Introduction to Geometric Processing through Optimization


As an introduction to the sphere, this text shows how to formulate several geometry-processing operations to resolve systems of equations in the“least-squares” sense. The equations are derived from native geometric relations using elementary concepts from analytic geometry, such as points, lines, planes, vectors, and polygons. Straightforward and helpful tools for interactive polygon mesh editing result from the most basic descent methods to resolve these optimization problems. Throughout the article, the author develops the mathematical formulations incrementally, keeping in mind that the objective is to implement straightforward software for interactive editing applications that works well in observe. Readers will implement higher-performance versions of those algorithms by replacing the easy solvers proposed here with more advanced ones.

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