# How does this function calculate normals of a mesh? [closed]

I have trouble understanding the following Javascript code.

It calculates, given a mesh described by its vertices vs and indices ind, the normals for each vertex. The mesh faces are a triangle list, and are oriented counterclockwise.

utilsObject.prototype.calculateNormals = function(vs, ind) {
var x = 0;
var y = 1;
var z = 2;
var ns = [];
// for each vertex, initialize normal x, normal y, normal z
for (var i = 0; i < vs.length; i++) {
ns[i] = 0.0;
}
// we work on triads of vertices to calculate normals so
// i = i+3 (i = indices index)
for (var i = 0; i < ind.length; i = i + 3) {
var v1 = [];
var v2 = [];
var normal = [];
// p1 - p0
v1[x] = vs[3 * ind[i + 1] + x] - vs[3 * ind[i] + x];
v1[y] = vs[3 * ind[i + 1] + y] - vs[3 * ind[i] + y];
v1[z] = vs[3 * ind[i + 1] + z] - vs[3 * ind[i] + z];
// p0 - p1
v2[x] = vs[3 * ind[i + 2] + x] - vs[3 * ind[i + 1] + x];
v2[y] = vs[3 * ind[i + 2] + y] - vs[3 * ind[i + 1] + y];
v2[z] = vs[3 * ind[i + 2] + z] - vs[3 * ind[i + 1] + z];
// cross product by Sarrus Rule
normal[x] = v1[y] * v2[z] - v1[z] * v2[y];
normal[y] = v1[z] * v2[x] - v1[x] * v2[z];
normal[z] = v1[x] * v2[y] - v1[y] * v2[x];
// update the normals of that triangle: sum of vectors
for (j = 0; j < 3; j++) {
ns[3 * ind[i + j] + x] = ns[3 * ind[i + j] + x] + normal[x];
ns[3 * ind[i + j] + y] = ns[3 * ind[i + j] + y] + normal[y];
ns[3 * ind[i + j] + z] = ns[3 * ind[i + j] + z] + normal[z];
}
}
}


How does this function work? For example, could you explain the use of indices in the instruction:

v1[x] = vs[3*ind[i+1]+x] - vs[3*ind[i]+x];


Rather than a high-level explanation, I am interested in the logic of the implementation details.

• What is it that you don't understand or want to do? This is hard to read because it's javascript without any sane abstractions... but at its core, it's only a cross product to compute the normal and addition to average the normals on shared vertices. Jan 10, 2017 at 19:13
• Seconded. I don't see a question so have no idea what it is you are asking about. Jan 10, 2017 at 19:32
• Never mind the first line and that is Javascript. I know what the code does. I know how to calculate normal in theory. But in practice, in the code, I do not understand the index management mechanism. I miss the sense of what is done.
– Nick
Jan 10, 2017 at 19:33
• Ok, I can't write an answer anymore but as best I can tell, vs is a vertex array and ns a corresponding normal array. Both are raw float arrays so they are indexed with i*3+0 (i*3+x in the code) for x component of vector number i, i*3+1 for y, i*3+2 for z. ind is an indirection array which contains vertex (and thus normal too) indices. It defines the triangle strips (the topology) within the arbitrary set of vertices. v1 and v2 are two edges of the triangle. Jan 11, 2017 at 0:07
• I have tried to reword the question to make it clearer. Feel free to edit or revert changes if I changed the intended meaning. Jan 11, 2017 at 6:51