The input is the iteration parameter H.
The output is a point cloud W involving N points.
W is N uniformly distributed points on an equilateral triangle.
The side length of an equilateral triangle is 2.
The relationship between H and N is as follows:
- H = [1 2 3 4 5 6 7 8 9];
- N = [6 18 36 60 90 126 168 216 270];
The results for cases where H is 1 to 6 are as follows.
Ex)
- [W,N] = lattice4(H=1) -> W = [1/3 sqrt(3)/3; 2/3 0; 2/3 sqrt(4/3); 4/3 0; 4/3 sqrt(4/3); 5/3 sqrt(3)/3]; N = 6;
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A very inspirational problem!!
When I saw this one, I started looking at the "holes" as much as the points retained in the cloud. I re-worked lattice 2, and worked all from 4 to 8 before posting any.
I certainly plan to review at least Tomoaki Takagi's and Rahul's solutions for lessons before going to other problems.