MATLAB复原三阶魔方

%% 块定义 % 块八顶点定义（魔方每一个小块上的8个顶点的相对坐标） blockVertices = [ 1,-1,-1; 1, 1,-1;-1, 1,-1;-1,-1,-1;... 1,-1, 1; 1, 1, 1;-1, 1, 1;-1,-1, 1]*0.95; % 块六面顶点索引（在上次的基础上优化了一下，用索引表示） blockFace{1} = [1,2,3,4]; blockFace{2} = [1,2,6,5]; blockFace{3} = [2,3,7,6]; blockFace{4} = [3,4,8,7]; blockFace{5} = [4,1,5,8]; blockFace{6} = [5,6,7,8]; %% 26块中心定义（先用半径1写，完事儿*2，简单快捷，以后想变大直接改） % 6轴 axisPosList = [0, 0,-1; 1, 0, 0; 0, 1, 0; -1, 0, 0; 0,-1, 0; 0, 0, 1]*2; % 8角 cornerPosList = [1,-1,-1; 1, 1,-1; -1, 1,-1; -1,-1,-1;... 1,-1, 1; 1, 1, 1; -1, 1, 1; -1,-1, 1]*2; % 12棱 edgePosList = [1, 0,-1; 0, 1,-1;-1, 0,-1; 0,-1,-1;... 1, 1, 0;-1, 1, 0;-1,-1, 0; 1,-1, 0; 1, 0, 1; 0, 1, 1;-1, 0, 1; 0,-1, 1]*2; %% 显示一下 figure plot3(axisPosList(:,1),axisPosList(:,2),axisPosList(:,3),'K*'),hold on plot3(edgePosList(:,1),edgePosList(:,2),edgePosList(:,3),'bo') plot3(cornerPosList(:,1),cornerPosList(:,2),cornerPosList(:,3),'r<') axis equal axis([-1,1,-1,1,-1,1]*4) grid on view([2,1,1]) %% 颜色与不透明度 白 蓝 红 绿 橙 黄 color = {[1,1,1],[0,0.2,0.8],[0.8,0,0],[0,0.8,0.2],... [1,0.4,0],[1,1,0],[0.1,0.1,0.1]}; colorAlpha = [1,1,1,1,1,1,0.7]; %% 26块6面上色 % 轴块属性初始化 axisBlock = cell(6,1); for n = 1:6 axisBlock{n}.RotateMatrix = [1,0,0;0,1,0;0,0,1]; axisBlock{n}.position = axisPosList(n,:); axisBlock{n}.color = ones(1,6)*7; axisBlock{n}.color(n) = n; end % 角块属性初始化 cornerBlock = cell(8,1); for n = 1:8 cornerBlock{n}.RotateMatrix = [1,0,0;0,1,0;0,0,1]; cornerBlock{n}.position = cornerPosList(n,:); cornerBlock{n}.color = ones(1,6)*7; end cornerBlock{1}.color([1,2,5]) = [1,2,5]; cornerBlock{2}.color([1,2,3]) = [1,2,3]; cornerBlock{3}.color([1,3,4]) = [1,3,4]; cornerBlock{4}.color([1,4,5]) = [1,4,5]; cornerBlock{5}.color([6,2,5]) = [6,2,5]; cornerBlock{6}.color([6,2,3]) = [6,2,3]; cornerBlock{7}.color([6,3,4]) = [6,3,4]; cornerBlock{8}.color([6,4,5]) = [6,4,5]; % 棱块属性初始化 edgeBlock = cell(12,1); for n = 1:12 edgeBlock{n}.RotateMatrix = [1,0,0;0,1,0;0,0,1]; edgeBlock{n}.position = edgePosList(n,:); edgeBlock{n}.color = ones(1,6)*7; end edgeBlock{1}.color([1,2]) = [1,2]; edgeBlock{2}.color([1,3]) = [1,3]; edgeBlock{3}.color([1,4]) = [1,4]; edgeBlock{4}.color([1,5]) = [1,5]; edgeBlock{5}.color([2,3]) = [2,3]; edgeBlock{6}.color([3,4]) = [3,4]; edgeBlock{7}.color([4,5]) = [4,5]; edgeBlock{8}.color([5,2]) = [5,2]; edgeBlock{9}.color([6,2]) = [6,2]; edgeBlock{10}.color([6,3]) = [6,3]; edgeBlock{11}.color([6,4]) = [6,4]; edgeBlock{12}.color([6,5]) = [6,5]; %魔方块的位置 blockIdx.axisIdx=[1,2,3,4,5,6]; blockIdx.cornerIdx=[1,2,3,4,5,6,7,8]; blockIdx.edgeIdx=[1,2,3,4,5,6,7,8,9,10,11,12]; %%操作 %FRULDBfruldbSMExyz [blockIdx, axisBlock, cornerBlock, edgeBlock]=operation(6, ... blockIdx,axisBlock,cornerBlock,edgeBlock) [blockIdx, axisBlock, cornerBlock, edgeBlock]=operation(12, ... blockIdx,axisBlock,cornerBlock,edgeBlock) % 轴块 for n = 1:6 for f = 1:6 V = (axisBlock{n}.position+blockVertices(blockFace{f},:))*axisBlock{n}.RotateMatrix; C = color{axisBlock{n}.color(f)}; A = colorAlpha(axisBlock{n}.color(f)); h = patch('Faces',[1 2 3 4],'Vertices',V,'FaceColor',C,... 'FaceAlpha',A); end end % 棱 for n = 1:12 for f = 1:6 V = (edgeBlock{n}.position+blockVertices(blockFace{f},:))*edgeBlock{n}.RotateMatrix; C = color{edgeBlock{n}.color(f)}; A = colorAlpha(edgeBlock{n}.color(f)); h = patch('Faces',[1 2 3 4],'Vertices',V,'FaceColor',C,... 