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

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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)
  4 Comments
luc
luc on 29 Apr 2015
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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Accepted Answer

luc
luc on 1 May 2015
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

More Answers (1)

pfb
pfb on 29 Apr 2015
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 Comment
luc
luc on 1 May 2015
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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