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Hamiltonian triangulations for fast rendering

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Abstract

High-performance rendering engines are often pipelined; their speed is bounded by the rate at which triangulation data can be sent into the machine. An ordering such that consecutive triangles share a face, which reduces the data rate, exists if and only if the dual graph of the triangulation contains a Hamiltonian path. We (1) show thatany set ofn points in the plane has a Hamiltonian triangulation; (2) prove that certain nondegenerate point sets do not admit asequential triangulation; (3) test whether a polygonP has a Hamiltonian triangulation in time linear in the size of its visibility graph; and (4) show how to add Steiner points to a triangulation to create Hamiltonian triangulations that avoid narrow angles.

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Correspondence to Martin Held.

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Arkin, E.M., Held, M., Mitchell, J.S.B. et al. Hamiltonian triangulations for fast rendering. The Visual Computer 12, 429–444 (1996). https://doi.org/10.1007/BF01782475

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Key words

  • Triangulations
  • Hamiltonian paths
  • Quadrangulation
  • Rendering
  • Computer graphics