kernel_montecarlo.h

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/*
 * Parts adapted from Open Shading Language with this license:
 *
 * Copyright (c) 2009-2010 Sony Pictures Imageworks Inc., et al.
 * All Rights Reserved.
 *
 * Modifications Copyright 2011, Blender Foundation.
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 * * Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 * * 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.
 * * Neither the name of Sony Pictures Imageworks 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,
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 * 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.
*/

#ifndef __KERNEL_MONTECARLO_CL__
#define __KERNEL_MONTECARLO_CL__

CCL_NAMESPACE_BEGIN

__device void to_unit_disk(float *x, float *y)
{
    float r, phi;
    float a = 2.0f * (*x) - 1.0f;
    float b = 2.0f * (*y) - 1.0f;
    if(a > -b) {
        if(a > b) {
            r = a;
             phi = M_PI_4_F *(b/a);
         } else {
             r = b;
             phi = M_PI_4_F *(2.0f - a/b);
         }
    } else {
        if(a < b) {
            r = -a;
            phi = M_PI_4_F *(4.0f + b/a);
        } else {
            r = -b;
            if(b != 0.0f)
                phi = M_PI_4_F *(6.0f - a/b);
            else
                phi = 0.0f;
        }
    }
    *x = r * cosf(phi);
    *y = r * sinf(phi);
}

__device void make_orthonormals_tangent(const float3 N, const float3 T, float3 *a, float3 *b)
{
    *b = cross(N, T);
    *a = cross(*b, N);
}

__device_inline void sample_cos_hemisphere(const float3 N,
    float randu, float randv, float3 *omega_in, float *pdf)
{
    // Default closure BSDF implementation: uniformly sample
    // cosine-weighted hemisphere above the point.
    to_unit_disk(&randu, &randv);
    float costheta = sqrtf(max(1.0f - randu * randu - randv * randv, 0.0f));
    float3 T, B;
    make_orthonormals(N, &T, &B);
    *omega_in = randu * T + randv * B + costheta * N;
    *pdf = costheta *M_1_PI_F;
}

__device_inline void sample_uniform_hemisphere(const float3 N,
                                             float randu, float randv,
                                             float3 *omega_in, float *pdf)
{
    float z = randu;
    float r = sqrtf(max(0.f, 1.f - z*z));
    float phi = 2.f * M_PI_F * randv;
    float x = r * cosf(phi);
    float y = r * sinf(phi);

    float3 T, B;
    make_orthonormals (N, &T, &B);
    *omega_in = x * T + y * B + z * N;
    *pdf = 0.5f * M_1_PI_F;
}

__device float3 sample_uniform_sphere(float u1, float u2)
{
    float z = 1.0f - 2.0f*u1;
    float r = sqrtf(fmaxf(0.0f, 1.0f - z*z));
    float phi = 2.0f*M_PI_F*u2;
    float x = r*cosf(phi);
    float y = r*sinf(phi);

    return make_float3(x, y, z);
}

__device float power_heuristic(float a, float b)
{
    return (a*a)/(a*a + b*b);
}

__device float2 concentric_sample_disk(float u1, float u2)
{
    float r, theta;
    // Map uniform random numbers to $[-1,1]^2$
    float sx = 2 * u1 - 1;
    float sy = 2 * u2 - 1;

    // Map square to $(r,\theta)$

    // Handle degeneracy at the origin
    if(sx == 0.0f && sy == 0.0f) {
        return make_float2(0.0f, 0.0f);
    }
    if(sx >= -sy) {
        if(sx > sy) {
            // Handle first region of disk
            r = sx;
            if(sy > 0.0f) theta = sy/r;
            else          theta = 8.0f + sy/r;
        }
        else {
            // Handle second region of disk
            r = sy;
            theta = 2.0f - sx/r;
        }
    }
    else {
        if(sx <= sy) {
            // Handle third region of disk
            r = -sx;
            theta = 4.0f - sy/r;
        }
        else {
            // Handle fourth region of disk
            r = -sy;
            theta = 6.0f + sx/r;
        }
    }

    theta *= M_PI_4_F;
    return make_float2(r * cosf(theta), r * sinf(theta));
}

__device float2 regular_polygon_sample(float corners, float rotation, float u, float v)
{
    /* sample corner number and reuse u */
    float corner = floorf(u*corners);
    u = u*corners - corner;

    /* uniform sampled triangle weights */
    u = sqrtf(u);
    v = v*u;
    u = 1.0f - u;

    /* point in triangle */
    float angle = M_PI_F/corners;
    float2 p = make_float2((u + v)*cosf(angle), (u - v)*sinf(angle));

    /* rotate */
    rotation += corner*2.0f*angle;

    float cr = cosf(rotation);
    float sr = sinf(rotation);

    return make_float2(cr*p.x - sr*p.y, sr*p.x + cr*p.y);
}

/* Spherical coordinates <-> Cartesion direction  */

__device float2 direction_to_spherical(float3 dir)
{
    float theta = acosf(dir.z);
    float phi = atan2f(dir.x, dir.y);

    return make_float2(theta, phi);
}

__device float3 spherical_to_direction(float theta, float phi)
{
    return make_float3(
        sinf(theta)*cosf(phi),
        sinf(theta)*sinf(phi),
        cosf(theta));
}

CCL_NAMESPACE_END

#endif /* __KERNEL_MONTECARLO_CL__ */