Ray Tracing

General

Ray Casting

• Ray casting traces only primary rays.
• It can replace rasterization plus depth buffering for visible-surface selection.
• It is especially important as a basis for volume rendering.
• If the first hit is shaded only with a local illumination model, the method is ray casting, not full ray tracing.

Ray Equation

• A ray starts at the camera position $e$ and passes through a screen point $s$.
• The parametric ray equation is:

• $t=0$ gives the camera position.
• $t=1$ gives the screen point.
• Only intersections with $t>0$ are in front of the camera.

Ray-Object Intersections

• For implicit objects, insert the ray equation into the object equation and solve for $t$.
• For triangles, equalize the ray equation and the triangle plane equation.
• This gives three equations and three unknowns:
  • $t$.
  • $\beta$.
  • $\gamma$.
• The checks should be ordered to avoid unnecessary work:
  • Compute and validate $t$.
  • Then validate $\gamma$.
  • Then validate $\beta$.
• The barycentric coordinates decide whether the hit lies inside the triangle.

Computational Cost

Main Cost Drivers

• Cost mainly depends on the number of pixels and rays.
• Higher image resolution means more primary rays.
• Distribution effects multiply the number of secondary rays.
• Triangle count can be handled sub-linearly with acceleration structures.

Acceleration Structures

• Object partitioning:
  • Put bounding boxes around objects or groups of triangles.
  • Traverse a bounding volume hierarchy before testing triangles.
  • Test triangles only inside hit boxes.
• Space partitioning:
  • Split the scene into cells.
  • Examples: BSP trees and Kd-trees.
  • Traverse only cells crossed by the ray.
• These structures reduce intersection tests dramatically.

Hardware

• Ray Tracing is embarrassingly parallel because pixels are mostly independent.
• Useful hardware:
  • Multi-core CPUs.
  • GPUs.
  • Render farms.
  • Specialized ray tracing units.
• Recursive ray traversal is harder for traditional GPU pipelines, so real-time systems often use hybrid rendering.

Secondary-Ray Effects

Shadows

• Hard shadows are cheap.
• Cast one shadow ray from the hit point to a point light.
• If the ray is blocked, the point is in shadow.
• If the ray reaches the light, the point is illuminated.

Soft Shadows

• Soft shadows need distribution ray tracing.
• Cast many shadow rays toward an area light.
• The fraction of unblocked rays determines shadow intensity.
• Larger light sources create wider penumbra regions.

Reflections

• Perfect reflections are relatively cheap.
• Compute the surface normal at the hit point.
• Reflect the incoming direction around the normal.
• Trace the reflected ray recursively.
• Backpropagate the returned color contribution.

Glossy Reflections

• Glossy reflections need distribution ray tracing.
• Spawn multiple slightly perturbed reflection rays.
• Average their results.
• Wider distributions create blurrier reflections.

Refractions

• Refraction happens when a ray hits transparent material.
• Use the material's refraction index and Snell's law to compute the transmitted direction.
• Trace the refracted ray recursively.
• Wavelength-dependent refraction can produce chromatic aberration.

Depth of Field

• Depth of field needs distribution ray tracing.
• Use multiple camera rays through a focal plane.
• Rays start from different positions on a finite lens area.
• Points on the focal plane stay sharp.
• Points away from the focal plane are averaged into blur.

Color Bleeding

• Color bleeding is indirect diffuse reflection of surface color onto other surfaces.
• It needs many random secondary rays.
• Pure ray tracing is inefficient for strong diffuse inter-reflection.
• Radiosity is better suited for that case.

Path Tracing

Distribution Ray Tracing

• Distribution ray tracing uses multiple randomly selected rays per effect.
• Quality depends on the number of samples.
• It supports:
  • Soft shadows.
  • Glossy reflections.
  • Depth of field.
  • Antialiasing.
• It is expensive because every additional sample can spawn more work.

Bidirectional Path Tracing

• Ordinary path tracing shoots paths from the camera.
• Bidirectional path tracing shoots paths from both the camera and the light.
• This is more efficient for difficult light transport.
• It helps with effects such as caustics.
• Photon mapping follows a similar idea.