I am following a tutorial where a cube is transformed into a sphere and I want to understand why this happens. I understand that ...
- each vertex can be described as a vector
- the position node gives me the x,y,z coordinates of the cube's vertices
- the length node gives me the length of each vector
- the divide node divedes 1 by the vectors length
- the coordinates of every vertex is scaled by the factor 1/vector length
- when multiplying a vector by a floa, each element of the vector is multiplied by the factor
but why does this operation lead to a sphere when applied to all of the cubes vertices? is there an INTUITIVE way to understand that? Or is this just a formula to be remembered?
1/vector_lengthforces every vertex to have magnitude 1.0 -- i.e., this is now a "unit sphere" (every vertex is exactly distance 1 from (0,0,0)). Multiplying it by some additional factor then changes this from a unit sphere into a sphere with a smaller or larger radius, depending on chosen factor. All calculations involved are continuous, so this transformation looks 'smooth'. $\endgroup$