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Zhaoxu Liu / slandarer
Última actividad el 3 de Mzo. de 2024

How To Draw a Crystal Heart In MATLAB

The creativity comes from the copper sulfate crystal heart made in junior high school. Copper sulfate is a triclinic crystal, and the same structure was not used here for convenience in drawing.

Part 1. Coordinate transformation

To draw a crystal heart, one must first be able to draw crystal clusters. To draw a crystal cluster, one must first be able to draw a crystal. To draw a crystal, we need this kind of structure:

We first need a point with a certain distance from the straight line and a perpendicular point of cutPnt, which is very easy to find, for example, cutPnt=[x0, y0, z0]; The direction of the central axis is V=[x1, y1, z1]; If the distance to the straight line is L, the following points clearly meet the conditions:

v2=[z1,z1,-x1-y1];
v2=v2./norm(v2).*L;
pnt=cutPnt+v2;

But finding only one point is not enough. We need to find four points, and each point is obtained by rotating the previous point around a straight line by

degrees. Therefore, we need to obtain our point rotation transformation matrix around a straight line

quite complex,right?

rotateMat=[u^2+(v^2+w^2)*cos(theta)       ,  u*v*(1-cos(theta))-w*sin(theta),  u*w*(1-cos(theta))+v*sin(theta),  (a*(v^2+w^2)-u*(b*v+c*w))*(1-cos(theta))+(b*w-c*v)*sin(theta);
           u*v*(1-cos(theta))+w*sin(theta),  v^2+(u^2+w^2)*cos(theta)       ,  v*w*(1-cos(theta))-u*sin(theta),  (b*(u^2+w^2)-v*(a*u+c*w))*(1-cos(theta))+(c*u-a*w)*sin(theta);
           u*w*(1-cos(theta))-v*sin(theta),  v*w*(1-cos(theta))+u*sin(theta),  w^2+(u^2+v^2)*cos(theta)       ,  (c*(u^2+v^2)-w*(a*u+b*v))*(1-cos(theta))+(a*v-b*u)*sin(theta);
           0                              ,  0                              ,  0                              ,  1];

Where [u, v, w] is the directional unit vector, and [a, b, c] is the initial coordinate of the axis:

Part 2. Crystal Cluster Drawing

function crystall
hold on
for i=1:50
    len=rand(1)*8+5;
    tempV=rand(1,3)-0.5;
    tempV(3)=abs(tempV(3));
    tempV=tempV./norm(tempV).*len;
    tempEpnt=tempV;
    drawCrystal([0 0 0],tempEpnt,pi/6,0.8,0.1,rand(1).*0.2+0.2)
    disp(i)
end
ax=gca;
ax.XLim=[-15,15];
ax.YLim=[-15,15];
ax.ZLim=[-2,15];
grid on
ax.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=[-67.6287 -204.5276   82.7879];
    function drawCrystal(Spnt,Epnt,theta,cl,w,alpha)
       %plot3([Spnt(1),Epnt(1)],[Spnt(2),Epnt(2)],[Spnt(3),Epnt(3)])
       mainV=Epnt-Spnt;
       cutPnt=cl.*(mainV)+Spnt;
       cutV=[mainV(3),mainV(3),-mainV(1)-mainV(2)];
       cutV=cutV./norm(cutV).*w.*norm(mainV);
       cornerPnt=cutPnt+cutV;
       cornerPnt=rotateAxis(Spnt,Epnt,cornerPnt,theta);
       cornerPntSet(1,:)=cornerPnt';
       for ii=1:3
           cornerPnt=rotateAxis(Spnt,Epnt,cornerPnt,pi/2);
           cornerPntSet(ii+1,:)=cornerPnt';
       end
       F = [1,3,4;1,4,5;1,5,6;1,6,3;...
           2,3,4;2,4,5;2,5,6;2,6,3];
       V = [Spnt;Epnt;cornerPntSet];
       patch('Faces',F,'Vertices',V,'FaceColor',[0 71 177]./255,...
           'FaceAlpha',alpha,'EdgeColor',[0 71 177]./255.*0.8,...
           'EdgeAlpha',0.6,'LineWidth',0.5,'EdgeLighting',...
           'gouraud','SpecularStrength',0.3)
    end
    function newPnt=rotateAxis(Spnt,Epnt,cornerPnt,theta)
        V=Epnt-Spnt;V=V./norm(V);
        u=V(1);v=V(2);w=V(3);
        a=Spnt(1);b=Spnt(2);c=Spnt(3);
        cornerPnt=[cornerPnt(:);1];
        
