demo: Implement connectivity analysis for meshlets

Since whether meshlet is connected or not is a very important criteria
for how well it will do in a hierarchical clusterization process, we now
compute the number of connected components in meshlet demo and count the
number of meshlets with more than one.

Notably, for now we do this analysis using indices; this means we do
connectivity analysis on original, non-positional, topology, and on some
geometry that looks visually connected we will naturally have many
disconnected meshlets.

demo/main.cpp

@@ -917,6 +917,18 @@ void shadow(const Mesh& mesh)
  (end - start) * 1000);
 }
 
+static int follow(int* parents, int index)
+{
+ while (index != parents[index])
+ {
+ int parent = parents[index];
+ parents[index] = parents[parent];
+ index = parent;
+ }
+
+ return index;
+}
+
 void meshlets(const Mesh& mesh, bool scan)
 {
  const size_t max_vertices = 64;
@@ -952,6 +964,7 @@ void meshlets(const Mesh& mesh, bool scan)
  double avg_vertices = 0;
  double avg_triangles = 0;
  size_t not_full = 0;
+ size_t not_connected = 0;
 
  for (size_t i = 0; i < meshlets.size(); ++i)
  {
@@ -960,14 +973,37 @@ void meshlets(const Mesh& mesh, bool scan)
  avg_vertices += m.vertex_count;
  avg_triangles += m.triangle_count;
  not_full += m.vertex_count < max_vertices;
+
+ // union-find vertices to check if the meshlet is connected
+ int parents[max_vertices];
+ for (unsigned int j = 0; j < m.vertex_count; ++j)
+ parents[j] = int(j);
+
+ for (unsigned int j = 0; j < m.triangle_count * 3; ++j)
+ {
+ int v0 = meshlet_triangles[m.triangle_offset + j];
+ int v1 = meshlet_triangles[m.triangle_offset + j + (j % 3 == 2 ? -2 : 1)];
+
+ v0 = follow(parents, v0);
+ v1 = follow(parents, v1);
+
+ parents[v0] = v1;
+ }
+
+ int roots = 0;
+ for (unsigned int j = 0; j < m.vertex_count; ++j)
+ roots += follow(parents, j) == int(j);
+
+ assert(roots != 0);
+ not_connected += roots > 1;
  }
 
  avg_vertices /= double(meshlets.size());
  avg_triangles /= double(meshlets.size());
 
- printf("Meshlets%c: %d meshlets (avg vertices %.1f, avg triangles %.1f, not full %d) in %.2f msec\n",
+ printf("Meshlets%c: %d meshlets (avg vertices %.1f, avg triangles %.1f, not full %d, not connected %d) in %.2f msec\n",
  scan ? 'S' : ' ',
- int(meshlets.size()), avg_vertices, avg_triangles, int(not_full), (end - start) * 1000);
+ int(meshlets.size()), avg_vertices, avg_triangles, int(not_full), int(not_connected), (end - start) * 1000);
 
  float camera[3] = {100, 100, 100};