Aane Arithmetic and Its Applications to Computer Graphics
Aane Arithmetic and Its Applications to Computer Graphics
复制标题
DOI：
--
复制
发表时间：
1990
期刊：
影响因子：
--
通讯作者：
Luiz Dihl Comba;J. Stolfi
中科院分区：
文献类型：
--
作者：
Luiz Dihl Comba;J. Stolfi
我们描述了一种新的数值计算方法，我们称之为NE算术(AA)。该模型类似于标准的区间算术，在某种程度上，它自动跟踪每个计算值的舍入和截断误差。然而，通过考虑操作数和子公式之间的相关性，AA能够为计算量提供更严格的界限，在输入变量的不确定性中具有近似二次的误差。我们还描述了AA在计算机图形学问题中的两个应用，其中这个特性特别有价值：即光线跟踪和隐式曲面的八叉树的构造。
We describe a new method for numeric computations, which we call a ne arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of 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.