        rotateMat=[u^2+(v^2+w^2)*cos(theta)       ,  u*v*(1-cos(theta))-w*sin(theta),  u*w*(1-cos(theta))+v*sin(theta),  (a*(v^2+w^2)-u*(b*v+c*w))*(1-cos(theta))+(b*w-c*v)*sin(theta);
                   u*v*(1-cos(theta))+w*sin(theta),  v^2+(u^2+w^2)*cos(theta)       ,  v*w*(1-cos(theta))-u*sin(theta),  (b*(u^2+w^2)-v*(a*u+c*w))*(1-cos(theta))+(c*u-a*w)*sin(theta);
                   u*w*(1-cos(theta))-v*sin(theta),  v*w*(1-cos(theta))+u*sin(theta),  w^2+(u^2+v^2)*cos(theta)       ,  (c*(u^2+v^2)-w*(a*u+b*v))*(1-cos(theta))+(a*v-b*u)*sin(theta);
                   0                              ,  0                              ,  0                              ,  1];
        
        newPnt=rotateMat*cornerPnt;
        newPnt(4)=[];
    end
end

Part 3. Drawing of Crystal Heart

function crystalHeart
clc;clear;close all
hold on
% drawCrystal([1,1,1],[3,3,3],pi/6,0.8,0.14)
sep=pi/8;
t=[0:0.2:sep,sep:0.02:pi-sep,pi-sep:0.2:pi+sep,pi+sep:0.02:2*pi-sep,2*pi-sep:0.2:2*pi];
x=16*sin(t).^3;
y=13*cos(t)-5*cos(2*t)-2*cos(3*t)-cos(4*t);
z=zeros(size(t));
plot3(x,y,z,'Color',[186,110,64]./255,'LineWidth',1)
for i=1:length(t)
    for j=1:6
        len=rand(1)*2.5+1.5;
        tempV=rand(1,3)-0.5;
        tempV=tempV./norm(tempV).*len;
        tempSpnt=[x(i),y(i),z(i)];
        tempEpnt=tempV+tempSpnt;
        drawCrystal(tempSpnt,tempEpnt,pi/6,0.8,0.14)
        disp([i,j])
    end
end
ax=gca;
ax.XLim=[-22,22];
ax.YLim=[-20,20];
ax.ZLim=[-10,10];
grid on
ax.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';
    function drawCrystal(Spnt,Epnt,theta,cl,w)
       %plot3([Spnt(1),Epnt(1)],[Spnt(2),Epnt(2)],[Spnt(3),Epnt(3)])
       mainV=Epnt-Spnt;
       cutPnt=cl.*(mainV)+Spnt;
       cutV=[mainV(3),mainV(3),-mainV(1)-mainV(2)];
       cutV=cutV./norm(cutV).*w.*norm(mainV);
       cornerPnt=cutPnt+cutV;
       cornerPnt=rotateAxis(Spnt,Epnt,cornerPnt,theta);
       cornerPntSet(1,:)=cornerPnt';
       for ii=1:3
           cornerPnt=rotateAxis(Spnt,Epnt,cornerPnt,pi/2);
           cornerPntSet(ii+1,:)=cornerPnt';
       end
       F = [1,3,4;1,4,5;1,5,6;1,6,3;...
           2,3,4;2,4,5;2,5,6;2,6,3];
       V = [Spnt;Epnt;cornerPntSet];
       patch('Faces',F,'Vertices',V,'FaceColor',[0 71 177]./255,...
           'FaceAlpha',0.2,'EdgeColor',[0 71 177]./255.*0.9,...
           'EdgeAlpha',0.25,'LineWidth',0.01,'EdgeLighting',...
           'gouraud','SpecularStrength',0.3)
    end
    function newPnt=rotateAxis(Spnt,Epnt,cornerPnt,theta)
        V=Epnt-Spnt;V=V./norm(V);
        u=V(1);v=V(2);w=V(3);
        a=Spnt(1);b=Spnt(2);c=Spnt(3);
        cornerPnt=[cornerPnt(:);1];
        
        rotateMat=[u^2+(v^2+w^2)*cos(theta)       ,  u*v*(1-cos(theta))-w*sin(theta),  u*w*(1-cos(theta))+v*sin(theta),  (a*(v^2+w^2)-u*(b*v+c*w))*(1-cos(theta))+(b*w-c*v)*sin(theta);
                   u*v*(1-cos(theta))+w*sin(theta),  v^2+(u^2+w^2)*cos(theta)       ,  v*w*(1-cos(theta))-u*sin(theta),  (b*(u^2+w^2)-v*(a*u+c*w))*(1-cos(theta))+(c*u-a*w)*sin(theta);
                   u*w*(1-cos(theta))-v*sin(theta),  v*w*(1-cos(theta))+u*sin(theta),  w^2+(u^2+v^2)*cos(theta)       ,  (c*(u^2+v^2)-w*(a*u+b*v))*(1-cos(theta))+(a*v-b*u)*sin(theta);
                   0                              ,  0                              ,  0                              ,  1];
        
        newPnt=rotateMat*cornerPnt;
        newPnt(4)=[];
    end
end

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Tips & Tricks

Zhaoxu Liu / slandarer
Última actividad el 2 de Mzo. de 2024

How To Draw A Rose Ball In MATLAB

So, how to draw a roseball just like this ?

