/*
 * Copyright 2011-2013 Blender Foundation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#pragma once

#include "kernel/bvh/bvh.h"
#include "kernel/sample/mapping.h"
#include "kernel/sample/pattern.h"

CCL_NAMESPACE_BEGIN

#ifdef __SHADER_RAYTRACE__

/* Planar Cubic BSSRDF falloff, reused for bevel.
 *
 * This is basically (Rm - x)^3, with some factors to normalize it. For sampling
 * we integrate 2*pi*x * (Rm - x)^3, which gives us a quintic equation that as
 * far as I can tell has no closed form solution. So we get an iterative solution
 * instead with newton-raphson. */

ccl_device float svm_bevel_cubic_eval(const float radius, float r)
{
  const float Rm = radius;

  if (r >= Rm)
    return 0.0f;

  /* integrate (2*pi*r * 10*(R - r)^3)/(pi * R^5) from 0 to R = 1 */
  const float Rm5 = (Rm * Rm) * (Rm * Rm) * Rm;
  const float f = Rm - r;
  const float num = f * f * f;

  return (10.0f * num) / (Rm5 * M_PI_F);
}

ccl_device float svm_bevel_cubic_pdf(const float radius, float r)
{
  return svm_bevel_cubic_eval(radius, r);
}

/* solve 10x^2 - 20x^3 + 15x^4 - 4x^5 - xi == 0 */
ccl_device_forceinline float svm_bevel_cubic_quintic_root_find(float xi)
{
  /* newton-raphson iteration, usually succeeds in 2-4 iterations, except
   * outside 0.02 ... 0.98 where it can go up to 10, so overall performance
   * should not be too bad */
  const float tolerance = 1e-6f;
  const int max_iteration_count = 10;
  float x = 0.25f;
  int i;

  for (i = 0; i < max_iteration_count; i++) {
    float x2 = x * x;
    float x3 = x2 * x;
    float nx = (1.0f - x);

    float f = 10.0f * x2 - 20.0f * x3 + 15.0f * x2 * x2 - 4.0f * x2 * x3 - xi;
    float f_ = 20.0f * (x * nx) * (nx * nx);

    if (fabsf(f) < tolerance || f_ == 0.0f)
      break;

    x = saturatef(x - f / f_);
  }

  return x;
}

ccl_device void svm_bevel_cubic_sample(const float radius,
                                       float xi,
                                       ccl_private float *r,
                                       ccl_private float *h)
{
  float Rm = radius;
  float r_ = svm_bevel_cubic_quintic_root_find(xi);

  r_ *= Rm;
  *r = r_;

  /* h^2 + r^2 = Rm^2 */
  *h = safe_sqrtf(Rm * Rm - r_ * r_);
}

/* Bevel shader averaging normals from nearby surfaces.
 *
 * Sampling strategy from: BSSRDF Importance Sampling, SIGGRAPH 2013
 * http://library.imageworks.com/pdfs/imageworks-library-BSSRDF-sampling.pdf
 */

#  ifdef __KERNEL_OPTIX__
extern "C" __device__ float3 __direct_callable__svm_node_bevel(
#  else
ccl_device float3 svm_bevel(
#  endif
    KernelGlobals kg,
    ConstIntegratorState state,
    ccl_private ShaderData *sd,
    float radius,
    int num_samples)
{
  /* Early out if no sampling needed. */
  if (radius <= 0.0f || num_samples < 1 || sd->object == OBJECT_NONE) {
    return sd->N;
  }

  /* Can't raytrace from shaders like displacement, before BVH exists. */
  if (kernel_data.bvh.bvh_layout == BVH_LAYOUT_NONE) {
    return sd->N;
  }

  /* Don't bevel for blurry indirect rays. */
  if (INTEGRATOR_STATE(state, path, min_ray_pdf) < 8.0f) {
    return sd->N;
  }

