
3.3 Range of Approaches 61
An alternative approach computes bounds on the total error instead. For exam-
ple, we can store a spatial data structure, such as a sphere, box, or other simple 3D
volume, with the simplified mesh elements. Here, the simple volume indicates the
size and locality of the total error thus far. We then accumulate the new incremental
error with the previous total error by growing the volume to contain the new incre-
mental error. We compose two volumes by computing the position and size of a new
volume that contains all the various component volumes (a type of 3D analog of in-
terval arithmetic).