### Abstract

We compress storage and accelerate performance of precomputed radiance transfer (PRT), which captures the way an object shadows, scatters, and reflects light. PRT records over many surface points a transfer matrix. At run-time, this matrix transforms a vector of spherical harmonic coefficients representing distant, low-frequency source lighting into exiting radiance. Per-point transfer matrices form a high-dimensional surface signal that we compress using clustered principal component analysis (CPCA), which partitions many samples into fewer clusters each approximating the signal as an affine subspace. CPCA thus reduces the high-dimensional transfer signal to a low-dimensional set of perpoint weights on a per-cluster set of representative matrices. Rather than computing a weighted sum of representatives and applying this result to the lighting, we apply the representatives to the lighting per-cluster (on the CPU) and weight these results perpoint (on the GPU). Since the output of the matrix is lower-dimensional than the matrix itself, this reduces computation. We also increase the accuracy of encoded radiance functions with a new least-squares optimal projection of spherical harmonics onto the hemisphere. We describe an implementation on graphics hardware that performs real-time rendering of glossy objects with dynamic self-shadowing and interreflection without fixing the view or light as in previous work. Our approach also allows significantly increased lighting frequency when rendering diffuse objects and includes subsurface scattering.

Original language | English (US) |
---|---|

Pages (from-to) | 382-391 |

Number of pages | 10 |

Journal | ACM Transactions on Graphics |

Volume | 22 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1 2003 |

Externally published | Yes |

Event | ACM SIGGRAPH 2003 - San Diego, CA, United States Duration: Jul 27 2003 → Jul 31 2003 |

### Fingerprint

### Keywords

- Graphics Hardware
- Illumination
- Monte Carlo Techniques
- Rendering
- Shadow Algorithms

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design

### Cite this

*ACM Transactions on Graphics*,

*22*(3), 382-391. https://doi.org/10.1145/882262.882281

**Clustered principal components for precomputed radiance transfer.** / Sloan, Peter Pike; Hall, Jesse; Hart, John C; Snyder, John.

Research output: Contribution to journal › Conference article

*ACM Transactions on Graphics*, vol. 22, no. 3, pp. 382-391. https://doi.org/10.1145/882262.882281

}

TY - JOUR

T1 - Clustered principal components for precomputed radiance transfer

AU - Sloan, Peter Pike

AU - Hall, Jesse

AU - Hart, John C

AU - Snyder, John

PY - 2003/7/1

Y1 - 2003/7/1

N2 - We compress storage and accelerate performance of precomputed radiance transfer (PRT), which captures the way an object shadows, scatters, and reflects light. PRT records over many surface points a transfer matrix. At run-time, this matrix transforms a vector of spherical harmonic coefficients representing distant, low-frequency source lighting into exiting radiance. Per-point transfer matrices form a high-dimensional surface signal that we compress using clustered principal component analysis (CPCA), which partitions many samples into fewer clusters each approximating the signal as an affine subspace. CPCA thus reduces the high-dimensional transfer signal to a low-dimensional set of perpoint weights on a per-cluster set of representative matrices. Rather than computing a weighted sum of representatives and applying this result to the lighting, we apply the representatives to the lighting per-cluster (on the CPU) and weight these results perpoint (on the GPU). Since the output of the matrix is lower-dimensional than the matrix itself, this reduces computation. We also increase the accuracy of encoded radiance functions with a new least-squares optimal projection of spherical harmonics onto the hemisphere. We describe an implementation on graphics hardware that performs real-time rendering of glossy objects with dynamic self-shadowing and interreflection without fixing the view or light as in previous work. Our approach also allows significantly increased lighting frequency when rendering diffuse objects and includes subsurface scattering.

AB - We compress storage and accelerate performance of precomputed radiance transfer (PRT), which captures the way an object shadows, scatters, and reflects light. PRT records over many surface points a transfer matrix. At run-time, this matrix transforms a vector of spherical harmonic coefficients representing distant, low-frequency source lighting into exiting radiance. Per-point transfer matrices form a high-dimensional surface signal that we compress using clustered principal component analysis (CPCA), which partitions many samples into fewer clusters each approximating the signal as an affine subspace. CPCA thus reduces the high-dimensional transfer signal to a low-dimensional set of perpoint weights on a per-cluster set of representative matrices. Rather than computing a weighted sum of representatives and applying this result to the lighting, we apply the representatives to the lighting per-cluster (on the CPU) and weight these results perpoint (on the GPU). Since the output of the matrix is lower-dimensional than the matrix itself, this reduces computation. We also increase the accuracy of encoded radiance functions with a new least-squares optimal projection of spherical harmonics onto the hemisphere. We describe an implementation on graphics hardware that performs real-time rendering of glossy objects with dynamic self-shadowing and interreflection without fixing the view or light as in previous work. Our approach also allows significantly increased lighting frequency when rendering diffuse objects and includes subsurface scattering.

KW - Graphics Hardware

KW - Illumination

KW - Monte Carlo Techniques

KW - Rendering

KW - Shadow Algorithms

UR - http://www.scopus.com/inward/record.url?scp=33646073780&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646073780&partnerID=8YFLogxK

U2 - 10.1145/882262.882281

DO - 10.1145/882262.882281

M3 - Conference article

AN - SCOPUS:33646073780

VL - 22

SP - 382

EP - 391

JO - ACM Transactions on Computer Systems

JF - ACM Transactions on Computer Systems

SN - 0730-0301

IS - 3

ER -