如何用Matlab画出以下这个方程 (x^2 + (9/4)*y^2 + z^2 - 1)^3 - x^2*z^3 - (9/80)y^2*z^3 = 0 matlab如何画出下面的图像 (x^2+9/4*...
matlab\u5982\u4f55\u753b\u51fa\u4e0b\u9762\u7684\u56fe\u50cf (x^2+9/4*y^2+z^2-1)^3-x^2*z^3-9/80*y^2*z^3=0f=@(x,y,z)(x.^2+9/4*y.^2+z.^2-1).^3-x.^2.*z.^3-9/80*y.^2.*z.^3 implicitmesh(f,[-5 5],150)-----------------------------function h=implicitmesh(f,xlimit,ylimit,zlimit,gd)%implicitmesh(f,span,gd):\u753b\u9690\u51fd\u6570\u66f2\u9762f(x,y,z)=0\u7684\u7f51\u683c\u56fe,% \u5404\u5750\u6807\u8303\u56f4\u5747\u9650\u5b9a\u5728span=[lb,ub],% \u7f51\u683c\u6570\u4e3agd\uff0c\u9ed8\u8ba4\u4e3a25if nargin==2 ylimit=xlimit;zlimit=xlimit;gd=25;elseif nargin==3 gd=ylimit;ylimit=xlimit;zlimit=xlimit;elseif nargin==4 gd=25;elseif nargin==5else error('Error in input arguments')endx=linspace(xlimit(1),xlimit(2),gd);y=linspace(ylimit(1),ylimit(2),gd);z=linspace(zlimit(1),zlimit(2),gd);[x,y,z]=meshgrid(x,y,z);val=f(x,y,z);[f,v]=isosurface(x,y,z,val,0);if isempty(f) warning('There is no graph in the range.'); p=[];else newplot; p=patch('Faces',f,'Vertices',v,'CData',v(:,3),'facecolor','w','EdgeColor','flat'); isonormals(x,y,z,val,p);view(3);grid onendif nargout==0else h=p;end\u5411\u5de6\u8f6c|\u5411\u53f3\u8f6c
f=@(x,y,z)(x.^2+9/4*y.^2+z.^2-1).^3-x.^2.*z.^3-9/80*y.^2.*z.^3
implicitmesh(f,[-5
5],150)
-----------------------------
function
h=implicitmesh(f,xlimit,ylimit,zlimit,gd)
%implicitmesh(f,span,gd):\u753b\u9690\u51fd\u6570\u66f2\u9762f(x,y,z)=0\u7684\u7f51\u683c\u56fe,
%
\u5404\u5750\u6807\u8303\u56f4\u5747\u9650\u5b9a\u5728span=[lb,ub],
%
\u7f51\u683c\u6570\u4e3agd\uff0c\u9ed8\u8ba4\u4e3a25
if
nargin==2
ylimit=xlimit;zlimit=xlimit;gd=25;
elseif
nargin==3
gd=ylimit;ylimit=xlimit;zlimit=xlimit;
elseif
nargin==4
gd=25;
elseif
nargin==5
else
error('Error
in
input
arguments')
end
x=linspace(xlimit
(1),xlimit
(2),gd);
y=linspace(ylimit(1),ylimit(2),gd);
z=linspace(zlimit(1),zlimit(2),gd);
[x,y,z]=meshgrid(x,y,z);val=f(x,y,z);
[f,v]=isosurface(x,y,z,val,0);
if
isempty(f)
warning('There
is
no
graph
in
the
range.');
p=[];
else
newplot;
p=patch('Faces',f,'Vertices',v,'CData',v(:,3),'facecolor','w','EdgeColor','flat');
isonormals(x,y,z,val,p);view
(3);grid
on
end
if
nargout==0
else
h=p;
end
这就是一个高次的三元方程, 在空间上对应平面图形
要画出来需要点技巧, 先解出函数表达式来, 再画.
命令如下:
Y=solve('(x^2 + (9/4)*y^2 + z^2 - 1)^3 - x^2*z^3 - (9/80)*y^2*z^3 = 0','y')
ezmesh(Y(1),200);
hold on
ezmesh(Y(2),200)
axis auto
axis equal
还有几个解应该是复空间里面的, 画不出来图形.
x=-2:0.03:2;y=-1:0.01:1;z=-1:0.01:1.5;
[x,y,z]=meshgrid(x,y,z);
f=(x.^2+(9/4)*y.^2+z.^2-1).^3-x.^2.*z.^3-(9/80)*y.^2.*z.^3;
p=patch(isosurface(x,y,z,f,0));
set(p,'Facecolor','r','EdgeColor','none');
daspect([1 1 1]);
view(3);
axis off
camlight;
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