Problem with Patch, trying to fill a surface based on points.

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luc
luc 2015-4-29
回答： luc 2015-5-1
I got an output of a few X Y and Z points, which I want to create into a patch object.
The output however, is more like a sliced potato.
Copy the code below, note that only the last bit about XXX, YYY and ZZZ give the coordinates. any idea how to create a nice consistent shape?
Thanks in advance guys!
PS; Related question; How can I plot a patch object? Say I created a patch object A=patch(x,y,z,1)
Now, after editing it (A.Vertices=[..,..,..]) I want to plot the object in figure(X). What would be the command to get it there?
clc;clear all;close all
r=20;
x=4;
y=6;
z=8;
x0=3;
y0=8;
z0=8;
FOV=pi;
x1=[ x/(x^2 + y^2 + z^2)^(1/2), y/(x^2 + y^2 + z^2)^(1/2), z/(x^2 + y^2 + z^2)^(1/2)]; %<--klopt.
yz=null(x1).'; %find the null spaces of normalised V
xyz=[x1;yz]; %The rows of this matrix are the axes of a normalised
U=xyz(2,:)';
W=xyz(3,:)';%U and W are a ortogonal normal basis for normalised A
a=U(1);b=U(2);c=U(3);d=W(1);e=W(2);f=W(3);
n=1;
tic
for FOV=0:0.1*pi:FOV
for alpha=0:0.2*pi:2*pi
XXX(n)=x0 - ((x/(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*(d*cos(alpha) + a*sin(alpha)))*(a*d*x*x0 + a*d*y*y0 + a*d*z*z0 - a*d*(abs(y + tan(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(z + tan(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(a*d*x + a*tan(FOV/2)*cos(conj(alpha))*abs(d)^2*(x^2 + y^2 + z^2)^(1/2) + d*tan(FOV/2)*sin(conj(alpha))*abs(a)^2*(x^2 + y^2 + z^2)^(1/2))^2/(abs(a)^2*abs(d)^2*(x^2 + y^2 + z^2)))^(1/2)*(x^2 + y^2 + z^2)^(1/2)*(r^2 - x0^2 - y0^2 - z0^2 + (abs(a)^2*abs(d)^2*(a*d*x*x0*cos(FOV/2) + a*d*y*y0*cos(FOV/2) + a*d*z*z0*cos(FOV/2) + a*x0*sin(FOV/2)*cos(conj(alpha))*abs(d)^2*(x^2 + y^2 + z^2)^(1/2) + d*x0*sin(FOV/2)*sin(conj(alpha))*abs(a)^2*(x^2 + y^2 + z^2)^(1/2) + a*d*y0*sin(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + a*d*z0*sin(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + a*d*y0*sin(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2) + a*d*z0*sin(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2))^2)/(a^2*d^2*(abs(a*d*x*cos(FOV/2) + a*sin(FOV/2)*cos(conj(alpha))*abs(d)^2*(x^2 + y^2 + z^2)^(1/2) + d*sin(FOV/2)*sin(conj(alpha))*abs(a)^2*(x^2 + y^2 + z^2)^(1/2))^2 + abs(y*cos(FOV/2) + sin(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + sin(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2))^2*abs(a)^2*abs(d)^2 + abs(z*cos(FOV/2) + sin(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + sin(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2))^2*abs(a)^2*abs(d)^2)))^(1/2) + a*x0*tan(FOV/2)*cos(conj(alpha))*abs(d)^2*(x^2 + y^2 + z^2)^(1/2) + d*x0*tan(FOV/2)*sin(conj(alpha))*abs(a)^2*(x^2 + y^2 + z^2)^(1/2) + a*d*y0*tan(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + a*d*z0*tan(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + a*d*y0*tan(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2) + a*d*z0*tan(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2)))/(a*d*(abs(y + tan(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(z + tan(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(a*d*x + a*tan(FOV/2)*cos(conj(alpha))*abs(d)^2*(x^2 + y^2 + z^2)^(1/2) + d*tan(FOV/2)*sin(conj(alpha))*abs(a)^2*(x^2 + y^2 + z^2)^(1/2))^2/(abs(a)^2*abs(d)^2*(x^2 + y^2 + z^2)))*(x^2 + y^2 + z^2)^(1/2));
YYY(n)= y0 - ((y/(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*(e*cos(alpha) + b*sin(alpha)))*(b*e*x*x0 + b*e*y*y0 + b*e*z*z0 - b*e*(abs(x + tan(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(z + tan(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(b*e*y + b*tan(FOV/2)*cos(conj(alpha))*abs(e)^2*(x^2 + y^2 + z^2)^(1/2) + e*tan(FOV/2)*sin(conj(alpha))*abs(b)^2*(x^2 + y^2 + z^2)^(1/2))^2/(abs(b)^2*abs(e)^2*(x^2 + y^2 + z^2)))^(1/2)*(x^2 + y^2 + z^2)^(1/2)*(r^2 - x0^2 - y0^2 - z0^2 + (abs(b)^2*abs(e)^2*(b*e*x*x0*cos(FOV/2) + b*e*y*y0*cos(FOV/2) + b*e*z*z0*cos(FOV/2) + b*y0*sin(FOV/2)*cos(conj(alpha))*abs(e)^2*(x^2 + y^2 + z^2)^(1/2) + e*y0*sin(FOV/2)*sin(conj(alpha))*abs(b)^2*(x^2 + y^2 + z^2)^(1/2) + b*e*z0*sin(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2) + b*e*x0*sin(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + b*e*z0*sin(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + b*e*x0*sin(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2))^2)/(b^2*e^2*(abs(b*e*y*cos(FOV/2) + b*sin(FOV/2)*cos(conj(alpha))*abs(e)^2*(x^2 + y^2 + z^2)^(1/2) + e*sin(FOV/2)*sin(conj(alpha))*abs(b)^2*(x^2 + y^2 + z^2)^(1/2))^2 + abs(x*cos(FOV/2) + sin(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + sin(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2))^2*abs(b)^2*abs(e)^2 + abs(z*cos(FOV/2) + sin(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + sin(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2))^2*abs(b)^2*abs(e)^2)))^(1/2) + b*y0*tan(FOV/2)*cos(conj(alpha))*abs(e)^2*(x^2 + y^2 + z^2)^(1/2) + e*y0*tan(FOV/2)*sin(conj(alpha))*abs(b)^2*(x^2 + y^2 + z^2)^(1/2) + b*e*z0*tan(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2) + b*e*x0*tan(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + b*e*z0*tan(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + b*e*x0*tan(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2)))/(b*e*(abs(x + tan(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(z + tan(FOV/2)*cos(conj(alpha))*conj(f)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(c)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(b*e*y + b*tan(FOV/2)*cos(conj(alpha))*abs(e)^2*(x^2 + y^2 + z^2)^(1/2) + e*tan(FOV/2)*sin(conj(alpha))*abs(b)^2*(x^2 + y^2 + z^2)^(1/2))^2/(abs(b)^2*abs(e)^2*(x^2 + y^2 + z^2)))*(x^2 + y^2 + z^2)^(1/2));
ZZZ(n)= z0 - ((z/(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*(f*cos(alpha) + c*sin(alpha)))*(c*f*x*x0 + c*f*y*y0 + c*f*z*z0 - c*f*(abs(x + tan(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(y + tan(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(c*f*z + c*tan(FOV/2)*cos(conj(alpha))*abs(f)^2*(x^2 + y^2 + z^2)^(1/2) + f*tan(FOV/2)*sin(conj(alpha))*abs(c)^2*(x^2 + y^2 + z^2)^(1/2))^2/(abs(c)^2*abs(f)^2*(x^2 + y^2 + z^2)))^(1/2)*(x^2 + y^2 + z^2)^(1/2)*(r^2 - x0^2 - y0^2 - z0^2 + (abs(c)^2*abs(f)^2*(c*f*x*x0*cos(FOV/2) + c*f*y*y0*cos(FOV/2) + c*f*z*z0*cos(FOV/2) + c*z0*sin(FOV/2)*cos(conj(alpha))*abs(f)^2*(x^2 + y^2 + z^2)^(1/2) + f*z0*sin(FOV/2)*sin(conj(alpha))*abs(c)^2*(x^2 + y^2 + z^2)^(1/2) + c*f*y0*sin(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2) + c*f*x0*sin(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + c*f*y0*sin(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + c*f*x0*sin(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2))^2)/(c^2*f^2*(abs(c*f*z*cos(FOV/2) + c*sin(FOV/2)*cos(conj(alpha))*abs(f)^2*(x^2 + y^2 + z^2)^(1/2) + f*sin(FOV/2)*sin(conj(alpha))*abs(c)^2*(x^2 + y^2 + z^2)^(1/2))^2 + abs(x*cos(FOV/2) + sin(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + sin(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2))^2*abs(c)^2*abs(f)^2 + abs(y*cos(FOV/2) + sin(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + sin(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2))^2*abs(c)^2*abs(f)^2)))^(1/2) + c*z0*tan(FOV/2)*cos(conj(alpha))*abs(f)^2*(x^2 + y^2 + z^2)^(1/2) + f*z0*tan(FOV/2)*sin(conj(alpha))*abs(c)^2*(x^2 + y^2 + z^2)^(1/2) + c*f*y0*tan(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2) + c*f*x0*tan(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + c*f*y0*tan(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + c*f*x0*tan(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2)))/(c*f*(abs(x + tan(FOV/2)*cos(conj(alpha))*conj(d)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(a)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(y + tan(FOV/2)*cos(conj(alpha))*conj(e)*(x^2 + y^2 + z^2)^(1/2) + tan(FOV/2)*sin(conj(alpha))*conj(b)*(x^2 + y^2 + z^2)^(1/2))^2/(x^2 + y^2 + z^2) + abs(c*f*z + c*tan(FOV/2)*cos(conj(alpha))*abs(f)^2*(x^2 + y^2 + z^2)^(1/2) + f*tan(FOV/2)*sin(conj(alpha))*abs(c)^2*(x^2 + y^2 + z^2)^(1/2))^2/(abs(c)^2*abs(f)^2*(x^2 + y^2 + z^2)))*(x^2 + y^2 + z^2)^(1/2));
n=n+1;
end
end
Patch=patch(XXX,YYY,ZZZ,1)
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luc
luc 2015-4-29
编辑：luc 2015-4-29
Okay, thanks for the advice :) I'll post the XXX YYY and ZZZ code then.
To answer pfd's questions: 1) Yes it is supposed to look like a dome
2) Patch draws a filled 2D polygon, but it draws the 2D polygon in 2D. If I would add enough points the shape will eventually look just like a dome. So I want to draw this complex 3D outer shell. out of multiple triangles.
Maybe a more general question would be; I have a set of points in X Y and Z, I want to use patch to draw a "terrain plot" using those points.
3) Thanks, I will.
luc
luc 2015-4-29
Added the matrices, so now the question boils down to:
I want to create a dome shape from these points using the patch command, what would be the best way to start?
Data attached.
Patch(XXX,YYY,ZZZ,1)

