_v3)
	return radius of circumcircle of tetrahedron (_v0,_v1,_v2,_v3)

template<typename Scalar >
Scalar	pointLineOrientation (const VectorT< Scalar, 2 > &_p, const VectorT< Scalar, 2 > &_v0, const VectorT< Scalar, 2 > &_v1)
	orientation of point _p w.r.t. line through _v0,_v1 in 2D

template<typename Scalar >
bool	isCCW (const VectorT< Scalar, 2 > &_v0, const VectorT< Scalar, 2 > &_v1, const VectorT< Scalar, 2 > &_v2)
	are 3 vertices in counterclockwise order? in 2D

template<typename Scalar >
bool	isCW (const VectorT< Scalar, 2 > &_v0, const VectorT< Scalar, 2 > &_v1, const VectorT< Scalar, 2 > &_v2)
	are 3 vertices in clockwise order? in 2D

bool	isNan (double x)
	Return false if x is not a number.

template<typename VectorT , typename ValueT >
ValueT	getFullangle (VectorT _vector1, VectorT _vector2, const VectorT &_normal, bool &_skip)

template<typename ValueT >
ValueT	angleDist (const ValueT &angle0, const ValueT &angle1)

template<typename ValueT >
ValueT	getAngle (const ValueT &_cos, const ValueT &_sin)

template<typename ValueT >
ValueT	radToDeg (const ValueT &_angle)

template<typename ValueT >
ValueT	degToRad (const ValueT &_angle)

Triangle Functions 3-Dimensional
template<typename Scalar >
bool	baryCoord (const VectorT< Scalar, 3 > &_p, const VectorT< Scalar, 3 > &_u, const VectorT< Scalar, 3 > &_v, const VectorT< Scalar, 3 > &_w, VectorT< Scalar, 3 > &_result)

template<typename Scalar >
bool	circumCenter (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2, VectorT< Scalar, 3 > &_result)
	return circumcenter of triangle (_v0,_v1,_v2)

template<typename Scalar >
Scalar	circumRadiusSquared (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2)
	return squared radius of circumcircle of triangle (_v0,_v1,_v2)

template<class VectorT >
int	isObtuse (const VectorT &_p0, const VectorT &_p1, const VectorT &_p2)

template<typename Scalar >
bool	minSphere (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2, VectorT< Scalar, 3 > &_center, Scalar &_radius)
	construct min. enclosing sphere

template<typename Scalar >
Scalar	minRadiusSquared (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2)
	return squared radius of min. enclosing circle of triangle (_v0,_v1,_v2)

template<typename Scalar >
Scalar	minRadius (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2)
	return radius of min. enclosing circle of triangle (_v0,_v1,_v2)

template<typename Scalar >
Scalar	circumRadius (const VectorT< Scalar, 3 > &_v0, const VectorT< Scalar, 3 > &_v1, const VectorT< Scalar, 3 > &_v2)
	return radius of circumcircle of triangle (_v0,_v1,_v2)

Triangle Functions N-Dimensional
template<class Vec >
Vec::value_type	triangleAreaSquared (const Vec &_v0, const Vec &_v1, const Vec &_v2)
	return squared area of triangle (_v0, _v1, _v2) More...

template<typename Scalar , int N>
Scalar	aspectRatio (const VectorT< Scalar, N > &_v0, const VectorT< Scalar, N > &_v1, const VectorT< Scalar, N > &_v2)
	return aspect ratio (length/height) of triangle More...

template<typename Scalar , int N>
Scalar	roundness (const VectorT< Scalar, N > &_v0, const VectorT< Scalar, N > &_v1, const VectorT< Scalar, N > &_v2)
	return roundness of triangle: 1=equilateral, 0=colinear More...

template<class Vec >
Vec::value_type	triangleArea (const Vec &_v0, const Vec &_v1, const Vec &_v2)
	return area of triangle (_v0, _v1, _v2) More...

