Pixel perfect textures in VRML

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david [at] frerichs.net

Designers often lament over how poor textures can look in VRML worlds. This quality is caused by the point-sampling technique of texture mapping used by most software rendering engines. Since textures are mapped into 3D space, they are subject to distortion when not perfectly aligned with the browser's camera. 

So what do I do if I want quality images? How do I get pixel perfect textures in VRML? Well, I have just the equation you are looking for. It turns out that if you align the Viewpoint with the texture and place the camera at just the right distance, the pixels in the texture exactly match the pixels on the screen.

To see the results, look at the embedded .wrl above. This world has a high-resolution texture that is pretty unreadable when it is at an angle. But click on the texture and it will snap to a viewpoint created using my equation. You will notice how you suddenly get a full fidelity view of the texture with perfect 1-to-1 mapping of texture pixels to screen pixels. Now you can read the text without getting eyestrain!

The diagram above explains how you do it:

If the embedded .wrl is narrower than it is tall, use this equation:

Zdist = [ embed_width * (x1-x2) ] / [ 2 * horiz_texture_res * tan(fov/2) ]

Zdist = [ embed_height * (y1-y2) ] / [ 2 * vert_texture_res * tan(fov/2) ]

• Zdist is the distance of the Viewpoint to the geometry. This is the quantity for which you are solving.
• embed_width (embed_height) is the size in pixels of the embedded VRML.
• x1, x2 (y1, y2) are the x (y) coordinates of the IndexFaceSet to which the texture is applied.
• horiz_texture_res (vert_texture_res) is the diplayed resolution in  pixels of the texture you want to align.
• fov is the fieldOfView of the viewpoint.

• The VRML file is embedded in an HTML file at a fixed resolution. Unless you fix the resolution of the VRML file, it is impossible to align for a 1 to 1 mapping of texture pixels to the screen.
• The Viewpoint is perpendicular to the IndexFaceSet. This is a given because your goal is to get a 1 to 1 correspondence of the pixels in the texture to the pixels in your VRML browser.
• The browser is not rescaling the texture. Although Cosmo Player will accept textures of arbitrary resolution, it rescales them such that each side is a power of 2. You can avoid aliasing due to rescaling by "padding" the texture with extra pixels so that its resolution will be in powers of 2. After you pad the texture, make sure you modify the texture coordinates on the IndexFaceSet so that only the area you want is showing.

In the above example, the height of the embed is smaller than the width, so we go with height. So per the second equation:

Zdist = [300 * (1-(-1))]/[2*256*tan(.785398/2)] = 2.829157172164

And that is it! You can take a look at the VRML source code to get the full picture. Now, put this equation to good use and get some beautiful looking textures in your worlds.