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采纳的回答

luc
luc 2015-5-1
I figured it out, I use a loop to get some double points in my patch object. So each ring gets a double ring. I then add all the ring points.
Here's the code.
for FOV=0:0.1*pi:FOV
for alpha=0:0.1*pi:2*pi
XXX=code
YYY=code
ZZZ=code
n=n+1;
end
end
scatter3(XXX,YYY,ZZZ)
hold on
[nietnodig,sizefov]=size([0:0.1*pi:FOV]);
[nietnodig,sizealpha]=size(0:0.1*pi:2*pi);
m=1;
for m=1:sizefov-1
XXX_s=XXX(((m-1)*sizealpha)+1:(m+1)*sizealpha);
YYY_s=YYY(((m-1)*sizealpha)+1:(m+1)*sizealpha);
ZZZ_s=ZZZ(((m-1)*sizealpha)+1:(m+1)*sizealpha);
Patch_s=patch(XXX_s,YYY_s,ZZZ_s,1);
if m==1
fv_combined1=Patch_s
end
nv1=length(fv_combined1.Vertices);
fv_combined1.Vertices=[fv_combined1.Vertices;Patch_s.Vertices];
fv_combined1.Faces=[fv_combined1.Faces; Patch_s.Faces+nv1];
end

更多回答（1 个）

pfb
pfb 2015-4-29
Not sure you can do that with the patch command "as it is".
You have to create some sort of mesh.
Something nicer is obtained with trisurf or trimesh.
tri = delaunay(XXX,YYY);
trisurf(tri,XXX,YYY,ZZZ);
It's not optimal yet, but I guess it is closer to what you actually want. I think it's also a matter of ordering of the points.
  1 个评论
luc
luc 2015-5-1
Hmm.. any idea on how to order the points? I was thinking of doing a mesh with a few double points...

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