Distance Functions ( N-Dimensional )
template<class Vec >
Vec::value_type	distPointLineSquared (const Vec &_p, const Vec &_v0, const Vec &_v1, Vec *_min_v=0)
	squared distance from point _p to line segment (_v0,_v1) More...

template<class Vec >
Vec::value_type	distPointTriangleSquared (const Vec &_p, const Vec &_v0, const Vec &_v1, const Vec &_v2, Vec &_nearestPoint)
	squared distance from point _p to triangle (_v0, _v1, _v2)

template<class Vec >
Vec::value_type	distPointTriangleSquaredStable (const Vec &_p, const Vec &_v0, const Vec &_v1, const Vec &_v2, Vec &_nearestPoint)
	squared distance from point _p to triangle (_v0, _v1, _v2) More...

template<typename VectorT , typename ValueT >
ValueT	distPointPlane (const VectorT &_porigin, const VectorT &_pnormal, const VectorT &_point)
	Checks the distance from a point to a plane. More...

template<class Vec >
Vec::value_type	distPointLine (const Vec &_p, const Vec &_v0, const Vec &_v1, Vec *_min_v=0)
	Compute distance from point to line segment. More...

template<class Vec >
Vec::value_type	distPointTriangle (const Vec &_p, const Vec &_v0, const Vec &_v1, const Vec &_v2, Vec &_nearestPoint)
	distance from point _p to triangle (_v0, _v1, _v2)

template<class Vec >
Vec::value_type	distPointTriangleStable (const Vec &_p, const Vec &_v0, const Vec &_v1, const Vec &_v2, Vec &_nearestPoint)
	distance from point _p to triangle (_v0, _v1, _v2) More...

Distance Functions ( 3-Dimensional )
template<typename Scalar >
Scalar	distLineLineSquared (const VectorT< Scalar, 3 > &_v00, const VectorT< Scalar, 3 > &_v01, const VectorT< Scalar, 3 > &_v10, const VectorT< Scalar, 3 > &_v11, VectorT< Scalar, 3 > _min_v0=0, VectorT< Scalar, 3 > _min_v1=0, bool _fastApprox=false)
	squared distance of lines (_v00, _v01) and (_v10, _v11)

template<typename Scalar >
Scalar	distLineLine (const VectorT< Scalar, 3 > &_v00, const VectorT< Scalar, 3 > &_v01, const VectorT< Scalar, 3 > &_v10, const VectorT< Scalar, 3 > &_v11, VectorT< Scalar, 3 > _min_v0=0, VectorT< Scalar, 3 > _min_v1=0)
	distance of lines (_v00, _v01) and (_v10, _v11)

Projection Functions ( N-Dimensional )
template<typename VectorT >
VectorT	projectToEdge (const VectorT &_start, const VectorT &_end, const VectorT &_point)

template<typename VectorT >
VectorT	projectToPlane (const VectorT &_porigin, const VectorT &_pnormal, const VectorT &_point)
	projects a point to a plane More...

Triangle Functions (2D Only!!)
template<typename Scalar >
bool	baryCoord (const VectorT< Scalar, 2 > &_p, const VectorT< Scalar, 2 > &_u, const VectorT< Scalar, 2 > &_v, const VectorT< Scalar, 2 > &_w, VectorT< Scalar, 3 > &_result)
	return circumcenter of triangle (_v0,_v1,_v2) More...

template<typename Scalar >
bool	circumCenter (const VectorT< Scalar, 2 > &_v0, const VectorT< Scalar, 2 > &_v1, const VectorT< Scalar, 2 > &_v2, VectorT< Scalar, 2 > &_result)
	return circumcenter of triangle (_v0,_v1,_v2) More...

template<typename Scalar >
bool	isInTriangle (const VectorT< Scalar, 2 > &_p, const VectorT< Scalar, 2 > &_u, const VectorT< Scalar, 2 > &_v, const VectorT< Scalar, 2 > &_w)
	is point _p in triangle (_v0,_v1,_v2) in 2D

Detailed Description

This namespace holds some geometric types as well as geometry algorithms.

