MATLAB 还只会画爱心？，教你画水晶簇以及水晶爱心

创意来自于初中时做的硫酸铜爱心，硫酸铜是三斜晶型，这里为了方便绘制并没有采用同样的结构。

效果：
果然还是自然生长出的晶体更好看呜呜呜

坐标变换
想要画出水晶新要先会画晶体簇，画晶体簇要先会画一个晶体，画晶体我们需要这样一个结构：


我们首先需要一个到直线距离一定且垂线落点为cutPnt的点，这个非常好找，例如cutPnt=[x0,y0,z0];中轴线方向为V=[x1,y1,z1];到直线距离为L则如下点显然符合条件：

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

但是广找到一个点还不够，我们要找到四个而且每个点都是之前的点绕直线旋转pi/2得到的，这就要请出我们的点绕直线旋转变换矩阵：

。。。。可以说是超级复杂了：
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];
其中[u,v,w]是方向单位向量，[a,b,c]是轴初始点坐标

水晶簇绘制完整代码
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 for ii=1:4 jj=mod(ii,4)+1; fill33(Spnt,cornerPntSet(ii,:),
cornerPntSet(jj,:),alpha) fill33(Epnt,cornerPntSet(ii,:),cornerPntSet(jj,:),
alpha) end end function fill33(p1,p2,p3,alpha) fill3([p1(1),p2(1),p3(1)],[p1(2),
p2(2),p3(2)],[p1(3),p2(3),p3(3)],... [0 71 177]./255,'FaceAlpha',alpha,
'EdgeColor',[0 71 177]./255.*0.8,'EdgeAlpha',0.6,... '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

水晶心绘制完整代码
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+2; 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 for ii=1:4 jj=mod(ii,4)+1;
fill33(Spnt,cornerPntSet(ii,:),cornerPntSet(jj,:)) fill33(Epnt,cornerPntSet(ii,:
),cornerPntSet(jj,:)) end end function fill33(p1,p2,p3) fill3([p1(1),p2(1),p3(1)
],[p1(2),p2(2),p3(2)],[p1(3),p2(3),p3(3)],[0 71 177]./255.*1.03,... 'FaceAlpha',
0.2,'EdgeColor',[0 71 177]./255.*0.9,'EdgeAlpha',0.25,'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

• « 上一篇：动态规划（九章算法）详细学习
• » 下一篇：【算法】排序1：直接插入排序、希尔排序、选择排序、堆排序