I'm looking for the most minimized equation to find the center coordinates and the radius of a tetrahedron circumsphere given four 3D points.
What I found on the internet mainly deal with the circum sphere of a flat 3D triangle, or some rough mathematical definitions, or some very single case such as regular tetrahedrons. Anyway I managed to find the equation below but I missed something :
-> -> -> let d1, d2, and d3 three vectors of any face of the triangle : | d1x d1y d1z | | x | | d1^2 | 2 * | d2x d2y d2z | * | y | = | d2^2 | | d3x d3y d3z | | z | | d3^2 |
My knowledge in this field has its limits but I think I can handle matrices and vector operations. But is the right part of the equation the square of the norm of each vectors ? (which are into a vector). Is the equation valid ? Is it just the writer who lazely forgot to write |d1|^2 ? Or Is it a common way to define some mathematical property.
PS : It's for a Delaunay Triangulation implementation. The equation (number 9) is in the following link : https://www2.mps.mpg.de/homes/daly/CSDS/t4h/tetra.htm