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41 lines
949 B
41 lines
949 B
3 years ago
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%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2022-01-24 13:48:58
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% @LastEditTime: 2022-01-24 14:32:52
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% Compute the barycentric weights for a point p in an n-gon Q
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% Assumes p is strictly within Q and the vertices qj of Q are ordered.
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% assumes weight w = 1
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% PARAS:
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% polygon: ordered vertices qj of Q
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%--------------------------
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function w = compute_barycentric(polygon, p)
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n = size(polygon, 1);
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w = zeros(n, 1);
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wsum = 0;
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for j = 0:n-1
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prev = mod(j + n - 1, n) + 1;
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next = mod(j + 1, n) + 1;
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jj = j+1;
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qj = polygon(jj, :);
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qp = polygon(prev, :);
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qn = polygon(next, :);
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ct = cotangent(p, qj, qp) + cotangent(p, qj, qn);
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w(jj) = ct / (norm(p - qj)^2 + 1e-9);
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wsum = wsum + w(jj);
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end
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w = w ./ wsum;
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end
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function ct = cotangent(a, b, c)
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ba = a-b;
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bc = c-b;
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ct = dot(bc, ba) / (norm(cross(bc, ba)) + 1e-9);
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end
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