%0 Conference Proceedings
%T Affine arithmetic and its applications to computer graphics
%A Comba, João Luiz Dihl,
%A Stolfi, Jorge,
%@affiliation Laboratório de Computação Gráfica (LCG-COPPE) da Universidade Federal do Rio de Janeiro
%@affiliation Departamento da Ciência da Computação (DCC) da Universidade Estadual de Campinas (UNICAMP)
%E Figueiredo, Luiz Henrique de,
%E Gomes, Jonas de Miranda,
%B Simpósio Brasileiro de Computação Gráfica e Processamento de Imagens, 6 (SIBGRAPI)
%8 19 - 22 out. 1993
%I Sociedade Brasileira de Computação
%J Porto Alegre
%K computer graphics, construction of octrees, implicit surfaces, arithmetic.
%X We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track or rounding and truncation errors for each computed value. However, by taking into account correlations between operands and sub-formulas, AA is able to provide much tighter bounds for the computed quantities, with errors that are approximately quadratic in the uncertainty of the input variables. We also describe two applications of AA to computer graphics problems, where this feature is particularly valuable: namely, ray tracing and the construction of octrees for implicit surfaces.
%3 2 Affine arithmetic and its applications to computer graphics.pdf