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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
Polar Coordinates: Problem Solving01:27

Polar Coordinates: Problem Solving

Directional radiation patterns are central to antenna analysis, as they illustrate how signal strength varies with direction. These patterns are often modeled using polar plots, where the radial distance from the origin represents signal intensity at a given angle. A commonly used idealized form is the four-lobed rose curve, which captures the concept of directional beams in a simplified mathematical form.The four-lobed rose curve, described by r = cos⁡(2θ), features four symmetric lobes, each...
Parseval's Theorem for Fourier transform01:15

Parseval's Theorem for Fourier transform

Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a signal's...
Trigonometric Fourier series01:17

Trigonometric Fourier series

Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Basic signals of Fourier Transform01:07

Basic signals of Fourier Transform

The Fourier Transform is a pivotal mathematical tool in signal processing, enabling the transformation of time-domain signals into their frequency-domain representations. Among the numerous elements within this domain, certain functions like the sinc function, delta function, and exponential signals hold significant importance due to their unique properties and implications.
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Related Experiment Video

Updated: Jul 8, 2026

Scattering And Absorption of Light in Planetary Regoliths
11:34

Scattering And Absorption of Light in Planetary Regoliths

Published on: July 1, 2019

Spherical piecewise constant basis functions for all-frequency precomputed radiance transfer.

Kun Xu1, Yun-Tao Jia, Hongbo Fu

  • 1Department of Computer Science and Technology, Tsinghua University, Beijing, People's Republic of China. xu-k@mails.tsinghua.ed.cn

IEEE Transactions on Visualization and Computer Graphics
|January 15, 2008
PubMed
Summary

This study introduces spherical piecewise constant basis functions (SPCBFs) for efficient precomputed radiance transfer. These functions enable real-time rendering of dynamic scenes with object rotation and on-the-fly material editing.

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Area of Science:

  • Computer Graphics
  • Rendering Techniques

Background:

  • Precomputed radiance transfer (PRT) is crucial for realistic rendering.
  • Efficiently handling dynamic scenes and material properties in PRT remains a challenge.

Purpose of the Study:

  • To introduce a novel basis function for PRT.
  • To enable efficient all-frequency rendering with dynamic elements.

Main Methods:

  • Developed spherical piecewise constant basis functions (SPCBFs).
  • Partitioned the illumination sphere and precomputed light coefficients.
  • Utilized summed-area tables (SAT) and visibility distance tables (VDT) for runtime approximation.

Main Results:

  • SPCBFs support efficient rotation and all-frequency signal representation.
  • Achieved real-time frame rates with graphics hardware acceleration.
  • Enabled dynamic scene rendering with object rotation and BRDF editing.

Conclusions:

  • SPCBFs offer a robust solution for advanced PRT.
  • The method facilitates novel real-time rendering effects.