Ray Tracing 2

Purpose: Enhance understanding of ray tracing techniques, optimizations, and additional effects.
Key Topics:
- Shadow rays and caches.
- Spatial data structures for ray traversal.
- Materials and optical effects.
- Advanced techniques like Constructive Solid Geometry (CSG) and fractals.

Purpose: Determine if a point is in shadow.
- A shadow ray is cast toward a light source from the intersection point.
- Any-hit traversal:
  - Stops as soon as any object between the point and the light is detected.
  - Faster than first-hit traversal for shadows.
Shadow Cache:
- Stores the last triangle hit by a shadow ray.
- On subsequent shadow rays, the cached triangle is tested first.
- Effective when ray coherency is high but less useful for parallel ray tracing or small triangles.

Why Use Them:
- Avoid testing all objects for every ray.
- Reduce complexity from O(n) to O(log⁡n) per ray.
- Examples:
  1. Bounding Volume Hierarchies (BVHs):
    - Organize objects into axis-aligned bounding boxes (AABBs).
    - Only test triangles within leaves of the BVH.
  2. BSP Trees (kd-trees):
    - Use planes to divide space recursively.
    - Traverse near and far sides of the plane in order.
  3. Grids:
    - Divide space into uniform cells.
    - Test only objects in cells intersected by the ray.
Optimizations:
- Precompute AABB/ray constants to speed up traversal.
- Skip-pointer Trees:
  - Use pointers for efficient traversal, avoiding recursion.
- Surface Area Heuristics (SAH):
  - Decide optimal splits for BVHs or kd-trees based on minimizing expected traversal costs.

Material Types:
1. Dielectrics (e.g., glass, plastic):
  - Refraction and reflection governed by Fresnel equations.
  - Follows Beer’s Law: Light intensity decreases exponentially with distance.
2. Metals:
  - Reflection color modulated by the material color.
  - Fresnel effect is wavelength-dependent (RGB-specific).
Fresnel Effect:
- Reflectance depends on the angle of incidence and the material’s refractive index.
- More reflection at shallow angles.
Beer’s Law:
- Describes light absorption in transparent media: $I (s) = I (0) e^{- C \cdot s}$
- Where CC is the attenuation coefficient and ss is the path length.

Constructive Solid Geometry (CSG):
- Combine objects using Boolean operations:
  - Union, Intersection, Difference.
- Requires computing all intersection points and applying Boolean operators.
Fractals:
- Use procedural methods to create complex geometry.
- Example: Sierpinski triangle or procedural terrain generation.
Blobs:
- Implicit surfaces (e.g., spheres) blended into smooth transitions.

Soft Shadows:
- Result from area or volume light sources.
- Produce penumbra and umbra regions.
Glossy Reflections:
- Trace multiple perturbed reflection rays for blurred effects.
Depth of Field:
- Simulate camera lens effects by tracing rays from different points on a virtual aperture.
Motion Blur:
- Temporal antialiasing by tracing rays over a time interval.
Participating Media:
- Simulate light scattering in fog, smoke, or clouds.

Spatial Data Structures:
- Draw and explain grids, octrees, kd-trees, and BVHs.
Key Concepts:
- Shadow cache, skip-pointer trees, Surface Area Heuristics (SAH).
- Describe ray/BVH intersection.
Material Behavior:
- Differences between metals and dielectrics.
CSG:
- Explain ray tracing with Boolean operations.

Ray tracing involves casting rays and using spatial data structures to optimize intersections.
Materials and optical effects enhance realism through physical models.
Advanced techniques like CSG and procedural methods expand the possibilities for geometry and lighting.

Jonas Notes