Jiaoying Shi
State Key Lab of CAD&CG
Zhejiang University, P.R.China

Background
• Pre-computed Radiance Transfer(PRT) [Sloan02, Ng03]
[Sloan03] is an efficient method for rendering soft shadow and inter-reflection under low frequency illumination.
• Radiance transfer information – occlusion and reflection relationship between geometry models, which is the most important in global illumination rendering
• Problems in traditional methods like Ray Tracing: slow computation of ray-model intersection for Radiance transfer information, unpractical for soft shadow/reflection rendering under complex lighting

Precomputed Radiance Transfer
• PRT aims at transferring the computation burden to precomputation process
• PRT precompute, compress and save the Radiance Transfer information to support fast global illumination rendering
• The key to PRT is the constraining mode of scene, the strategy of precomputation, and the data compress method.

Precomputed Radiance Transfer
• PRT method for single object or static scene, in which the radiance transfer information is fixed
• Precomputation method obtain the occlusion, reflection information for each model vertex at every direction occlusion inter-reflection

Precomputed Radiance Transfer
• Analysis for the complex illumination using orthonormal basis function, such as Spherical Harmonics, Wavelets.
• Analysis for the precomputed Radiance Transfer information at each vertex with same basis function
• Efficient shading computation using these analysis coefficients

PRT for dynamical scene
• Radiance Transfer information changes at every frame of dynamical scene
• Previous PRT for dynamical scene [Sloan02]- not a practical approach

• SRTMs – Real-time global illumination rendering method for multiple dynamical objects
• Process each object independently
• Precompute the mutual radiance transfer information, occlusion and reflection, on a bounding sphere of each dynamical object.
• In rendering, these information can be obtained easily by searching the precomputed results

• The Radiance Transfer information for each vertex is dynamical, so the orthonormal analysis cannot be used like previous PRT method
• The orthonormal analysis cannot be used for illumination either.
• We decompose the complex illumination into many directional lights[Agarwla03], and process each light in rendering independently

• Large data amounts of 4D function, compression needed
• Inconvenient storage and search for data on sphere
• Computation of ray-model intersection is reduced to that of ray-bounding sphere intersection, but can this computation be simplified furthest?

Spherical Shadow Map
• Spherical Shadow Map(SSM) for soft shadow rendering.
• Sampling a planar shadow map at every direction, as rearrangement of sampling on bounding sphere
• Small data amount utilizing the insensitivity of human eyes to shape of shadow under complex illumination, reducing the density of sampling directions,
• Uniform resolution of planar shadow map, easy for compression
• Capability to support fast rendering, avoid trigonometric computation

Spherical Shadow Map
• Self shadow map precompute and store self occlusion of each object vertex at every sampling direction
• Shadow Rendering Process
• For each vertex, to determine if every light is occluded by the object itself or by other dynamical object
• Firstly for rendering self shadow, we determine self occlusion by searching precomputed result in self shadow map

Spherical Shadow Map
• Mutual shadow rendering (shadow casted on A by B)
For each vertex of A, if some light is not occluded by A itself, judge if it is occluded by other objects
Firstly, two cases of unocclusion are examined

Spherical Shadow Map
• Mutual shadow rendering (shadow casted on A by B)
Then, s earch the planar map in SSM to determine occlusion x

 q
 x
T y

 q
 y
T

Spherical Shadow Map
• Rendering with light clusters – further acceleration
• Some results

Spherical Shadow Map
Results comparison rendering by SSM rendering by ray-tracing

Spherical Reflection Map
• Spherical Reflection Map(SRM) for soft inter-reflection rendering
• Percomputation process sample a planar map at each direction ( relatively low sampling resolution on each planar map) find the direction of reflection of every sampling ray ignore multi-fold reflection sample self reflection map

Spherical Reflection Map
Inter-reflection rendering
• Reflection rendering is more complicated than shadow rendering
• Compute self reflection firstly
• Computer mutual inter-reflection with SRM

Spherical Reflection Map
• Occlusion problem in reflection rendering
• Judge occlusion using shadow computation results

Demos

Future Work
• Sampling of Radiance Transfer information on various bounding shell
• SRTM for transparent objects
• SRTM for deformable objects
• Using SRTM with BRDF and BTF