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Exploded view diagrams of mathematical surfaces.

Olga Karpenko1, Wilmot Li, Niloy J Mitra

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This study introduces a new method for visualizing complex mathematical surfaces using exploded views. The technique partitions surfaces into slices to reveal internal structures and aid understanding of shape variations.

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Area of Science:

  • Computer Graphics
  • Computational Geometry
  • Scientific Visualization

Background:

  • Visualizing complex mathematical surfaces is challenging.
  • Existing methods may not effectively reveal internal structures or variations.

Purpose of the Study:

  • To develop a novel technique for visualizing complicated mathematical surfaces.
  • To generate exploded views that expose internal structures and aid comprehension.

Main Methods:

  • Inspired by hand-designed topological illustrations.
  • Partitions surfaces into parallel slices along a linear explosion axis.
  • Develops design rules and automatic algorithms for axis selection and plane placement based on shape symmetries.
  • Works directly on triangle meshes without requiring surface parameterization.

Main Results:

  • Successfully generates exploded views for various mathematical surfaces.
  • Demonstrates a technique for revealing internal structure and cross-sectional variations.
  • Provides a method for selecting explosion axes based on model symmetries.

Conclusions:

  • The proposed technique offers an effective way to visualize complex mathematical surfaces.
  • The method aids in understanding surface shape and cross-sectional changes.
  • Algorithms are robust and applicable to triangle meshes.