## Posts Tagged ‘texture mapping’

### Quad meshing in matlab using gptoolbox

Friday, February 17th, 2017

This morning I played around with a very simple way of quad meshing a triangle mesh. This is more or less the “ideal pipeline” for quad meshing via parameterization. It will likely only work for very simple meshes. I’m pleasantly surprised that it works at all.

% Load a mesh with boundary and no topological (donut) holes
V = V*axisangle2matrix([1 0 0],-pi/2);
% Construct the LSCM matrix
[~,Q] = lscm(V,F,[],[]);
M = massmatrix(V,F);
% Use Fiedler vector as parameterization
[EV,ED] = eigs(Q,repdiag(M,2),5,'sm');
U = reshape(EV(:,end-3),[],2);
% try to find "canonical" rotation
[sU,sS,sV] = svd(U'*U);
U = U*sU;
% Lay down a grid in 2D
h = ((max(U(:,1))-min(U(:,1)))/(160-2));
[X,Y] = meshgrid(min(U(:,1))-h:h:max(U(:,1))+h,min(U(:,2))-h:h:max(U(:,2))+h);
% Find all quads that are strictly inside the parameterized mesh
[QQ,QU] = surf2patch(X,Y,0*Y);QU = QU(:,1:2);
[sqrD,I,C] = signed_distance([QU QU(:,1)*0],[U U(:,1)*0],F);
QQ = QQ(all(abs(sqrD(QQ))<1e-10,2),:);
[QU,I] = remove_unreferenced(QU,QQ);
QQ = fliplr(I(QQ));
% Snap boundary vertices of quad mesh to boundary of mesh, and
% solve little Dirichlet problem to diffuse the displacements smoothly
QF = [QQ(:,[1 2 3]);QQ(:,[1 3 4])];
L = cotmatrix(QU,QF);
b = unique(outline(QQ));
[~,~,QU(b,:)] = point_mesh_squared_distance(QU(b,:),U,outline(F));
% Locate each quad mesh vertex in the parameterized mesh
[sqrD,I,C] = signed_distance([QU QU(:,1)*0],[U U(:,1)*0],F);
B = barycentric_coordinates(C(:,1:2),U(F(I,1),:),U(F(I,2),:),U(F(I,3),:));
% Interpolate 3D positions at quad mesh vertex locations
QV = V(F(I,1),:).*B(:,1) + V(F(I,2),:).*B(:,2) + V(F(I,3),:).*B(:,3);


To create the image above use:

clf;
hold on;
tq = tsurf(QQ,QV,'FaceVertexCData',repmat(blue,size(QV,1),1),'EdgeColor','none',fsoft,fphong);
tt = tsurf(F,V-[0.8 0 0],'FaceVertexCData',repmat(1-0.8*(1-blue),size(V,1),1),'EdgeAlpha',0.5,fsoft,fphong);
axis equal;
camproj('persp');
view(-38,17);
drawn;
camlight;
plot_edges(QV,[QQ(:,2:3);QQ(:,[4 1])],'Color',orange);
plot_edges(QV,[QQ(:,1:2);QQ(:,3:4)],'w');hold off;
l = light('Position',[-10 0 10],'Style','infinite');
set(gca,'Visible','off');
set(gcf,'Color','w');


There’s a lot to improve about the quad mesh: the boundaries are not aligned with the meshing direction, the meshing directions are not always aligned with principle curvature, etc. Not bad for 30 mins of coding using tools that are just lying around.

### Using patcht to texture map a triangle mesh in matlab

Friday, August 9th, 2013

Recently I found the patcht script which lets you texture map a triangle mesh in matlab. It unfortunately does it in a brute force way: creating a textured surface for every triangle. But it’s at least something. Here’s how I use it for 2d meshes of images using the xy positions as texture coordinates:

im = imread('woody.png');
patcht(F,V,F,[max(V(:,2))-V(:,2) V(:,1)],im);
axis equal


which produces:

We thank Scott Schaefer for providing the wooden gingerbread man image from “Image Deformation Using Moving Least Squares”.

### TexMapPreview: simple texture mapping utility

Wednesday, September 21st, 2011

I posted the source and binary of TexMapPreview. It’s a little texture mapping utility I’ve been using to visualize texture maps on the meshes I deform. It takes as input a mesh (with texture coordinates) and an (texture) image. Then it can either write the visualization of the texture mapped mesh to an output file or display it in a GLUT window. Glut is the only dependency. TexMapPreview itself can only read and write .tga image files. But, I include a bash script wrapper which uses ImageMagick’s convert tool to enable reading and writing of all sorts of file formats (.png, .jpg, .tiff, whatever convert can read/write).

We thank Scott Schaefer for providing the wooden gingerbread man image from “Image Deformation Using Moving Least Squares”.