RETURN

Introduction

  • Good at simulating specular effects
  • Rays are reflected, refracted or absorbed
  • 三角形法向：$N=\frac{(P_1-P_0)\times(P_2-P_0)}{|(P_1-P_0)\times(P_2-P_0)|}$
  • 计算每个顶点法向：$N_v=\frac{\sum_{i=1}^k}{|\sum_{i=1}^k|}$
  • Tangent Space:
    • normal vecotr $N$
    • tangent vector $T$
    • bitangent vector $B$

求交

  • Shpere
    • Definition: $x^2+y^2+z^2-r^2=0$
    • Definition: $x=r\sin\theta\cos\phi,y=r\sin\theta\sin\phi,z=r\cos\theta$
  • Cylinder
    • Definition: $\phi=u\phi_{\max},x=r\cos\phi,y=r\sin\phi,z=z_{\min}+v(z_{\max}-z_{\min})$
  • Disk
    • Definition: $\phi=u\phi_{\max},x=((1-v)r_i+vr)\cos\phi,y=((1-v)r_i+vr)\sin\phi,z=h$
  • Triangle Mesh

Acceleration

  • Testing each object for each ray is slow
  • Fewer Rays
    • Adaptive sampling: 减少采样，内插
    • depth control
  • Generalized Rays
    • beam tracing
    • cone tracing
    • pencil tracing
  • Faster Intersection
    • Object subdivision approaches
      • BVH (Bounding Volumne boxes)：recursively finding bounding box of objects and split objects into two groups
    • Space subdivision approaches

      • Uniform Grid

        Find bounding box - Determine grid resolution - Place object in cell if its bounding box overlaps the cell- Check that object overlaps cell(expensive!)

        Teapot in a stadium Problem: Not adaptive to distribution of primitives

      • kd-Tree

        SAH(Surface Area Heuristic): 分割平面代价评估函数

    • Building Time: BVH < KD-Tree
    • Ray intersection test: BVH > KD-Tree

Shading

  • 计算交点的能量：the sading of each intersection point is the sum of contributions from all light sources
  • Material properties: diffusion, specular, shininess, emission
  • Light types: Ambient light, point light, …
  • Classic Ray Tracing
    • Perfect focus
    • Perfect reflections
    • Sharp shadow
  • Distributed Ray Tracing: randomly oversampling to reduce aliasing artifacts in rendered images
    • antialiasing: super-sampling and averaging down
      • Jittering: randomly generate a ray within each grid
    • soft shadows: sample area light
    • depth-of-field: sample on Lens
    • motion blur: sample on time
    • glossy reflections: 介于漫反射与镜面反射

Parallelization

  • Threading(Pthread, OpenMP) distributes rays across cores
  • MPI distributes rays across processors on different machiens (Message Passing Interface)
  • OptiX/CUDA distributes rays on the GPU
  • Memory coherency