  /* Setup for multi intersection. */
  LocalIntersection isect;
  uint lcg_state = lcg_state_init(INTEGRATOR_STATE(state, path, rng_hash),
                                  INTEGRATOR_STATE(state, path, rng_offset),
                                  INTEGRATOR_STATE(state, path, sample),
                                  0x64c6a40e);

  /* Sample normals from surrounding points on surface. */
  float3 sum_N = make_float3(0.0f, 0.0f, 0.0f);

  /* TODO: support ray-tracing in shadow shader evaluation? */
  RNGState rng_state;
  path_state_rng_load(state, &rng_state);

  for (int sample = 0; sample < num_samples; sample++) {
    float disk_u, disk_v;
    path_branched_rng_2D(kg, &rng_state, sample, num_samples, PRNG_BEVEL_U, &disk_u, &disk_v);

    /* Pick random axis in local frame and point on disk. */
    float3 disk_N, disk_T, disk_B;
    float pick_pdf_N, pick_pdf_T, pick_pdf_B;

    disk_N = sd->Ng;
    make_orthonormals(disk_N, &disk_T, &disk_B);

    float axisu = disk_u;

    if (axisu < 0.5f) {
      pick_pdf_N = 0.5f;
      pick_pdf_T = 0.25f;
      pick_pdf_B = 0.25f;
      disk_u *= 2.0f;
    }
    else if (axisu < 0.75f) {
      float3 tmp = disk_N;
      disk_N = disk_T;
      disk_T = tmp;
      pick_pdf_N = 0.25f;
      pick_pdf_T = 0.5f;
      pick_pdf_B = 0.25f;
      disk_u = (disk_u - 0.5f) * 4.0f;
    }
    else {
      float3 tmp = disk_N;
      disk_N = disk_B;
      disk_B = tmp;
      pick_pdf_N = 0.25f;
      pick_pdf_T = 0.25f;
      pick_pdf_B = 0.5f;
      disk_u = (disk_u - 0.75f) * 4.0f;
    }

    /* Sample point on disk. */
    float phi = M_2PI_F * disk_u;
    float disk_r = disk_v;
    float disk_height;

    /* Perhaps find something better than Cubic BSSRDF, but happens to work well. */
    svm_bevel_cubic_sample(radius, disk_r, &disk_r, &disk_height);

    float3 disk_P = (disk_r * cosf(phi)) * disk_T + (disk_r * sinf(phi)) * disk_B;

    /* Create ray. */
    Ray ray ccl_optional_struct_init;
    ray.P = sd->P + disk_N * disk_height + disk_P;
    ray.D = -disk_N;
    ray.t = 2.0f * disk_height;
    ray.dP = differential_zero_compact();
    ray.dD = differential_zero_compact();
    ray.time = sd->time;

    /* Intersect with the same object. if multiple intersections are found it
     * will use at most LOCAL_MAX_HITS hits, a random subset of all hits. */
    scene_intersect_local(kg, &ray, &isect, sd->object, &lcg_state, LOCAL_MAX_HITS);

    int num_eval_hits = min(isect.num_hits, LOCAL_MAX_HITS);

    for (int hit = 0; hit < num_eval_hits; hit++) {
      /* Quickly retrieve P and Ng without setting up ShaderData. */
      float3 hit_P;
      if (sd->type & PRIMITIVE_TRIANGLE) {
        hit_P = triangle_refine_local(
            kg, sd, ray.P, ray.D, ray.t, isect.hits[hit].object, isect.hits[hit].prim);
      }
#  ifdef __OBJECT_MOTION__
      else if (sd->type & PRIMITIVE_MOTION_TRIANGLE) {
        float3 verts[3];
        motion_triangle_vertices(kg, sd->object, isect.hits[hit].prim, sd->time, verts);
        hit_P = motion_triangle_refine_local(
            kg, sd, ray.P, ray.D, ray.t, isect.hits[hit].object, isect.hits[hit].prim, verts);
      }
#  endif /* __OBJECT_MOTION__ */

