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68 lines
1.8 KiB
68 lines
1.8 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2022-01-29 17:12:57
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% @LastEditTime: 2022-01-29 19:32:45
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% PARAs:
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% nodes: query_points to generate distance field, [n,3]
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% sp, ep: start and end points of mmc, [1,3]
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% t is the width
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%--------------------------
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function phi = signed_distance(nodes, sp, ep, t)
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rim = calculatevector(sp, ep, nodes);
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distm = dist2linevectorization(sp, ep, nodes);
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qm_sp = nodes - sp(:)';
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qm_ep = nodes - ep(:)';
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sp_norm = vecnorm(qm_sp,2,2);
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ep_norm = vecnorm(qm_ep,2,2);
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phi = distm - t;
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Index = (rim<=0);
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phi(Index) = sp_norm(Index) - t;
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Index = (rim>=1);
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phi(Index) = ep_norm(Index) - t;
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phi = -phi;
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% % test
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% scatter3(nodes(phi < 0, 1), nodes(phi < 0, 2), nodes(phi < 0, 3), 'k'); hold on;
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% scatter3(nodes(phi > 0, 1), nodes(phi > 0, 2), nodes(phi > 0, 3), 'filled', 'r'); hold on;
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%
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% x = [sp(1),ep(1)];
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% y = [sp(2),ep(2)];
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% z = [sp(3),ep(3)];
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% plot3(x',y',z','LineWidth',2, 'Color','b'); hold on;
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end
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function r = calculatevector(a,b,pm)
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% Input: a, start point of the line segment, 1x3 array
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% Input: b, end point of the line segment, 1x3 array
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% Input: pm, query point matrix, nx3
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% Output: r, distance matrix, nx1
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ap = pm - a(:)'; % n,3
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ab = b-a; % 1,3
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tempdot = sum(ap .* ab(:)', 2); % n,3
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r = tempdot ./ (norm(ab,2)^2);
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end
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function [dm] = dist2linevectorization(v1, v2, pm)
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% Input: v1, start point of the line segment, 1x3 array
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% Input: v2, end point of the line segment, 1x3 array
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% pm: query matrix, n x3 array
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m = -pm + v1(:)'; % n,3
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n = v1 - v2;
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nn = repmat(n(:)', size(pm,1), 1);
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tempcross = cross(nn', m'); % 3,n
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dm = vecnorm(tempcross', 2, 2) ./ norm(n,2);
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end
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