Function Documentation

template<typename ValueT >

ValueT ACG::Geometry::angleDist	(	const ValueT &	angle0,
		const ValueT &	angle1
	)

inline

Calculate the difference between two angles ( minimum distance )

Parameters

angle0	angle1
angle1	angle2

Returns: The difference between the angles (0..PI)

Definition at line 123 of file AlgorithmsAngleT.cc.

template<typename Scalar , int N>

Scalar ACG::Geometry::aspectRatio	(	const VectorT< Scalar, N > &	_v0,
		const VectorT< Scalar, N > &	_v1,
		const VectorT< Scalar, N > &	_v2
	)

return aspect ratio (length/height) of triangle

Parameters

_v0	First point of triangle
_v1	Second point of triangle
_v2	Third point of triangl

Definition at line 1266 of file Algorithms.cc.

template<typename Vec >

bool ACG::Geometry::axisAlignedBBIntersection	(	const Vec &	_o,
		const Vec &	_dir,
		const Vec &	_bbmin,
		const Vec &	_bbmax,
		typename Vec::value_type &	_t0,
		typename Vec::value_type &	_t1
	)

Intersect a ray and an axis aligned bounding box.

Computes the intersection point between a ray and an axis aligned bounding box

Parameters

_o	Origin of the ray
_dir	direction vector of the ray
_bbmin	lower left front corner of the bounding box
_bbmax	upper right back corner of the bounding box
_t0	if there was an intersection, this value marks the entry point
_t1	if there was an intersection, this value marks the exit point

Returns: true if an intersection was found

Definition at line 1367 of file Algorithms.cc.

template<typename Scalar >

bool ACG::Geometry::baryCoord	(	const VectorT< Scalar, 3 > &	_p,
		const VectorT< Scalar, 3 > &	_u,
		const VectorT< Scalar, 3 > &	_v,
		const VectorT< Scalar, 3 > &	_w,
		VectorT< Scalar, 3 > &	_result
	)

barycentric coord of _p w.r.t. (_u,_v,_w) in 3D _p has to lie in plane (_u,_v,_w)

Definition at line 93 of file Algorithms.cc.

template<typename Scalar >

bool ACG::Geometry::baryCoord	(	const VectorT< Scalar, 2 > &	_p,
		const VectorT< Scalar, 2 > &	_u,
		const VectorT< Scalar, 2 > &	_v,
		const VectorT< Scalar, 2 > &	_w,
		VectorT< Scalar, 3 > &	_result
	)

return circumcenter of triangle (_v0,_v1,_v2)

barycentric coord of _p w.r.t. (_u,_v,_w) in 2D

Definition at line 1183 of file Algorithms.cc.

template<typename Scalar >

bool ACG::Geometry::circumCenter	(	const VectorT< Scalar, 2 > &	_v0,
		const VectorT< Scalar, 2 > &	_v1,
		const VectorT< Scalar, 2 > &	_v2,
		VectorT< Scalar, 2 > &	_result
	)

return circumcenter of triangle (_v0,_v1,_v2)

barycentric coord of _p w.r.t. (_u,_v,_w) in 2D

Definition at line 1236 of file Algorithms.cc.

template<typename ValueT >

ValueT ACG::Geometry::degToRad ( const ValueT & _angle )

inline

Convert angle from degree to radians

Parameters

_angle in degree

Returns: angle in radians

Definition at line 162 of file AlgorithmsAngleT.cc.

template<class Vec >

Vec::value_type ACG::Geometry::distPointLine	(	const Vec &	_p,
		const Vec &	_v0,
		const Vec &	_v1,
		Vec *	_min_v = `0`
	)

Compute distance from point to line segment.

Compute the distance from a point p to a line segment and possibly return closest point on segment

Parameters

_p	Point to test
_v0	Start of line segment
_v1	End of line segment
_min_v	Pointer to vector, to get the closest point or 0 if it's not required

Returns: Distance to line segment

Definition at line 295 of file Algorithms.hh.

template<class Vec >

Vec::value_type ACG::Geometry::distPointLineSquared	(	const Vec &	_p,
		const Vec &	_v0,
		const Vec &	_v1,
		Vec *	_min_v = `0`
	)

squared distance from point _p to line segment (_v0,_v1)

Parameters

_p	Point to test
_v0	Start of line segment
_v1	End of line segment
_min_v	Pointer to vector, to get the closest point or 0 if it's not required

Returns: Distance to line segment

Definition at line 300 of file Algorithms.cc.

template<typename VectorT , typename ValueT >

ValueT ACG::Geometry::distPointPlane	(	const VectorT &	_porigin,
		const VectorT &	_pnormal,
		const VectorT &	_point
	)

inline

Checks the distance from a point to a plane.

