> computed the location of each Voronoi vertex by solving a 4 X 4 > linear system with a solver from LAPACK. For the life of me, I > can't figure what you used to solve for the Voronoi verticesTo find the location of the center of a voronoi tetrahedron, you have to find the center of a sphere through the four vertices of the tetrahedron (A, B, C, D). The coordinates (x,y,z) of that point P are such that: AP = BP = CP = DP = radius of the sphere or in coordinate form: (a[0] - x)^2 + (a[1] - y)^2 + (a[2] - z)^2 = (b[0] - x)^2 + (b[1] - y)^2 + (b[2] - z)^2 = (c[0] - x)^2 + (c[1] - y)^2 + (c[2] - z)^2 = (d[0] - x)^2 + (d[1] - y)^2 + (d[2] - z)^2 These equations can be rewritten pairwise, in terms of x, y, z. taking the first and second lines above and solving yields: (2a[0]-2b[0])*x + (2a[1]-2b[1])*y + (2a[2]-2b[2])*z = = a[0]^2 + a[1]^2 + a[2]^2 - b[0]^2 - b[1]^2 - b[2]^2 You get 3 such equations that you can simplify and solve using LAPACK. Looking at my code, the equation that i solve with LAPACK seems to be: Ax = b where A is the 4x4 matrix: 2a[0] 2a[1] 2a[2] -1 2b[0] 2b[1] 2b[2] -1 2c[0] 2c[1] 2c[2] -1 2d[0] 2d[1] 2d[2] -1 and b is the vector: a[0]^2 + a[1]^2 + a[2]^2 b[0]^2 + b[1]^2 + b[2]^2 c[0]^2 + c[1]^2 + c[2]^2 d[0]^2 + d[1]^2 + d[2]^2 Please let me know if this is in the lines of what you're looking for. Good luck on your project :o) -manolis