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ACM Transactions on Graphics (TOG), Volume 16 Issue 3, July 1997

Global illumination using local linear density estimation
Bruce Walter, Philip M. Hubbard, Peter Shirley, Donald P. Greenberg
Pages: 217-259
DOI: 10.1145/256157.256158
This article presents the density estimation framework for generating view-independent global illumination solutions. It works by probabilistically simulating the light flow in an environment with light particles that trace random walks...

Color image quantization by minimizing the maximum intercluster distance
Zhigang Xiang
Pages: 260-276
DOI: 10.1145/256157.256159
One of the numerical criteria for color image quantization is to minimize the maximum discrepancy between original pixel colors and the corresponding quantized colors. This is typically carried out by first grouping color points into tight...

Smooth invariant interpolation of rotations
F. C. Park, Bahram Ravani
Pages: 277-295
DOI: 10.1145/256157.256160
We present an algorithm for generating a twice-differentiable curve on the rotation group SO(3) that interpolated a given ordered set of rotation matrices at their specified knot times. In our approach we regard SO(3) as a Lie group with a...

Some characterizations of families of surfaces using functional equations
Enrique Castillo, Andrés Iglesias
Pages: 296-318
DOI: 10.1145/256157.256161
In this article functional equations are used to characterize some families of surfaces. First, the most general surfaces in implicit form f(x, y, z) = 0, such that any arbitrary intersection with the planes...

The symmetric analogue of the polynomial power basis
J. Sánchez-Reyes
Pages: 319-357
DOI: 10.1145/256157.256162
A new polynomial basis over the unit interval t∈0,1 is proposed. The work is motivation by the fact that the monomial (power) form is not suitable in CAGD, as...