Problem 60466. Generate a point cloud on an equilateral triangle 3

Tomoaki Takagi

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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 = [4 9 16 25 36 49 64 81 100];
The results for cases where H is 1 to 6 are as follows.
Ex)
[W,N] = lattice3(H=1) -> W = [0 0; 1 sqrt(3)/3; 1 sqrt(3); 2 0]; N = 4;
[W,N] = lattice3(H=2) -> W = [0 0; 0.5 sqrt(3)/6; 0.5 sqrt(3)/2; 1 0; 1 sqrt(4/3); 1 sqrt(3); 1.5 sqrt(3)/6; 1.5 sqrt(3)/2; 2 0]; N = 9;