Controlled precision volume integration
- 1 January 1992
- conference paper
- Published by Association for Computing Machinery (ACM)
Abstract
Traditional methods for evaluating the low-albedo vol- ume rendering integral do not include bounds on the magnitude of approximation error. In this paper, we ex- amine three techniques for solving this integral with er- ror bounds: trapezoid rule, Simpson's rule, and a power series method. In each case, the expression for the error bound provides a mechanism for computing the inte- gral to any specified precision. The formulations pre- sented are appropriate for polynomial reconstruction from point samples; however, the approach is consid- erably more general. The three techniques we present differ in relative efficiency for computing results to a given precision. The trapezoid rule and Simpson's rule are most efficient for low- to medium-precision solu- tions. The power series method converges rapidly to a machine precision solution, providing both an efficient means for high-accuracy volume rendering, and a ref- erence standard by which other approximations may be measured.Keywords
This publication has 0 references indexed in Scilit: