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

• Created by Tomoaki Takagi
• Appears in Generate a point cloud

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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;

Solve

Solution Stats

38.46% Correct | 61.54% Incorrect

• 13 Solutions
• 4 Solvers

Last Solution submitted on Apr 09, 2025

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