Re: Divide a triangle into N^2 sub-triangles, where N is the subdivision frequency?
In Reply to: Divide a triangle into N^2 sub-triangles, where N is the subdivision frequency? posted by Sean on March 09, 2005 at 02:53:59:
: Is there any subdivision algorithm for dividing a triangle into N^2 sub-triangles, where N is the subdivision frequency? The algorithm works as follows. For example, given N=7, each edge of a triangle is divided into 7 pieces by inserting 6 new points on each edge. Then, we can get 49 sub-triangles.
Yes, there is. Imagine an equaliteral triangle. Add your vertices on the edges. Now draw horizontal lines across the triangle between vertices on the left and right sides. Build a triangle strip for each quad shape that results. The number of triangles in each strip is 1, 3, 5, 7, ...
In general, the total number of triangles is Sum_i=0...n 1+2i where n is the number of vertices inserted on the edges. Some basic math shows that this sum is (n+1)^2, which yields the desired number of triangles. I'm not sure if you were asking for existence of such an algorithm or pseudo-code. Certainly this text shows that such an algorithm exists and gives vague hints on implementation.