在3D空间中旋转图像的一部分

Question

Here's the setup: This is for an ecommerce art site where some paintings are canvas transfers. The painting wraps around the sides and top and bottom of the canvas. We have high-res images of the entire painting, but what we want to display is a quasi-3D representation of the image in which you can see how the sides of the painting wrap around the canvas. Here's a rough sketch of what I'm talking about:

My question is, how can I rotate an image in 3D space? The approach I think I'd like to take, is to cut off a portion of the top and side of the image, and rotate then in 3D and then stich it back on to the top and side to give it the 3D look. How do I go about about doing that? It can be done using any .Net technology (GDI+, WPF etc.).

Answer 1

In WPF using the ViewPort3D class you can create a cuboid which is 8x5x1 units. Create the image as a texture and then apply the texture to the front face (8x5) and the side faces (5x1) and the top and bottom faces (8x1) using texture coordinates. The front face coordinates should be: (1/9, 1/6), (8/9, 1/6), (1/9, 5/6) and (8/9, 5/6) for the front face, and from the nearest edge to those coordinates for the sides, eg for the left side: (0, 1/6), (1/9, 1/6), (0, 5/6) and (1/9, 5/6) for the left side.

Edit: If you then want to be able to perform rotations on the 3D canvas model you can follow the advice here: How can I do 3D transformation in WPF?

Answer 2

It looks like you're not needing to do real 3D, but only needing to fake it.

Chop off four strips along the top, bottom, left and right of the image. Toss the bottom and right (going by your sketch in the question). Scale and shear the strips (I'm not expert enough at .net/wpf to know how, but it can do it). The top would be scaled vertically by a factor of 0.5 (a guess - choose to fit the desired final 3D-looking image) and sheared horizontally. The result is composited onto the output image as the top side of the canvas. The left strip would be scaled horizontally and sheared vertically.

If the end user is to view the 3D canvas from different angles interactively, this method is probably faster than rendering an honest 3D model, which would have to do texture mapping and rasterizing the model into a final image, which amounts to doing the same math. The fun part is figuring out how to adjust the scaling and shearing parameters.

This page might be educational: http://www.idomaths.com/linear_transformation.php
and this could be useful reference http://en.csharp-online.net/GDIplus_Graphics_Transformation%E2%80%94Image_Transformation

Answer 3

I dont have any experience in this kind of stuff. But when i saw this question, the first thing comes to my mind is the funny Unicornify for SO.

In this making of article by balpha , he explained how the 2d unicorn sphere is rotated in 3d space.

But the code is written in python. If you are interested, you can take a look into that. But am not exactly sure this would help you.

Answer 4

The brute force approach (which might be the easiest approach), is to map the u,v texture coordinates for each of the three faces, onto three billboards representing three sides of the canvas (a billboard is just two triangles that make a rectangle). Then, rotate the whole canvas (all three billboards) using matrix transforms. Tada!

Alternately, you can move the 3-space camera position with a transform, rather than the canvas. Six of one, half the other - as they say.