/**
 * Precomputed Atmospheric Scattering
 * Copyright (c) 2008 INRIA
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 * 3. Neither the name of the copyright holders nor the names of its
 *    contributors may be used to endorse or promote products derived from
 *    this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 */

/**
 * Author: Eric Bruneton
 */

// computes transmittance table T using Eq (5)

#ifdef _VERTEX_

void main() {
    gl_Position = gl_Vertex;
}

#else

void getTransmittanceRMu(out float r, out float muS) {
    r = gl_FragCoord.y / float(TRANSMITTANCE_H);
    muS = gl_FragCoord.x / float(TRANSMITTANCE_W);
#ifdef TRANSMITTANCE_NON_LINEAR
    r = Rg + (r * r) * (Rt - Rg);
    muS = -0.15 + tan(1.5 * muS) / tan(1.5) * (1.0 + 0.15);
#else
    r = Rg + r * (Rt - Rg);
    muS = -0.15 + muS * (1.0 + 0.15);
#endif
}

float opticalDepth(float H, float r, float mu) {
    float result = 0.0;
    float dx = limit(r, mu) / float(TRANSMITTANCE_INTEGRAL_SAMPLES);
    float xi = 0.0;
    float yi = exp(-(r - Rg) / H);
    for (int i = 1; i <= TRANSMITTANCE_INTEGRAL_SAMPLES; ++i) {
        float xj = float(i) * dx;
        float yj = exp(-(ieeesqrt(r * r + xj * xj + 2.0 * xj * r * mu) - Rg) / H);
        result += (yi + yj) / 2.0 * dx;
        xi = xj;
        yi = yj;
    }
    return mu < -ieeesqrt(1.0 - (Rg / r) * (Rg / r)) ? 1e9 : result;
}

void main() {
    float r, muS;
    getTransmittanceRMu(r, muS);
    vec3 depth = betaR * opticalDepth(HR, r, muS) + betaMEx * opticalDepth(HM, r, muS);
    gl_FragColor = vec4(exp(-depth), 0.0); // Eq (5)
}

#endif