create_regular_grid

function [F, UV, res, edge_norms] = ...  create_regular_grid(xRes, yRes, xWrap, yWrap, near, far)% Creates list of triangle vertex indices for a rectangular domain,% optionally wrapping around in X/Y direction.%% Usage:%   [F, UV, res,edge_norms] = create_regular_grid(xRes, yRes, xWrap, yWrap)%% Input:%   xRes, yRes: number of points in X/Y direction%   wrapX, wrapY: wrap around in X/Y direction%   near, far: near and far should be fractions of one which control the%              pinching of the domain at the center and sides%% Output:%   UV: UV coordinates in interval [0,1]x[0,1]%   F : mesh connectivity (triangles)%   res: mesh resolution%% See corresponding paper: "Mixed finite elements for variational surface% modeling" by Alec Jacobson, Elif Tosun, Olga Sorkine, and Denis Zorin, SGP% 2010%% Copyright 2010, Alec Jacobson, Denis Zorin, Elif Tosun, NYU%if (nargin<3) wrapX=0; endif (nargin<4) wrapY=0; endif (nargin<5) overlap=0; end%res = [yRes, xRes];res_wrap = [yRes+yWrap, xRes+xWrap];%xSpace = linspace(0,1,xRes+xWrap); if (xWrap) xSpace = xSpace(1:end-1); end%ySpace = linspace(0,1,yRes+yWrap); if (yWrap) ySpace = ySpace(1:end-1); endxSpace = linspace(0,1,xRes+xWrap);ySpace = linspace(0,1,yRes+yWrap);[X, Y] = meshgrid(xSpace, ySpace);UV_wrap = [X(:), Y(:)];% Must perform pinch before edge_norms are takenif(exist('near') & exist('far'))  if(near>0 & far>0)  t = ( ...      UV_wrap(:,1).*(UV_wrap(:,1)<0.5)+ ...      (1-UV_wrap(:,1)).*(UV_wrap(:,1)>=0.5) ...    )/0.5;  t = 1-sin(t*pi/2+pi/2);  UV_wrap(:,2) = ...    far/2 + ...    near*(UV_wrap(:,2)-0.5).*(1-t) + ...    far*(UV_wrap(:,2)-0.5).*t;  else    %error('Pinch must be between 0 and 1');  endendidx_wrap = reshape(1:prod(res_wrap), res_wrap);v1_wrap = idx_wrap(1:end-1, 1:end-1); v1_wrap=v1_wrap(:)';v2_wrap = idx_wrap(1:end-1, 2:end  ); v2_wrap=v2_wrap(:)';v3_wrap = idx_wrap(2:end  , 1:end-1); v3_wrap=v3_wrap(:)';v4_wrap = idx_wrap(2:end  , 2:end  ); v4_wrap=v4_wrap(:)';F_wrap = [v1_wrap;v2_wrap;v3_wrap; v2_wrap;v4_wrap;v3_wrap];F_wrap = reshape(F_wrap, [3, 2*length(v1_wrap)])';% 三角形的索引% old way% edges = [F_wrap(:,1) F_wrap(:,2); F_wrap(:,2) F_wrap(:,3); F_wrap(:,3) F_wrap(:,1)];% edge_norms = sqrt(sum((UV_wrap(edges(:,1),:)-UV_wrap(edges(:,2),:)).^2,2));% edge_norms = reshape(edge_norms,size(F_wrap,1),3);% edges numbered same as opposite verticesedge_norms = [ ...  sqrt(sum((UV_wrap(F_wrap(:,2),:)-UV_wrap(F_wrap(:,3),:)).^2,2)) ...  sqrt(sum((UV_wrap(F_wrap(:,3),:)-UV_wrap(F_wrap(:,1),:)).^2,2)) ...  sqrt(sum((UV_wrap(F_wrap(:,1),:)-UV_wrap(F_wrap(:,2),:)).^2,2)) ...  ];%边长% correct indicesres = [yRes,xRes];idx = reshape(1:prod(res),res);if (xWrap) idx = [idx, idx(:,1)]; endif (yWrap) idx = [idx; idx(1,:)]; endidx_flat = idx(:);%重复右和下各重复一个像素% this might not be neccessary, could just rebuild UV like beforeUV = reshape(UV_wrap,[size(idx_wrap),2]);%分两层UV = UV(1:end-yWrap,1:end-xWrap,:);UV = reshape(UV,xRes*yRes,2);%   UV: UV coordinates in interval [0,1]x[0,1]， 没重复部分的UV坐标F = [idx_flat(F_wrap(:,1)),idx_flat(F_wrap(:,2)),idx_flat(F_wrap(:,3))];