520還在畫玫瑰？教你用MATLAB畫個玫瑰花球

效果如下：

原理

(資料圖片)

玫瑰繪制

要畫花球我們要先會繪制一朵花： 如何畫一朵花可以看看這篇：MATLAB 3D玫瑰花繪制

三維坐標變化

主要用下面的坐標變化方法：

正十二面體球

想像這里有一個正十二面體球，我們把每一面放上一朵花，也就是說每兩朵花之間夾角是pi-acos(-1/sqrt(5))，我們可以通過多次x軸旋轉和多次z軸旋轉將每朵花放到合適的角度

完整代碼

function roseBallclear;clc%曲面數據計算%==========================================================================[x,t]=meshgrid((0:24)./24,(0:0.5:575)./575.*20.*pi+4*pi);p=(pi/2)*exp(-t./(8*pi));change=sin(15*t)/150;u=1-(1-mod(3.6*t,2*pi)./pi).^4./2+change;y=2*(x.^2-x).^2.*sin(p);r=u.*(x.*sin(p)+y.*cos(p));h=u.*(x.*cos(p)-y.*sin(p));%顏色映射表%==========================================================================hMap=(h-min(min(h)))./(max(max(h))-min(min(h)));col=size(hMap,2);colorList=[0.0200    0.0400    0.3900         0    0.0900    0.5800         0    0.1300    0.6400    0.0200    0.0600    0.6900         0    0.0800    0.7900    0.0100    0.1800    0.8500         0    0.1300    0.9600    0.0100    0.2600    0.9900         0    0.3500    0.9900    0.0700    0.6200    1.0000    0.1700    0.6900    1.0000];% colorList=[0.2100    0.0900    0.3800%     0.2900    0.0700    0.4700%     0.4000    0.1100    0.4900%     0.5500    0.1600    0.5100%     0.7500    0.2400    0.4700%     0.8900    0.3200    0.4100%     0.9700    0.4900    0.3700%     1.0000    0.5600    0.4100%     1.0000    0.6900    0.4900%     1.0000    0.8200    0.5900%     0.9900    0.9200    0.6700%     0.9800    0.9500    0.7100];colorFunc=colorFuncFactory(colorList);dataMap=colorFunc(hMap");colorMap(:,:,1)=dataMap(:,1:col);colorMap(:,:,2)=dataMap(:,col+1:2*col);colorMap(:,:,3)=dataMap(:,2*col+1:3*col);    function colorFunc=colorFuncFactory(colorList)        xx=(0:size(colorList,1)-1)./(size(colorList,1)-1);        y1=colorList(:,1);y2=colorList(:,2);y3=colorList(:,3);        colorFunc=@(X)[interp1(xx,y1,X,"linear")",interp1(xx,y2,X,"linear")",interp1(xx,y3,X,"linear")"];    end%曲面旋轉及繪制%==========================================================================surface(r.*cos(t),r.*sin(t),h+0.35,"EdgeAlpha",0.05,...    "EdgeColor",[0 0 0],"FaceColor","interp","CData",colorMap)hold onsurface(r.*cos(t),r.*sin(t),-h-0.35,"EdgeAlpha",0.05,...    "EdgeColor",[0 0 0],"FaceColor","interp","CData",colorMap)Xset=r.*cos(t);Yset=r.*sin(t);Zset=h+0.35;yaw_z=pi*72/180;roll_x=pi-acos(-1/sqrt(5));R_z_2=[cos(yaw_z),-sin(yaw_z),0;    sin(yaw_z),cos(yaw_z),0;    0,0,1];R_z_1=[cos(yaw_z/2),-sin(yaw_z/2),0;    sin(yaw_z/2),cos(yaw_z/2),0;    0,0,1];R_x_2=[1,0,0;     0,cos(roll_x),-sin(roll_x);     0,sin(roll_x),cos(roll_x)]; [nX,nY,nZ]=rotateXYZ(Xset,Yset,Zset,R_x_2);surface(nX,nY,nZ,"EdgeAlpha",0.05,..."EdgeColor",[0 0 0],"FaceColor","interp","CData",colorMap)for k=1:4    [nX,nY,nZ]=rotateXYZ(nX,nY,nZ,R_z_2);    surface(nX,nY,nZ,"EdgeAlpha",0.05,...    "EdgeColor",[0 0 0],"FaceColor","interp","CData",colorMap)end   [nX,nY,nZ]=rotateXYZ(nX,nY,nZ,R_z_1);for k=1:5    [nX,nY,nZ]=rotateXYZ(nX,nY,nZ,R_z_2);    surface(nX,nY,-nZ,"EdgeAlpha",0.05,...    "EdgeColor",[0 0 0],"FaceColor","interp","CData",colorMap)end    %--------------------------------------------------------------------------    function [nX,nY,nZ]=rotateXYZ(X,Y,Z,R)        nX=zeros(size(X));        nY=zeros(size(Y));        nZ=zeros(size(Z));        for i=1:size(X,1)            for j=1:size(X,2)                v=[X(i,j);Y(i,j);Z(i,j)];                nv=R*v;                nX(i,j)=nv(1);                nY(i,j)=nv(2);                nZ(i,j)=nv(3);            end        end    end%axes屬性調整%==========================================================================ax=gca;grid onax.GridLineStyle="--";ax.LineWidth=1.2;ax.XColor=[1,1,1].*0.4;ax.YColor=[1,1,1].*0.4;ax.ZColor=[1,1,1].*0.4;ax.DataAspectRatio=[1,1,1];ax.DataAspectRatioMode="manual";ax.CameraPosition=[-6.5914  -24.1625   -0.0384];end

另： 補兩張古早之前做的折紙花球：

我好像在詭異配色的道路上越走越遠了。。。其實后面第二種配色還可以不是嘛 。。。 配色1：配色2：配色3：配色4：配色4的數據上下顛倒是這樣的：

這幾種顏色大家可以試試看，我真的盡力了。。。。 顏色數據：

colorList1=[0.2000    0.0800    0.4300    0.2000    0.1300    0.4600    0.2000    0.2100    0.5000    0.2000    0.2800    0.5300    0.2000    0.3700    0.5800    0.1900    0.4500    0.6200    0.2000    0.4800    0.6400    0.1900    0.5400    0.6700    0.1900    0.5700    0.6900    0.1900    0.7500    0.7800    0.1900    0.8000    0.8100];colorList2=[0.1300    0.1000    0.1600    0.2000    0.0900    0.2000    0.2800    0.0800    0.2300    0.4200    0.0800    0.3000    0.5100    0.0700    0.3400    0.6600    0.1200    0.3500    0.7900    0.2200    0.4000    0.8800    0.3500    0.4700    0.9000    0.4500    0.5400    0.8900    0.7800    0.7900];colorList3=[0.3200    0.3100    0.7600    0.3800    0.3400    0.7600    0.5300    0.4200    0.7500    0.6400    0.4900    0.7300    0.7200    0.5500    0.7200    0.7900    0.6100    0.7100    0.9100    0.7100    0.6800    0.9800    0.7600    0.6700];colorList4=[0.9500    0.2300    0.6600    0.7500    0.2100    0.6000    0.6200    0.2000    0.5700    0.4500    0.1800    0.5200    0.3200    0.2100    0.5200    0.2700    0.3100    0.6000    0.2500    0.3600    0.6400    0.1900    0.4800    0.7400];

后注：兩個面夾角為pi-acos(-1/sqrt(5))，同平面旋轉為了五等分要轉72度，因而yaw_z，和roll_x取值并不相同，代碼和原文描述已經做出相應更改。