To begin with, we need to know how to draw a single rose in MATLAB:

function drawrose
set(gca,'CameraPosition',[2 2 2])
hold on
grid on
[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));
surface(r.*cos(t),r.*sin(t),h,'EdgeAlpha',0.1,...
    'EdgeColor',[0 0 0],'FaceColor','interp')
end

Tts pretty easy, Now we are trying to dye it the desired color:

function drawrose
set(gca,'CameraPosition',[2 2 2])
hold on
grid on
[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));
map=[0.9176    0.9412    1.0000
    0.8353    0.8706    0.9922
    0.8196    0.8627    0.9804
    0.7020    0.7569    0.9412
    0.5176    0.5882    0.9255
    0.3686    0.4824    0.9412
    0.3059    0.4000    0.9333
    0.2275    0.3176    0.8353
    0.1216    0.2275    0.6471];
Xi=1:size(map,1);Xq=linspace(1,size(map,1),100);
map=[interp1(Xi,map(:,1),Xq,'linear')',...
     interp1(Xi,map(:,2),Xq,'linear')',...
     interp1(Xi,map(:,3),Xq,'linear')'];
surface(r.*cos(t),r.*sin(t),h,'EdgeAlpha',0.1,...
    'EdgeColor',[0 0 0],'FaceColor','interp')
colormap(map)
end

I try to take colors from real roses and interpolate them to make them more realistic

Then, how can I put these colorful flowers on to a ball ?

We need to place the drawn flowers on each face of the polyhedron sphere through coordinate transformation. Here, we use a regular dodecahedron:

Move the flower using the following rotation formula:

We place a flower on each plane, which means that the angle between every two flowers is

degrees. We can place each flower at the appropriate angle through multiple x-axis rotations and multiple z-axis rotations. The code is as follows:

function roseBall(colorList)
%曲面数据计算
%==========================================================================
[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));
%颜色映射表
%==========================================================================
hMap=(h-min(min(h)))./(max(max(h))-min(min(h)));
col=size(hMap,2);
if nargin<1
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];
end
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
%曲面旋转及绘制
%==========================================================================
surface(r.*cos(t),r.*sin(t),h+0.35,'EdgeAlpha',0.05,...
    'EdgeColor',[0 0 0],'FaceColor','interp','CData',colorMap)
hold on
surface(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=72*pi/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属性调整
%==========================================================================
ax=gca;
grid on
ax.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

TRY DIFFERENT COLORS !!

colorList1=[0.2000    0.0800    0.4300
2000    0.1300    0.4600
2000    0.2100    0.5000
2000    0.2800    0.5300
2000    0.3700    0.5800
1900    0.4500    0.6200
2000    0.4800    0.6400
1900    0.5400    0.6700
1900    0.5700    0.6900
1900    0.7500    0.7800
1900    0.8000    0.8100
];
colorList2=[0.1300    0.1000    0.1600
2000    0.0900    0.2000
2800    0.0800    0.2300
4200    0.0800    0.3000
5100    0.0700    0.3400
6600    0.1200    0.3500
7900    0.2200    0.4000
8800    0.3500    0.4700
9000    0.4500    0.5400
8900    0.7800    0.7900
];
colorList3=[0.3200    0.3100    0.7600
3800    0.3400    0.7600
5300    0.4200    0.7500
6400    0.4900    0.7300
7200    0.5500    0.7200
7900    0.6100    0.7100
9100    0.7100    0.6800
9800    0.7600    0.6700
];
colorList4=[0.2100    0.0900    0.3800
2900    0.0700    0.4700
4000    0.1100    0.4900
5500    0.1600    0.5100
7500    0.2400    0.4700
8900    0.3200    0.4100
9700    0.4900    0.3700
0000    0.5600    0.4100
0000    0.6900    0.4900
0000    0.8200    0.5900
9900    0.9200    0.6700
9800    0.9500    0.7100];

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Tips & Tricks

Zhaoxu Liu / slandarer
Última actividad el 5 de Mzo. de 2024

rose bouquet for MATLABer

code is here

https://www.mathworks.com/matlabcentral/fileexchange/154496-rose-bouquet

You can also see the animated version of the competition here

https://www.mathworks.com/matlabcentral/communitycontests/contests/6/entries/14747

rose bouquet

rose bouquet by slandarer

www.mathworks.com

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