explain icosphere number of points calculation without citing BY-NC l…

…icense

crates/bevy_render/src/mesh/shape/icosphere.rs

@@ -26,9 +26,36 @@ impl Default for Icosphere {
 impl From<Icosphere> for Mesh {
     fn from(sphere: Icosphere) -> Self {
         if sphere.subdivisions >= 80 {
-            // https://oeis.org/A005901
-            let subdivisions = sphere.subdivisions + 1;
-            let number_of_resulting_points = (subdivisions * subdivisions * 10) + 2;
+            /*
+            Number of triangles:
+            N = 20
+
+            Number of edges:
+            E = 30
+
+            Number of vertices:
+            V = 12
+
+            Number of points within a triangle (triangular numbers):
+            inner(s) = (s^2 + s) / 2
+
+            Number of points on an edge:
+            edges(s) = s
+
+            Add up all vertices on the surface:
+            vertices(s) = edges(s) * E + inner(s - 1) * N + V
+
+            Expand and simplify. Notice that the triangular number formula has roots at -1, and 0, so translating it one to the right fixes it.
+            subdivisions(s) = 30s + 20((s^2 - 2s + 1 + s - 1) / 2) + 12
+            subdivisions(s) = 30s + 10s^2 - 10s + 12
+            subdivisions(s) = 10(s^2 + 2s) + 12
+
+            Factor an (s + 1) term to simplify in terms of calculation
+            subdivisions(s) = 10(s + 1)^2 + 12 - 10
+            resulting_vertices(s) = 10(s + 1)^2 + 2
+            */
+            let temp = sphere.subdivisions + 1;
+            let number_of_resulting_points = temp * temp * 10 + 2;
 
             panic!(
                 "Cannot create an icosphere of {} subdivisions due to there being too many vertices being generated: {}. (Limited to 65535 vertices or 79 subdivisions)",