how do I do “reverse” texture mapping from texture image x,y to 3d space?

3
votes

I am using WPF 3D, but I think this question should apply to any 3d texture mapping.

Suppose I have a model of a cow, and I want to draw a circular spot on the cow (and I want to do this dynamically -- supposed I don't know the location of the spot until run-time). I could do this by coloring the vertexes (vertexes are assigned a color based on their distance from the center of the spot), but if the model is fairly low-poly, that will give a pretty jagged-edged circle.

I could do it using a pixel shader, where the shader colors each pixel based on its distance from the center of the spot. But suppose I don't have access to pixel shaders (since I don't in WPF).

So, it seems that what I want to do is dynamically create a texture with the circle pattern on it, and texture the cow with it.

The question is: As I'm drawing that texture, how can I know what 3d coordinate in model space a given xy coordinate on the texture image corresponds to?

That is, suppose I have already textured my model with a plain white texture -- I've set up texture coordinates, done texture mapping, but don't have the texture image yet. So I have this 1000x1000 (or whatever) pixel image that gets draped nicely over the cow according to some nice texture coordinates that have been set up on the model beforehand. I understand that when the 3D hardware goes to draw a given triangle, it uses the texture coordinates of the vertexes of the triangle to find the corresponding triangular region of the image, and then interpolates across the surface of the triangle to fill displayed model pixels with colors from that triangular region of the image.

How do I go the other way? How do I say, for this given xy point on my texture image, and given the texture coordinates that have already been set up on the model, what's the 3d coordinate in model space that this image pixel is going to correspond to once texture mapping happens?

If I had such a function, I could color my texture map image such that all the points (in 3d space) within a certain distance of the circle center point on the cow would get one color, and all points outside that distance would get another color, and I'd end up with a nice, crisp circular spot on the cow, even with a relatively low-poly model. Does that sound right?

I do understand that given the texture coordinates for the vertexes of each triangle, I can step through the triangles in my model, find the corresponding triangle on the texture image, and do my own interpolation, across the texture pixels in that triangle, by interpolating across the 3d plane determined by the vertex points. And that doesn't sound too hard. But I'm just trying to understand if there is some standard 3d concept/function where I can just call a ready-made function to give me the model space coordinates for a given texture xy.

2
wpf3dtexture-mappinguv-mapping
I don't know any standard approach. But what I would probably do is to draw a UV-map from the current view. So instead of drawing the actual color, draw the texture coordinates. Then you can draw the circle in the rendered image, look up the texture coordinates and draw the according pixels in the texture. I am not that familiar with WPF 3D, but I assume it is pretty hard to implement this when you don't have direct access to DirectX. – Nico Schertler
Just as an aside, once you have the coordinates, you don't have to draw into the original texture, but you could also draw into a second texture which is otherwise transparent, and superimpose it on the original texture as a second layer of Material. – hbarck
You have 2D point on texture and you want to get 3D point in space, where is that texture mapped. But it is not possible - there can be thousands of 3D points, which contain that point of texture. All triangles can have mapped the same part of texture on them. – Ivan Kuckir
Ivan, you are correct that in general a given texture point can map to any number of model points. In my case, however, I am working with a "well-behaved" texture, like a regular texture you'd use in covering a 3D head with a face and hair. – M Katz

2 Answers

3
votes

I did end up getting this working. I walk every point on the texture (1024 x 1024 points). Using the model's texture coordinates, I determine which polygon face, if any, the given u,v point is inside of. If it's inside of a face, I get the model coordinates for each point on that face. I then do a barycentric interpolation as described here: http://paulbourke.net/texture_colour/interpolation/

That is, for each u,v point on the texture, I use an inside-polygon check to determine which quad it's in on the 2D texture sheet and then I use an interpolation on that same 2D geometry as described in the link above, but instead of interpolating colors or normals I'm interpolating 3D coordinates.

I can then use the 3D coordinate to color the point on the texture (e.g., to color a circular spot on the cow based on how far in model space the given texture point is from the spot center point). And then I can apply the texture to the model, and it works.

Again, it seems like this must be a standard procedure with a name...

One issue is that the result is very sensitive to the quality of the the texturing as set up by the modeler. For instance, if a relatively large quad on the cow corresponds to a small quad on the texture image, there just aren't enough pixels to work with to get a smooth curve within that model quad once the texture is applied. You can of course use a higher-res texture, such as 2048x2048, but then your loop time is 4x.

1
votes

It's actually a rasterization process if I didn't misunderstand your question. In lightmapping, one may also need to find the corresponding positions and normals in world space for each texel in the lightmap space and then baking irradiance. (which seems similar to your goal)

You can use standard Graphics API to do this task instead of writing your own implementation. Let:

  • Size of texture -> Size of G-buffers
  • UVs of each mesh triangle -> Vertex positions vec3(u, v, 0) of the input stage
  • Indices of each mesh triangle -> Indices of the input stage
  • Positions (and normals, etc.) of each mesh triangle -> Attributes of the input stage

After the rasterizer stage of the graphics pipeline, all fragments that lie within the UV triangle are generated, and the attributes that have been supplied are interpolated automatically. You can do whatever you want now in pixel shader!