Function: bezout (p1, p2, x) an alternative to the resultant command. It returns a matrix. determinant of this matrix is the desired resultant. Each face is a vector containing the indices (0 based) of 3 points from the points vector. faces (introduced in version 2014.03) Vector of faces which collectively enclose the solid. This enhancement was developed by Efi Fogel, who also developed a new decomposition strategy, which can handle polygons with holes, essentially enabling the computation of Minkowski sum of two polygons with holes using the decomposition approach.
These functions are typically considerably slower than their counterparts that employ the convolution approach. Examples: (%i1) divide (x + y, x — y, x); (%o1) [1, 2 y] (%i2) divide (x + y, x — y); (%o2) [- 1, 2 x] Note that y is the main variable in the second example. Computing Minkowski Sum using Convolutions The function template minkowski_sum_2(P, Q) accepts two polygons \( P\) and \( Q\) and computes their Minkowski sum \( S = P \oplus Q\) using the convolution approach. Polyhedron with badly oriented polygons Succinct description of a ‘Polyhedron’ * Points define all of the points/vertices in the shape. * Faces is a list of flat polygons that connect up the points/vertices.
When center is true, the cube is centered on the origin. The convolution cycle induces an arrangement with three faces, whose winding numbers are indicated. Points which describe a single face must all be on the same plane. convexity Integer. Filtering Out Holes If a hole in one polygon is relatively small compared to the other polygon, the hole is irrelevant for the computation of \(P\oplus Q \) bfhhm-epsph-15; It implies that the hole can be removed (that is, filled up) before the main computation starts.