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Interactive Visualization of Rotational Symmetry Fields on Surfaces.

Jonathan Palacios, Eugene Zhang

IEEE Transactions on Visualization and Computer Graphics

|September 22, 2010

Summary

This study presents an algorithm for visualizing N-way rotational symmetry (N-RoSy) fields in computer graphics. The method adapts line integral convolution to faithfully represent N-RoSy fields, overcoming visualization ambiguities.

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Area of Science:

Computer Graphics
Geometric Modeling
Scientific Visualization

Background:

Rotational symmetries (RoSys) are crucial in computer graphics for applications like surface parameterization and geometry synthesis.
Visualizing N-way rotational symmetry (N-RoSy) fields is challenging due to inherent directional ambiguities.

Purpose of the Study:

To develop a robust algorithm for the faithful and interactive representation of N-RoSy fields.
To address the visualization challenges posed by the multiple directions in N-RoSy fields.

Main Methods:

Adaptation of the Line Integral Convolution (LIC) technique, originally used for vector and tensor fields.
Decomposition of N-RoSy fields into multiple vector fields.
Generation and blending of LIC images from decomposed fields.
Application of probability theory to correct contrast loss in blended images.

Main Results:

Successful faithful and interactive representation of N-RoSy fields in both planar and surface domains.
Preservation of directional information despite blending multiple LIC images.
Contrast correction without frame-by-frame image analysis.

Conclusions:

The proposed algorithm effectively visualizes N-RoSy fields, enhancing computer graphics applications.
The method provides an interactive and accurate solution to a long-standing visualization problem.
Leveraging probability theory offers an efficient approach to improving image quality in scientific visualization.