To What Extent Are Existing Volume Mapping Algorithms Practically Useful?

Mappings between geometric domains play a crucial role in many algorithms in geometry processing and are heavily used in various applications. Despite the significant progress made in recent years, the challenge of reliably mapping two volumes still needs to be solved to an extent that is satisfactory for practical applications. This paper offers a review of provably robust volume mapping algorithms, evaluating their performances in terms of time, memory and ability to generate a correct result both with exact and inexact numerical models. We have chosen and evaluated the two most advanced methods currently available, using a state-of-the-art benchmark designed specifically for this type of analysis. We are sharing both the statistical results and specific volume mappings with the community, which can be utilized by future algorithms for direct comparative analysis. We also provide utilities for reading, writing, and validating volume maps encoded with exact rational coordinates, which is the natural form of output for robust algorithms in this class. All in all, this benchmark offers a neat overview of where do we stand in terms of ability to reliably solve the volume mapping problem, also providing practical data and tools that enable the community to compare future algorithmic developments without the need to re-run existing methods.