Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
As-rigid-as-possible shape interpolation
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Dynamic generators of topologically embedded graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Greedy optimal homotopy and homology generators
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
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An introduction to geometry processing using discrete exterior calculus (DEC), which provides a simple, flexible, and efficient framework for building a unified geometry-processing platform. The course provides essential mathematical background as well as a large array of real-world examples. It also provides a short survey of the most relevant recent developments in digital geometry processing and discrete differential geometry. Compared to previous SIGGRAPH courses, this course focuses heavily on practical aspects of DEC, with an emphasis on implementation and applications. The course begins with the core ideas from exterior calculus, in both the smooth and discrete setting. Then it shows how a large number of fundamental geometry-processing tools (smoothing, parameterization, geodesics, mesh optimization, etc.) can be implemented quickly, robustly, and efficiently within this single common framework. It concludes with a discussion of recent extensions of DEC that improve efficiency, accuracy, and versatility. The course notes grew out of the discrete differential geometry course taught over the past five years at the California Institute of Technology, for undergraduates and beginning graduate students in computer science, applied mathematics, and associated fields. The notes also provide guided exercises (both written and coding) that attendees can later use to deepen their understanding of the material.