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L. H. de Figueiredo, J. Stolfi, Adaptive enumeration of implicit surfaces with a#ne arithmetic, Proc. Implicit Surfaces '95, 161--170.

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Sampling implicit objects with physically-based particle.. - de Figueiredo, Gomes (1996)   Self-citation (De figueiredo)   (Correct)

....called a#ne arithmetic, has been proposed to overcome this problem [8] A#ne arithmetic does handle coupling in expressions and is therefore able to provide better estimates. Adaptive enumeration of implicit objects using a#ne arithmetic is a promising technique, specially for rendering [9] (Fig. 6) to appear in Computer Graphics 20 #3 (1996) special issue Computer Graphics in Brazil ) 4 Figure 6: Adaptive enumeration with a#ne arithmetic; h(x, y) x 2 y 2 xy (xy) 2 2 1 4. Physically based sampling Let V be an object given implicitly in R n by a ....

L. H. de Figueiredo, J. Stolfi, Adaptive enumeration of implicit surfaces with a#ne arithmetic, Proc. Implicit Surfaces '95, 161--170.


A Methodology for Piecewise Linear Approximation of Surfaces - Velho, de Figueiredo, Gomes (1997)   Self-citation (De figueiredo)   (Correct)

....of implementation and performance. This is mainly due to the 3D combinatorics of the problem, as well as, the need of space and time resources. Recently, however, range analysis techniques [21] have been used successfully to avoid full enumeration of implicit surfaces in high resolution meshes [22 25]. 4.3 A New Strategy for Adaptation We propose a general methodology to solve the adaptive polygonization problem. Using this methodology we are able to develop two new algorithms for the approximation of parametric and implicit surfaces. These two polygonization methods will be described ....

L. H. de Figueiredo and J. Stolfi. Adaptive enumeration of implicit surfaces with a#ne arithmetic. In Proceedings of Implicit Surfaces '95, pages 161--170, April 1995. Extended version to appear in Computer Graphics Forum.

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