public static Mesh generate(int triangle_budget)
{
Mesh original_mesh = TessellatedMesh.generate(Octahedron.octahedron_mesh(), triangle_budget, 1)[0];
Vector2[] uvs = new Vector2[original_mesh.vertices.Length];
for (int vertex = 0; vertex < original_mesh.vertices.Length; vertex += 1)
{
if (original_mesh.vertices[vertex] != Vector3.down) // almost every point uses polar coordinates from the underlying texture
{
float angle = Vector3.SignedAngle(Vector3.right, Vector3.ProjectOnPlane(original_mesh.vertices[vertex], Vector3.up).normalized, Vector3.up) * Mathf.Deg2Rad;
float radius = Vector3.Angle(Vector3.up, original_mesh.vertices[vertex]) * Mathf.Deg2Rad;
Vector2 uv = new Vector2(Mathf.Cos(angle), Mathf.Sin(angle));
uv *= (radius / Mathf.PI);
uv = uv / 2 + new Vector2(0.5f, 0.5f);
uvs[vertex] = uv;
}
else // for points at 2PI, the four corners are identical and need to be handled separately.
{
if (original_mesh.uv[vertex] == Vector2.one)
{
uvs[vertex] = (new Vector2(+1, +1)).normalized;
}
else if (original_mesh.uv[vertex] == Vector2.up)
{
uvs[vertex] = (new Vector2(-1, +1)).normalized;
}
else if (original_mesh.uv[vertex] == Vector2.zero)
{
uvs[vertex] = (new Vector2(-1, -1)).normalized;
}
else //if (original_mesh.uv[vertex] == Vector2.right)
{
uvs[vertex] = (new Vector2(+1, -1)).normalized;
}
}
}
original_mesh.uv = uvs;
return(original_mesh);
}
public static Mesh generate(int triangle_budget)
{
return(TessellatedMesh.generate(Octahedron.octahedron_mesh(), triangle_budget, 1)[0]);
}