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Orientation Tests


Functions

template<typename T>
T geom::computeOrientationDeterminant (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c)
 Compute the orientation determinant.
template<typename T>
T geom::computeInCircleDeterminant (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c, const ads::FixedArray< 2, T > &d)
 Compute the in-circle determinant.
template<typename T>
bool geom::isInCircle (const ads::FixedArray< 2, T > &a, const ads::FixedArray< 2, T > &b, const ads::FixedArray< 2, T > &c, const ads::FixedArray< 2, T > &d)
 Return true if d is inside the circle with a, b, and c on its boundary.

Function Documentation

template<typename T>
T geom::computeInCircleDeterminant ( const ads::FixedArray< 2, T > &  a,
const ads::FixedArray< 2, T > &  b,
const ads::FixedArray< 2, T > &  c,
const ads::FixedArray< 2, T > &  d 
)

Compute the in-circle determinant.

Return the determinant of:

\[ \Gamma = \left[ \begin{array}{cccc} 1 & a_0 & a_1 & a_2\\ 1 & b_0 & b_1 & b_2\\ 1 & c_0 & c_1 & c_2\\ 1 & d_0 & d_1 & d_2 \end{array} \right] \]

where $a_2 = a_0^2 + a_1^2$. Point d lies inside the circle passing through a, b, and c if and only if $\mathrm{det}(\Delta) \cdot \mathrm{det}(\Gamma) < 0$.

See Geometry and Topology for Mesh Generation.

template<typename T>
T geom::computeOrientationDeterminant ( const ads::FixedArray< 2, T > &  a,
const ads::FixedArray< 2, T > &  b,
const ads::FixedArray< 2, T > &  c 
)

Compute the orientation determinant.

Return the determinant of:

\[ \Delta = \left[ \begin{array}{ccc} 1 & a_0 & a_1 \\ 1 & b_0 & b_1 \\ 1 & c_0 & c_1 \end{array} \right] \]

It is positive for a left turn, negative for a right turn, and zero if the points are colinear.

See Geometry and Topology for Mesh Generation.

template<typename T>
bool geom::isInCircle ( const ads::FixedArray< 2, T > &  a,
const ads::FixedArray< 2, T > &  b,
const ads::FixedArray< 2, T > &  c,
const ads::FixedArray< 2, T > &  d 
) [inline]

Return true if d is inside the circle with a, b, and c on its boundary.

Point d lies inside the circle passing through a, b, and c if and only if $\mathrm{det}(\Delta) \cdot \mathrm{det}(\Gamma) < 0$.

See Geometry and Topology for Mesh Generation.

Generated on Fri Aug 24 12:56:00 2007 for Computational Geometry Package by  doxygen 1.4.7