C++ class Geometry::Triangle
_{template< typename T_ >}
Triangle

Inheritance Graph

graph BT
	Triangle
	click Triangle "classGeometry_1_1Triangle"

Description

Triangle defined by three vertices.

Author: Benjamin Eikel

Date: 2011-12-02

*      c
*      X
*     / \
*    /   \
*   X-----X
*   a     b
*

Creation

Operators

Information

Modification

Calculation

Serialization

Public Types

Documentation

function
Geometry::Triangle::Triangle

Default constructor.

_{Defined in Geometry/Triangle.h:53}

function
Geometry::Triangle::Triangle

Default constructor with vertices.

_{Defined in Geometry/Triangle.h:56}

function
Geometry::Triangle::operator==

Equality operator.

_{Defined in Geometry/Triangle.h:63}

function
Geometry::Triangle::getVertexA

Return the first vertex.

_{Defined in Geometry/Triangle.h:71}

function
Geometry::Triangle::getVertexB

Return the second vertex.

_{Defined in Geometry/Triangle.h:75}

function
Geometry::Triangle::getVertexC

Return the third vertex.

_{Defined in Geometry/Triangle.h:79}

function
Geometry::Triangle::operator[]

array-access operator

_{Defined in Geometry/Triangle.h:84}

function
Geometry::Triangle::operator[]

const array-access operator

_{Defined in Geometry/Triangle.h:90}

function
Geometry::Triangle::getEdgeAB

Return the first edge.

_{Defined in Geometry/Triangle.h:96}

function
Geometry::Triangle::getEdgeBC

Return the second edge.

_{Defined in Geometry/Triangle.h:100}

function
Geometry::Triangle::getEdgeCA

Return the third edge.

_{Defined in Geometry/Triangle.h:104}

function
Geometry::Triangle::getEdgeBA

Return the first reverse edge.

_{Defined in Geometry/Triangle.h:109}

function
Geometry::Triangle::getEdgeCB

Return the second reverse edge.

_{Defined in Geometry/Triangle.h:113}

function
Geometry::Triangle::getEdgeAC

Return the third reverse edge.

_{Defined in Geometry/Triangle.h:117}

function
Geometry::Triangle::setVertexA

Assign the first vertex.

_{Defined in Geometry/Triangle.h:125}

function
Geometry::Triangle::setVertexB

Assign the second vertex.

_{Defined in Geometry/Triangle.h:129}

function
Geometry::Triangle::setVertexC

Assign the third vertex.

_{Defined in Geometry/Triangle.h:133}

function
Geometry::Triangle::calcArea

Return the area of the triangle.

Returns

The area.

_{Defined in Geometry/Triangle.h:146}

function
Geometry::Triangle::calcNormal

Return the unit length normal of this triangle.

Returns

Normal vector

_{Defined in Geometry/Triangle.h:156}

function
Geometry::Triangle::calcPoint

Calculate a point inside the triangle based on two barycentric coordinates with vertex A as origin.

Parameters

u

Barycentric coordinate in AB direction

v

Barycentric coordinate in AC direction

Returns

Point corresponding to the given barycentric coordinates

_{Defined in Geometry/Triangle.h:168}

function
Geometry::Triangle::calcBarycentricCoordinates

Calculate the barycentric coordinates of the given pointpwith reference to this triangle.

Parameters

p

Position in Cartesian coordinates that should be converted to barycentric coordinates

Returns

Barycentric coordinates

See also: http://science.kennesaw.edu/~plaval/math4490/barycentric.pdf

*           c
*           X
*          /.\
*         / . \
*        /  .  \      alpha = A_a / A
*       /A_b.A_a\     beta = A_b / A
*      /   .X.   \    gamma = A_c / A
*     /  .  p  .  \
*    /.    A_c    .\
*   X---------------X
*   a               b
*

_{Defined in Geometry/Triangle.h:192}

function
Geometry::Triangle::calcCircumcenter

Calculate the circumcenter of the triangle, i.e., the center of the sphere that is defined by the three triangle vertices.

See also: http://mathworld.wolfram.com/BarycentricCoordinates.html

Returns

Circumcenter of the triangle

_{Defined in Geometry/Triangle.h:222}

function
Geometry::Triangle::closestPoint

Return the point of this triangle that has minimum distance to a pointp.

Implementation taken from Christer Ericson: Real-Time Collision Detection. Morgan Kaufmann, 2004.

Parameters

p

Query position

barycentric

Barycentric coordinates of the point inside the triangle

Returns

Point of this triangle with minimum distance to the query position

*         c
*         X   result
*        / \  |      p
*       /   \ /  _,--X
*      /     X--´
*     /       \
*    /         \
*   X-----------X
*   a           b
*

_{Defined in Geometry/Triangle.h:254}

function
Geometry::Triangle::distanceSquared

Calculate the squared distance of a pointpto this triangle.

Parameters

p

Query position

Returns

Squared distance ofpto the triangle

*         c
*         X
*        / \         p
*       /   \    _,--X
*      /     X--´|
*     /       \  distance
*    /         \
*   X-----------X
*   a           b
*

_{Defined in Geometry/Triangle.h:333}

function
Geometry::Triangle::isDegenerate

Check if the triangle is degenerate. The check is done by testing if the area of the triangle is nearly zero.

Returns

trueif this is a degenerate triangle,falseotherwise.

_{Defined in Geometry/Triangle.h:344}

typedef
Geometry::Triangle::vec_t

_{Defined in Geometry/Triangle.h:38}

typedef
Geometry::Triangle::value_t

_{Defined in Geometry/Triangle.h:39}