How to find triangles third vertex C(x,y,z) if we known:
1. other two vertices A(x,y,z), B(x,y,z)
2. lengths of all triangles sides
3. the triangle's normal
I understand how to solve it in a graph, but can't find an analytical solution.
Thanks, for the answer. Yes #3 is normal or the triangle. We can't use solution with circle because i need three coordinates for C point. I have found one solution, but it is not very elegant:
1. calculate angle between (AC and AB) and (BA and BC) in 2D - where we can easily calculate C coordinates (by the low of cosines)
2. rotate AB vector about normal with two angles - which give us two vectors(lines)
3. find point of intersection on these two lines - it will be our C point.
You did not understand Plato's question. What do you mean by "the normal to a triangle". Do you mean the normal to the plane determined by the triangle? I think Plato was assuming you were working in a given plane. Of course, being given the normal to the plane means you are given a plane.
But what I would do is this: suppose we are given points and as well as normal vector <X, Y, Z> and are told that the length of AC is , the length of BC is . Let C be the unknown point .
Then we seek the intersection of three surfaces: the sphere , the sphere , and the plane . That gives three equations to solve for x, y, and z.