Ray-Tracing

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