Geometric Modeling with Conical Meshes and Developable Surfaces

By Yang Liu, Helmut Pottmann, Johannes Wallner, Yong-Liang Yang, Wenping Wang. ACM Transactions on Graphics, 2006

476 citations recorded by the source corpus.

In architectural freeform design, the relation between shape and fabrication poses new challenges and requires more sophistication from the underlying geometry. The new concept of conical meshes satisfies central requirements for this application: They are quadrilateral meshes with planar faces, and therefore particularly suitable for the design of freeform glass structures. Moreover, they possess a natural offsetting operation and provide a support structure orthogonal to the mesh. Being a discrete analogue of the network of principal curvature lines, they represent fundamental shape characteristics. We show how to optimize a quad mesh such that its faces become planar, or the mesh becomes even conical. Combining this perturbation with subdivision yields a powerful new modeling tool for all types of quad meshes with planar faces, making subdivision attractive for architecture design and providing an elegant way of modeling developable surfaces.

View Paper: https://www.semanticscholar.org/paper/5a0cb7a9343ecbb5e5efc8633b857b629d17796b

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Citations in the corpus

Extracting lines of curvature from noisy point clouds (2009, background): “(29) use principal directions to create conical meshes.”