Robust and Error-Free Geometric Computing

This is a how-to book for solving geometric problems robustly or error free in actual practice. The contents and accompanying source code are based on the feature requests and feedback received from industry professionals and academics who want both the descriptions and source code for implementations of geometric algorithms. The book provides a framework for geometric computing using several arithmetic systems and describes how to select the appropriate system for the problem at hand. Key Features: A framework of arithmetic systems that can be applied to many geometric algorithms to obtain robust or error-free implementations Detailed derivations for algorithms that lead to implementable code Teaching the readers how to use the book concepts in deriving algorithms in their fields of application The Geometric Tools Library, a repository of well-tested code at the Geometric Tools website, https://www.geometrictools.com, that implements the book concepts

1.Introduction. 2. Arbitrary Precision Arithmetic. 3. Interval Arithmetic. 4. Computational Geometry Algorithms. 5. Distance Queried. 6. Intersection Queries. 7. Mixed-Mode Computing. 8. Robust Floating-Point Computing. 9. Implementation of Arithmetic

Dave Eberly is the Chief Technologist for Geometric Tools, a company that provides contracting and consulting services for software development in computational mathematics in the fields of geometry, graphics, and physics. Previously, he worked at Microsoft on various projects including multisensor cameras for volumetric video, Microsoft Surface Hub, Microsoft HoloLens, and the machine-learning-based Custom Vision Service associated with the Artificial Intelligence and Research Initiative. He also worked at Omnivor Inc., a start-up company that develops algorithms and software for volumetric video.