Convert 3D polygon into homogeneous matrix

2 views (last 30 days)
Hi. I have defined a 3D polygon creating a vertice and a face matrix to use the function Patch. Now i would like to know: how do i transform my 3D polygon in an homogeneous matrix.
Any clues ?
Thanks for the help.
  2 Comments
Walter Roberson
Walter Roberson on 13 Oct 2012
What would the homogenous matrix consist of? For example are you looking to render it into a matrix? If so what value do you want at each location, taking into account that the polygon would in general be colored ?
João Viveiros
João Viveiros on 13 Oct 2012
Edited: Walter Roberson on 13 Oct 2012
I need it homogeneous in order to aply geométric transformatrions to my polygon. I have this at the moment:
clc;clear all;close all;
vert=[2,0,0;2,1,0;1,1,0;1,0,0;1,0,1;2,0,1;2,1,1;1,1,1;1,2,1;0,2,1;0,1,1;
0,1,0;1,2,0;0,2,0;0,0,0;1,1,2;0,1,2;0,0,2;1,0,2;0,0,1;];
faces=[1,2,3,4;2,3,8,7;1,4,5,6;5,6,7,8;1,2,7,6;
3,8,9,13;3,12,14,13;9,13,14,10;11,12,14,10;8,9,10,11;
19,18,17,16;20,11,17,18;16,8,11,17;5,8,16,19;18,19,5,20;
20,11,12,15;5,20,15,4;3,4,15,12;];
P=patch('Faces',faces,'Vertices',vert,'FaceColor','r');
axis equal;
axis([-6 6 -6 6 -6 6])
xlabel('x');ylabel('y');zlabel('z');
hold on;grid on;
view(140,40);
'I need that P to be the homogeneous matrix so i can apply the geométric transformation to it by doing B=translation(3,0,0)*P (For example)
B is the new polygon transformed.
thanks

Sign in to comment.

Accepted Answer

Walter Roberson
Walter Roberson on 13 Oct 2012
The matrix "vert" in your code is your homogenous matrix for your purposes described in your comment.
  1 Comment
João Viveiros
João Viveiros on 13 Oct 2012
Thanks. I homegenised my "vert" then, did a transformation to that matrix then i just re-patched.

Sign in to comment.

More Answers (2)

Matt J
Matt J on 13 Oct 2012
Couldn't you just transform all of the vertices and recreate the patch? E.g.,
vert_translated=bsxfun(@plus, vert, [3,0,0]);
P=patch('Faces',faces,'Vertices',vert_translated,'FaceColor','r');
Note that invertible linear/affine transformations don't change the faces.

Matt J
Matt J on 13 Oct 2012
Instead of using PATCH, you could also consider using these 2 FEX files,
So first, this willl let you obtain your polyhedron as a set of inequalities A*x<=b
[A,b]=lcon2vert(vert);
Now you can transform the polyhedron as you like by appropriately transforming A and b. In the case of your translation, this would be
Anew=A;
bnew=b-A*[3;0;0];
Finally, you can plot using the plotregion() tool
plotregion(-Anew,-bnew);

Categories

Find more on Elementary Polygons in Help Center and File Exchange

Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!