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Frontiers of Engineering Reports on Leading-Edge Engineering From the 2000 NAE Symposium on Frontiers in Engineering (2001) / Chapter Skim
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Digital Geometry Processing
Pages 41-44

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From page 41...
... This has led to an explosion in digital signal processing research, aimed at the development of suitable mathematical representations, their manipulation, and associated computational paradigms. One example is the ubiquitous use of digital sound, from portable CD players to musical instruments and digital cellular phones.
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From page 42...
... There are no equispaced sampling patterns on the sphere beyond those given by the five Platonic solids. A digital image produced by one of today's cameras, however, is a regular matrix of picture elements, each representing a sample of the image irradience on the two-dimensional image plane.
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From page 43...
... Additional complications arise in software and hardware implementations. What used to be simple arrays or streams of regularly arranged data is now a complex topological data structure requiring much more sophisticated algorithms to handle.
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From page 44...
... Imagine a file format for geometry that has the property that the first bits in the file provide a rough outline of the shape, and as more bits arrive, more and more details of the shape are revealed. CONCLUSIONS The fourth wave of multimedia that of geometry creates new mathematical and algorithmic challenges that cannot be answered with straightforward extensions of signal processing techniques from the Euclidean setting.
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Key Terms

  • digital geometry
  • signal processing
  • geometry processing
  • respective type
  • euclidean geometry

  • handle digital
  • digital sound
  • regular spacing
  • digital signal
  • euclidean setting

  • curved geometry
  • sampling patterns
  • regular sampling
  • processing toolbox
  • compute power

  • fundamental algorithms
  • network bandwidth
  • associated computational
  • hierarchical transforms
  • fourth wave

  • platonic solids
  • standard subdivision
  • underlying technology
  • element allows
  • wavelet transform

  • processing techniques
  • fourier analysis
  • regular cartesian
  • wring usefulness
  • structure requiring


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