Parameters

_porigin	Planes origin
_pnormal	Plane normal ( has to be normalized!)
_point	point to test

Returns: distance

Definition at line 872 of file Algorithms.cc.

template<class Vec >

Vec::value_type ACG::Geometry::distPointTriangleSquaredStable	(	const Vec &	_p,
		const Vec &	_v0,
		const Vec &	_v1,
		const Vec &	_v2,
		Vec &	_nearestPoint
	)

squared distance from point _p to triangle (_v0, _v1, _v2)

In the stable version the distance to the longest edge is returned if the triangle is degenerate.

Parameters

_p	point to test against triangle
_v0	First point of triangle
_v1	Second point of triangle
_v2	Third point of triangle

Returns: Computed distance

Definition at line 476 of file Algorithms.cc.

template<class Vec >

Vec::value_type ACG::Geometry::distPointTriangleStable	(	const Vec &	_p,
		const Vec &	_v0,
		const Vec &	_v1,
		const Vec &	_v2,
		Vec &	_nearestPoint
	)

distance from point _p to triangle (_v0, _v1, _v2)

In the stable version the distance to the longest edge is returned if the triangle is degenerate.

Parameters

_v0	First point of triangle
_v1	Second point of triangle
_v2	Third point of triangle

Returns: Computed distance

Definition at line 352 of file Algorithms.hh.

template<typename Scalar >

bool ACG::Geometry::edgeConvexPolygonIntersection	(	std::vector< VectorT< Scalar, 3 > >	_polygon_points,
		VectorT< Scalar, 3 >	_v0,
		VectorT< Scalar, 3 >	_v1,
		VectorT< Scalar, 3 > &	_result
	)

Get intersection point of a ray and a convex polygon.

Gets two vertices, _v0 and _v1, and a convex polygon defined by its vertices stored in _polygon_points Computes the intersection point of the ray defined by _v0 and _v1 and stores it to _result Returns true if the intersection point lies inside the polygon

Parameters

_v0	The first vertex of a ray
_v1	The second vertex if a ray
_polygon_points	vector of the points bounding the polygon
_result	contains the intersection point after the computation

Definition at line 182 of file Algorithms.cc.

template<typename ValueT >

ValueT ACG::Geometry::getAngle	(	const ValueT &	_cos,
		const ValueT &	_sin
	)

inline

Calculate the correct 2D angle if cos and sin of the angle are given This function calculates based on the signs of the acos and asin of the given angles, in which quadrant the angle is and returns the full angle in radians

Parameters

_cos	cos of angle
_sin	sin of angle

Returns: angle

Definition at line 131 of file AlgorithmsAngleT.cc.

template<typename VectorT , typename ValueT >

ValueT ACG::Geometry::getFullangle	(	VectorT	_vector1,
		VectorT	_vector2,
		const VectorT &	_normal,
		bool &	_skip
	)

Return a fully parametrized angle

Parameters

_vector1	vector pointing away from center, angle = 0
_vector2	vector for which the angle should be calculated
_normal	the normal used to compute if vector2 is left or right of vecor1
_skip	Flag to catch nan. If true nan occurred and value should not be used

Returns: the angle (0 .. 2 * PI)

Definition at line 86 of file AlgorithmsAngleT.cc.

template<class VectorT >

int ACG::Geometry::isObtuse	(	const VectorT &	_p0,
		const VectorT &	_p1,
		const VectorT &	_p2
	)

test angles in triangle return 0 if all smaller than 90? return 1 if angle at _p0 ist greater than 90? return 2 if angle at _p1 ist greater than 90? return 3 if angle at _p2 ist greater than 90?

Definition at line 1013 of file Algorithms.cc.

template<typename Scalar >

VectorT< Scalar, 3 > ACG::Geometry::perpendicular ( const VectorT< Scalar, 3 > & _v )

find a vector that's perpendicular to _v

This function takes a vector and generates a new arbitrary vector that is perpendicular to the input vector.

