Problem 60491. Generate a point cloud on an equilateral triangle 6

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 = [7 10 14 19 24 30 37 44 52];
The results for cases where H is 1 to 6 are as follows.
Ex)
[W,N] = lattice6(H=1) -> W = [0 0; 2/3 0; 2/3 sqrt(4/3); 1 sqrt(3)/3; 1 sqrt(3); 5/3 sqrt(3)/3; 2 0]; N = 7;
[W,N] = lattice6(H=2) -> W = [0 0; 1/2 0; 1/2 sqrt(3)/2; 3/4 sqrt(3)/4; 3/4 sqrt(3)*3/4; 5/4 sqrt(3)/4; 5/4 sqrt(3)*3/4; 3/2 0; 3/2 sqrt(3)/2; 2 0]; N = 10;