%CONSTRUCT_TriangulationInfo%

useful information about the triangulation

retrieve some information on the triangulation of some given alias. The use can ask for involving a norm.

begin_construct{} "whatever" = CONSTRUCT(%CONSTRUCT_TriangulationInfo%, identifier, m_norm, "aliasConcerned" ) # number triangles end_construct

begin_construct{} "Ntria" = CONSTRUCT(%CONSTRUCT_TriangulationInfo%, 1, 1, "*" ) # number triangles "Ltria_mean" = CONSTRUCT(%CONSTRUCT_TriangulationInfo%, 2, 1, "*" ) # mean triangle length due to a given norm represented by the exponent m_norm "Ltria_min" = CONSTRUCT(%CONSTRUCT_TriangulationInfo%, 3, 1, "*" ) # min triangle length "Ltria_max" = CONSTRUCT(%CONSTRUCT_TriangulationInfo%, 4, 1, "*" ) # max triangle length "Ltria_min_mean" = CONSTRUCT(%CONSTRUCT_TriangulationInfo%, 5, 1, "*" ) # mean triangle length "Ltria_max_mean" = CONSTRUCT(%CONSTRUCT_TriangulationInfo%, 6, 1, "*" ) # mean triangle length end_construct

Ltria_mean = \( \sqrt{ 2 \cdot \left( \frac{ \sum \limits_{i=1...N} {{ A_i }^{m\_norm}} }{\sum \limits_i^N{1}} \right)^{\frac{1}{m\_norm}} }\) Ltria_min = \( \min \limits_{i=1...N} \left( { Lmin_i } \right)\) Ltria_max = \( \max \limits_{i=1...N} \left( { Lmax_i } \right)\) Ltria_min_mean = \( \left( \frac{ \sum \limits_{i=1...N} {{ Lmin_i }^{m\_norm}} }{\sum \limits_{i=1...N}{1}} \right)^{\frac{1}{m\_norm}}\) Ltria_max_mean = \( \left( \frac{ \sum \limits_{i=1...N} {{ Lmax_i }^{m\_norm}} }{\sum \limits_{i=1...N}{1}} \right)^{\frac{1}{m\_norm}}\) where: \( N\) is the number of triangles in the given patch of "aliasConcerned", \( Lmin_i\) is the smallest side length of triangle \( i\) \( Lmax_i\) is the biggest side length of triangle \( i\) \( m\_norm\) defines the norm to be used. if 1: classical average . if going towards infinity: classical maximums norm. If going to 0: classical minimums norm.