# Why texture coordinate of flat surface reflection is calculated like this in fragment shader? [closed]

The whole project is here: https://developer.apple.com/library/mac/#samplecode/GLEssentials/Introduction/Intro.html

The rendering flow is like this:

1. Render the character upside down to a texture.
2. Render the character normally.
3. Render the flat reflection surface below the character using the texture from step 1.

I don't understand the texture coordinate calculation in the fragment shader, specifically the block marked with `???` below:

``````precision highp float;

// Color of tint to apply (blue)
const vec4 tintColor = vec4(0.0, 0.0, 1.0, 1.0);

// Amount of tint to apply
const float tintFactor = 0.2;

varying vec3  varNormal;
varying vec3  varEyeDir;

uniform sampler2D diffuseTexture;

void main (void)
{
// Compute reflection vector
vec3 reflectDir = reflect(varEyeDir, varNormal);

// Compute altitude and azimuth angles
vec2 texcoord;

texcoord.t = normalize(reflectDir).y;
// ???????????????????????????????????????????????
reflectDir.y = 0.0; // Why clear reflectDir.y?
texcoord.s = normalize(reflectDir).x * 0.5; // Why times 0.5?

// Translate index values into proper range
if (reflectDir.z >= 0.0) {
texcoord = (texcoord + 1.0) * 0.5;
} else {
texcoord.t = (texcoord.t + 1.0) * 0.5;
texcoord.s = (-texcoord.s) * 0.5 + 1.0; // Why translation of s is like this, different from t?
}
// ???????????????????????????????????????????????

// Do a lookup into the environment map.
vec4 texColor = texture2D(diffuseTexture, texcoord);

// Add some blue tint to the image so it looks more like a mirror or glass
gl_FragColor = mix(texColor, tintColor, tintFactor);
}
``````

Thanks in advance to anyone who can demystify this for me!

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## closed as too localized by Sean Middleditch, bummzack, Byte56♦, Josh Petrie♦, AnkoApr 7 '13 at 16:32

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They seem to be using a kind of quasi-polar coordinates for the texture. The code you marked off is concerned with measuring the relationship of `reflectDir` to the coordinate axes and mapping that into texture coordinates.
First, it takes `reflectDir.y` to be the t component of the texture coordinate. In both cases of the if-statement, it adds 1 to this and multiplies by 0.5 in order to map it from the [-1, 1] interval to [0, 1].
It then zeroes out the `reflectDir.y` and renormalizes, in order to look only at the horizontal components of the vector in what follows. For the horizontal component there are two cases, based on whether z is positive or negative. In either case, it uses `reflectDir.x` for the s component of the texture coordinate, but mapped in a different way: for positive z, it maps [-1, 1] to [.25, .75], and for negative z it maps [-1, 1] to [1.25, .75]. After texture wrapping, the latter case will end up occupying the intervals [.75, 1.0] and [0, .25], so it fills the parts of the texture not already occupied by the positive-z case.
Thanks. I found I missed a very important detail before, i.e., the reflection surface's normal is set to point to +Z instead of +Y, and the latter is what I thought naturally as the case. After figuring this out, some confusions are easily solved. However, as to the different treatments of `texcoord.s` for positive and negative `reflectDir.z`, I think they are very arbitrary and only make sense for this specific scene and are not general math formulae, right? In fact, [1.25, .75] of `texcoord.s` does not make much sense because it uses `GL_CLAMP_TO_EDGE` and `reflectDir.z` is never < 0 here. – an0 Mar 23 '13 at 16:00
@an0 Well, it could be used as a general environment mapping - the math works out, although this mapping would seem to have serious issues with texture distortion. The different treatments for positive and negative z are just to get the whole 360 degrees of the environment into the texture. The use of `GL_CLAMP_TO_EDGE` may just be a mistake on the part of the coder of the sample. And you may be right that the z < 0 part is not necessary here, but the coder may have forgotten to optimize it or chosen not to, to leave the code more generalized. – Nathan Reed Mar 23 '13 at 16:21