Radiosity

• Ray tracing:

  • Great for specular effects (reflection, transmission)

  • Poor at handling diffuse scattering unless extended (e.g., path tracing)

• Radiosity:

  • Efficient for diffuse interreflections (global illumination at diffuse surfaces)

  • Inefficient for specular effects (like mirrors or glass)

• → They are complementary: each handles what the other struggles with

• Based on heat transfer principles

• Best suited for indoor scenes with diffuse interreflections

• Scene is divided into surface patches (uniform or adaptive)

• Light energy is computed patch-to-patch (including light sources)

• Computational cost is O(n²) for n patches

• Operates in object space, unlike ray tracing which is image space

• Produces smooth, realistic diffuse lighting via precomputed interpolation

• An approximation of the Nusselt analog

• Projects scene geometry onto a cube centered on dAᵢ

• Uses flat projection planes for efficiency

• Typically 2×2 top face and 2×1 side faces

• Subdivided into a grid (e.g., 512×512)

• Polygons are projected onto cube faces with Z-buffering for visibility

• Form factor is computed by summing contributions of covered cells

• Efficient and GPU-friendly, but introduces approximation errors

• Subdivides surface Aⱼ into small differential elements (dAⱼ)

• For each dAⱼ:

  • Cast a ray to dAᵢ

  • If visible, compute partial form factor

• More accurate than hemicube (especially with occlusion)

• Slower, but precision can be adaptively increased

• Preferred in modern systems for high-quality results

• Hemicube is faster, area sampling is more physically accurate

• Radiosity B_i = energy per unit area leaving patch A_i

• Composed of:

  
  

  • Emitted energy E_i

  • Reflected energy from other patches:

• Form factor reciprocity simplifies the equation

• Integration becomes a summation for discrete patches

• Yields one equation per patch → a system of n linear equations

• Gathering:

  • Each patch collects light from all other patches

  • Updates one patch per step:

    B_i = E_i + R_i \sum_j B_j F_{ij}

  • Viewpoint-oriented (camera-centric)

  • Requires multiple iterations to converge

• Shooting:

  • Each patch sends out its unshot energy to others

  • Updates all patches from a single emitting patch in each step

  • Energy-centric (light transport view)

  • Often prioritizes high-energy patches first

• Both methods converge to same solution, just different update directions

• An iterative approach that improves image quality over time

• Each iteration adds more light transport detail

• Useful for real-time preview:

  • Shows partial results immediately

  • Gradually refines image until convergence (no visual change)

• Allows dynamic stopping conditions (e.g., when scene changes stop)

• Frame rate is inversely related to iteration time (fewer bounces = faster)

• Uniform low-resolution patches cause artifacts:

  • Blocky shadows

  • Mach bands

  • Unresolved discontinuities

• Increasing patch resolution globally:

  • Improves quality

  • Significantly reduces performance

• Best practice: use adaptive patch subdivision

  • High resolution only where needed (e.g. shadows, fine detail)

  • Coarser mesh in less critical areas

  • Balances accuracy and efficiency

1. Mesh the surface into patches

   • Uniform or adaptive resolution

2. Compute form factors

   • Methods: hemicube, area sampling

3. Solve the linear system

   • Direct (e.g., matrix inversion)

   • Iterative (e.g., Gauss-Seidel, shooting)

4. Reconstruct the solution

   • Interpolate low-res radiosity onto high-res geometry

   • Blend for smooth final appearance

Radiosity is view-independent

• No need to recompute if only camera changes

GPU-accelerated solutions exist (e.g. realtimeradiosity.com)