'FaceAlpha',A); end end % 角块 for n = 1:8 for f = 1:6 V = (cornerBlock{n}.position+blockVertices(blockFace{f},:))*cornerBlock{n}.RotateMatrix; C = color{cornerBlock{n}.color(f)}; A = colorAlpha(cornerBlock{n}.color(f)); h = patch('Faces',[1 2 3 4],'Vertices',V,'FaceColor',C,... 'FaceAlpha',A); end end function R = getRotateMatrix(alpha,beta,gamma) % alpha,beta,gamma 为1或-1，分别表示顺时针转和逆时针转 alpha = -pi/2*alpha; beta = -pi/2*beta; gamma = -pi/2*gamma; Rx = [1,0,0;0,cos(alpha),-sin(alpha);0,sin(alpha),cos(alpha)]; Ry = [cos(beta),0,sin(beta);0,1,0;-sin(beta),0,cos(beta)]; Rz = [cos(gamma),-sin(gamma),0;sin(gamma),cos(gamma),0;0,0,1]; R = (Rx*Ry*Rz)'; end function [blockIdx, axisBlock, cornerBlock, edgeBlock] = operation(opt, ... blockIdx, axisBlock, cornerBlock, edgeBlock) switch opt case 1 % F R = getRotateMatrix(1,0,0); for n = blockIdx.cornerIdx([1,2,6,5]) cornerBlock{n}.RotateMatrix = cornerBlock{n}.RotateMatrix*R; end for n = blockIdx.edgeIdx([1,5,9,8]) edgeBlock{n}.RotateMatrix = edgeBlock{n}.RotateMatrix*R; end blockIdx.cornerIdx([1,2,6,5]) = blockIdx.cornerIdx([2,6,5,1]) ; blockIdx.edgeIdx([1,5,9,8]) = blockIdx.edgeIdx([5,9,8,1]); case -1 % F' R = getRotateMatrix(-1,0,0); for n = blockIdx.cornerIdx([1,2,6,5]) cornerBlock{n}.RotateMatrix = cornerBlock{n}.RotateMatrix*R; end for n = blockIdx.edgeIdx([1,5,9,8]) edgeBlock{n}.RotateMatrix = edgeBlock{n}.RotateMatrix*R; end blockIdx.cornerIdx([1,2,6,5]) = blockIdx.cornerIdx([5,1,2,6]) ; blockIdx.edgeIdx([1,5,9,8]) = blockIdx.edgeIdx([8,1,5,9]); case 2 % R R = getRotateMatrix(0,1,0); for n = blockIdx.cornerIdx([2,3,7,6]) cornerBlock{n}.RotateMatrix = cornerBlock{n}.RotateMatrix*R; end for n = blockIdx.edgeIdx([2,6,10,5]) edgeBlock{n}.RotateMatrix = edgeBlock{n}.RotateMatrix*R; end blockIdx.cornerIdx([2,3,7,6]) = blockIdx.cornerIdx([3,7,6,2]) ; blockIdx.edgeIdx([2,6,10,5]) = blockIdx.edgeIdx([6,10,5,2]); case -2 % R' R = getRotateMatrix(0,-1,0); for n = blockIdx.cornerIdx([2,3,7,6]) cornerBlock{n}.RotateMatrix = cornerBlock{n}.RotateMatrix*R; end for n = blockIdx.edgeIdx([2,6,10,5]) edgeBlock{n}.RotateMatrix = edgeBlock{n}.RotateMatrix*R; end blockIdx.cornerIdx([2,3,7,6]) = blockIdx.cornerIdx([6,2,3,7]) ; blockIdx.edgeIdx([2,6,10,5]) = blockIdx.edgeIdx([5,2,6,10]); case 3 % U R = getRotateMatrix(0,0,1); for n = blockIdx.cornerIdx([5,6,7,8]) cornerBlock{n}.RotateMatrix = cornerBlock{n}.RotateMatrix*R; end for n = blockIdx.edgeIdx([9,10,11,12]) edgeBlock{n}.RotateMatrix = edgeBlock{n}.RotateMatrix*R; end blockIdx.cornerIdx([5,6,7,8]) = blockIdx.cornerIdx([6,7,8,5]) ; blockIdx.edgeIdx([9,10,11,12]) = blockIdx.edgeIdx([10,11,12,9]); case -3 % U' R = getRotateMatrix(0,0,-1); for n = blockIdx.cornerIdx([5,6,7,8]) cornerBlock{n}.RotateMatrix = cornerBlock{n}.RotateMatrix*R; end for n = blockIdx.edgeIdx([9,10,11,12]) edgeBlock{n}.RotateMatrix = edgeBlock{n}.RotateMatrix*R; end blockIdx.cornerIdx([5,6,7,8]) = blockIdx.cornerIdx([8,5,6,7]) ; blockIdx.edgeIdx([9,10,11,12]) = blockIdx.edgeIdx([12,9,10,11]); case 4 % B R = getRotateMatrix(-1,0,0); for n = blockIdx.cornerIdx([3,4,8,7]) cornerBlock{n}.RotateMatrix = cornerBlock{n}.RotateMatrix*R; end for n = blockIdx.edgeIdx([3,7,11,6]) edgeBlock{n}.RotateMatrix = edgeBlock{n}.RotateMatrix*R; end blockIdx.cornerIdx([3,4,8,7]) = blockIdx.cornerIdx([4,8,7,3]) ; blockIdx.edgeIdx([3,7,11,6]) = blockIdx.edgeIdx([7,11,6,3]); case -4 % B' R = g