      /* Get geometric normal. */
      float3 hit_Ng = isect.Ng[hit];
      int object = isect.hits[hit].object;
      int object_flag = kernel_tex_fetch(__object_flag, object);
      if (object_flag & SD_OBJECT_NEGATIVE_SCALE_APPLIED) {
        hit_Ng = -hit_Ng;
      }

      /* Compute smooth normal. */
      float3 N = hit_Ng;
      int prim = isect.hits[hit].prim;
      int shader = kernel_tex_fetch(__tri_shader, prim);

      if (shader & SHADER_SMOOTH_NORMAL) {
        float u = isect.hits[hit].u;
        float v = isect.hits[hit].v;

        if (sd->type & PRIMITIVE_TRIANGLE) {
          N = triangle_smooth_normal(kg, N, prim, u, v);
        }
#  ifdef __OBJECT_MOTION__
        else if (sd->type & PRIMITIVE_MOTION_TRIANGLE) {
          N = motion_triangle_smooth_normal(kg, N, sd->object, prim, u, v, sd->time);
        }
#  endif /* __OBJECT_MOTION__ */
      }

      /* Transform normals to world space. */
      if (!(object_flag & SD_OBJECT_TRANSFORM_APPLIED)) {
        object_normal_transform(kg, sd, &N);
        object_normal_transform(kg, sd, &hit_Ng);
      }

      /* Probability densities for local frame axes. */
      float pdf_N = pick_pdf_N * fabsf(dot(disk_N, hit_Ng));
      float pdf_T = pick_pdf_T * fabsf(dot(disk_T, hit_Ng));
      float pdf_B = pick_pdf_B * fabsf(dot(disk_B, hit_Ng));

      /* Multiple importance sample between 3 axes, power heuristic
       * found to be slightly better than balance heuristic. pdf_N
       * in the MIS weight and denominator canceled out. */
      float w = pdf_N / (sqr(pdf_N) + sqr(pdf_T) + sqr(pdf_B));
      if (isect.num_hits > LOCAL_MAX_HITS) {
        w *= isect.num_hits / (float)LOCAL_MAX_HITS;
      }

      /* Real distance to sampled point. */
      float r = len(hit_P - sd->P);

      /* Compute weight. */
      float pdf = svm_bevel_cubic_pdf(radius, r);
      float disk_pdf = svm_bevel_cubic_pdf(radius, disk_r);

      w *= pdf / disk_pdf;

      /* Sum normal and weight. */
      sum_N += w * N;
    }
  }

  /* Normalize. */
  float3 N = safe_normalize(sum_N);
  return is_zero(N) ? sd->N : (sd->flag & SD_BACKFACING) ? -N : N;
}

template<uint node_feature_mask, typename ConstIntegratorGenericState>
#  if defined(__KERNEL_OPTIX__)
ccl_device_inline
#  else
ccl_device_noinline
#  endif
    void
    svm_node_bevel(KernelGlobals kg,
                   ConstIntegratorGenericState state,
                   ccl_private ShaderData *sd,
                   ccl_private float *stack,
                   uint4 node)
{
  uint num_samples, radius_offset, normal_offset, out_offset;
  svm_unpack_node_uchar4(node.y, &num_samples, &radius_offset, &normal_offset, &out_offset);

  float3 bevel_N = sd->N;

  IF_KERNEL_NODES_FEATURE(RAYTRACE)
  {
    float radius = stack_load_float(stack, radius_offset);

#  ifdef __KERNEL_OPTIX__
    bevel_N = optixDirectCall<float3>(1, kg, state, sd, radius, num_samples);
#  else
    bevel_N = svm_bevel(kg, state, sd, radius, num_samples);
#  endif

    if (stack_valid(normal_offset)) {
      /* Preserve input normal. */
      float3 ref_N = stack_load_float3(stack, normal_offset);
      bevel_N = normalize(ref_N + (bevel_N - sd->N));
    }
  }

  stack_store_float3(stack, out_offset, bevel_N);
}

#endif /* __SHADER_RAYTRACE__ */

CCL_NAMESPACE_END
