参考材料 | 文献:
代码参考：Heart Model for Valentine’s Day
创意来源：Matlab 可以做一些什么有意思的事？
参考文献：Wolfram MathWorld Heart Surface
代码运行效果:
完整代码:
function heartSudoku2
sizeTheta=30;
sizeFai=40;
theta=linspace(0,pi,sizeTheta)';
nudge=0.0001; % used to avoid the operlapping
fai=linspace(0+nudge,pi/2-nudge,round(sizeFai/4));
a=9/4;
b=9/80;
A=1+(a-1)*(sin(theta).^2)*(sin(fai).^2);
B=(sin(theta).^2.*cos(theta).^3) * (1+(b-1)*(sin(fai).^2));
rou = zeros(size(A));
for iLoop=1:numel(A)
curA=A(iLoop);
curB=B(iLoop);
% this is the polar coordinates version of the sextic equation found on
% http://mathworld.wolfram.com/HeartSurface.html
polyFactors=[curA^3,-curB,-3*curA^2,0,3*curA,0,-1];
solutions=roots(polyFactors);
realRou=real(solutions(abs(imag(solutions))<1e-9));
rou(iLoop)=realRou(realRou>0);
end
% x,y,z for the quater of whole heart
x=rou.*(sin(theta)*cos(fai));
y=rou.*(sin(theta)*sin(fai));
z=rou.*(cos(theta)*ones(size(fai)));
% x,y,z for the whole heart
cordX=[x,-fliplr(x),-x,fliplr(x)];
cordY=[y,fliplr(y),-y,-fliplr(y)];
cordZ=[z,fliplr(z),z,fliplr(z)];
heartSudokuFig=figure('units','pixels',...
'position',[200 50 630 630],...
'Numbertitle','off',...
'menubar','none',...
'resize','off',...
'name','heart sudoku',...
'color',[0.99 0.99 0.99]);
for i=1:3
for j=1:3
heartSudokuAxes(i,j)=axes('Units','pixels',...
'parent',heartSudokuFig,...
'Position',[(i-1)*210-25,(j-1)*210-25-10,210+50,210+50],...
'Color',[0.99 0.99 0.99],...
'Box','on', ...
'XLim',[-1.28,1.28],'YLim',[-1.28,1.28],'ZLim',[-1.28,1.28],...
'XColor','none','YColor','none','ZColor','none');
hold(heartSudokuAxes(i,j),'on')
camtarget([0, 0, 0]);
view(30,20);
end
end
markerColor=[248 150 170]./255;
lineColor=[248 150 170]./255;
lineWidth=0.8;
%[1 1]=====================================================================
for iLoop=1:3:size(cordX,1)
plot3(heartSudokuAxes(1,1),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(1,1),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=1:4:size(cordX,2)
plot3(heartSudokuAxes(1,1),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
%[1 2]=====================================================================
for iLoop=1:3:size(cordX,1)
plot3(heartSudokuAxes(1,2),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(1,2),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),'color',...
lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=1:size(cordX,2)
plot3(heartSudokuAxes(1,2),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),'color',...
lineColor,'LineStyle','-','LineWidth',lineWidth);
end
%[1 3]=====================================================================
for iLoop=1:size(cordX,1)
plot3(heartSudokuAxes(1,3),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(1,3),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=1:size(cordX,2)
plot3(heartSudokuAxes(1,3),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
%[2 1]=====================================================================
for iLoop=[2 8 15 25]
plot3(heartSudokuAxes(2,1),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(2,1),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=1:2:size(cordX,2)
plot3(heartSudokuAxes(2,1),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
%[2 2]=====================================================================
for iLoop=1:2:size(cordX,1)
plot3(heartSudokuAxes(2,2),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(2,2),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=1:2:size(cordX,2)
plot3(heartSudokuAxes(2,2),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
%[2 3]=====================================================================
for iLoop=[1 3 5 9 20 25 27]
plot3(heartSudokuAxes(2,3),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(2,3),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=1:size(cordX,2)
plot3(heartSudokuAxes(2,3),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
%[3 1]=====================================================================
for iLoop=[2 6 8 15 ]
plot3(heartSudokuAxes(3,1),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(3,1),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=[8 9 18 21 30 32 35 40]
plot3(heartSudokuAxes(3,1),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
%[3 2]=====================================================================
for iLoop=[8 12 15 18 23 25]
plot3(heartSudokuAxes(3,2),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(3,2),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=[8 9 18 21 25 28 30 32 35 40]
plot3(heartSudokuAxes(3,2),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
%[3 3]=====================================================================
for iLoop=[8 18 25]
plot3(heartSudokuAxes(3,3),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'Marker','.','MarkerSize',3.5,'MarkerEdgeColor',markerColor,'LineStyle','none');
plot3(heartSudokuAxes(3,3),cordX(iLoop,:),cordY(iLoop,:),cordZ(iLoop,:),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
for iLoop=1:3:40
plot3(heartSudokuAxes(3,3),cordX(:,iLoop),cordY(:,iLoop),cordZ(:,iLoop),...
'color',lineColor,'LineStyle','-','LineWidth',lineWidth);
end
end
注：
由于各心形的形状要体现随机性，故各个心形的数据是单独编辑的，如果想要获得规整的心形，不妨采用如下方法：
效果：
另：
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Copyright © 2009, Xin Zhao
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