Parameters

_v	Input vector

Returns: Perpendicular vector

Definition at line 1162 of file Algorithms.cc.

template<typename VectorT >

VectorT ACG::Geometry::projectToEdge	(	const VectorT &	_start,
		const VectorT &	_end,
		const VectorT &	_point
	)

project one point to an edge. If its projection is not on the edge itself, the start or the endpoint is returned

Parameters

_start	beginning of edge
_end	end of the edge
_point	point to be projected

Definition at line 884 of file Algorithms.cc.

template<typename VectorT >

VectorT ACG::Geometry::projectToPlane	(	const VectorT &	_porigin,
		const VectorT &	_pnormal,
		const VectorT &	_point
	)

inline

projects a point to a plane

Parameters

_porigin	Planes origin
_pnormal	Plane normal ( has to be normalized! )
_point	point to project

Returns: projected point

Definition at line 904 of file Algorithms.cc.

template<typename ValueT >

ValueT ACG::Geometry::radToDeg ( const ValueT & _angle )

inline

Convert angle from radians to degree

Parameters

_angle in radians

Returns: angle in degree

Definition at line 155 of file AlgorithmsAngleT.cc.

template<typename Scalar >

bool ACG::Geometry::rotationOfTwoVectors	(	const VectorT< Scalar, 3 > &	_v0,
		const VectorT< Scalar, 3 > &	_v1,
		VectorT< Scalar, 3 > &	_axis,
		Scalar &	_angle,
		bool	_degree = `true`
	)

Get rotation axis and signed angle of rotation between two vectors.

Get two vectors, _v0 and _v1, and compute rotation axis _v0 % _v1 as well the angle between _v0 and _v1. Note that the angle is always negative. We consider the rotation to be performed from _v0 to _v1. The angle is given in degree if not explicitly demanded in radiant (pass false as fifth parameter).

Parameters

_v0	The first vector
_v1	The second vector
_axis	A reference to a vector in which the rotation axis is stored
_angle	A reference to a scalar type in which the signed angle is stored ( in degree)
_degree	Indicates whether the angle should be given in degree or radiant

Definition at line 973 of file Algorithms.cc.

template<typename Scalar , int N>

Scalar ACG::Geometry::roundness	(	const VectorT< Scalar, N > &	_v0,
		const VectorT< Scalar, N > &	_v1,
		const VectorT< Scalar, N > &	_v2
	)

return roundness of triangle: 1=equilateral, 0=colinear

Parameters

_v0	First point of triangle
_v1	Second point of triangle
_v2	Third point of triangl

Definition at line 1302 of file Algorithms.cc.

template<class Vec >

Vec::value_type ACG::Geometry::triangleArea	(	const Vec &	_v0,
		const Vec &	_v1,
		const Vec &	_v2
	)

return area of triangle (_v0, _v1, _v2)

Parameters

_v0	First point of triangle
_v1	Second point of triangle
_v2	Third point of triangl

Definition at line 602 of file Algorithms.hh.

template<class Vec >

Vec::value_type ACG::Geometry::triangleAreaSquared	(	const Vec &	_v0,
		const Vec &	_v1,
		const Vec &	_v2
	)

return squared area of triangle (_v0, _v1, _v2)

Parameters

_v0	First point of triangle
_v1	Second point of triangle
_v2	Third point of triangl

Definition at line 173 of file Algorithms.cc.

template<typename Vec >

bool ACG::Geometry::triangleIntersection	(	const Vec &	_o,
		const Vec &	_dir,
		const Vec &	_v0,
		const Vec &	_v1,
		const Vec &	_v2,
		typename Vec::value_type &	_t,
		typename Vec::value_type &	_u,
		typename Vec::value_type &	_v
	)

Intersect a ray and a triangle.

Computes the intersection point between a ray and a triangle. The orientation of the triangle does not matter. The distance returned in t will be negative if the triangle is not in the direction given but in the opposite direction.

Parameters

_o	origin of the ray
_dir	direction vector of the ray
_v0	first point of the triangle
_v1	second point of the triangle
_v2	third point of the triangle
_t	returned distance from the origin to the intersection, in units of _dir ( negative if before origin!)
_u	returned first barycentric coordinate of the intersection point in the triangle
_v	returned second barycentric coordinate of the intersection point in the triangle

Returns: true if an intersection was found

Definition at line 1317 of file Algorithms.cc.

Classes

Typedefs

Functions

Detailed Description

Function Documentation