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Composing Surfaces with Conformal Rotors

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Abstract

Conformal immersions are harmonic and numerically stable surfaces whose tangents scale isometrically, providing many elegant geometric properties of use in design. This paper maps these forms within the context of discrete differential geometry and conformal geometric algebra in order to outline an approach to synthesizing curved surfaces with applications in architectural geometry, machining, and computer graphics. Inspired by Dorst and Valkenburg’s “Square Root and Logarithm of Rotors” paper of 2011, we reformulate the rationalization of cyclidic nets, piecewise smooth surfaces characterized and controlled directly by their tangents.

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Authors and Affiliations

  1. AlloSphere Research Group, Media Arts and Technology Program, California NanoSystems Institute, University of California, Santa Barbara, 3309 Phelps Hall, Santa Barbara, CA, 93106-6065, USA

    Pablo Colapinto

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  1. Pablo Colapinto
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Correspondence to Pablo Colapinto.

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This work is funded in part by a Robert W. Deutsch Foundation Fellowship at the AlloSphere Research Facility in UC Santa Barbara’s Media Arts and Technology Program. An early version of this paper exists in unpublished form as a dissertation chapter in [5].

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Colapinto, P. Composing Surfaces with Conformal Rotors. Adv. Appl. Clifford Algebras 27, 453–474 (2017). https://doi.org/10.1007/s00006-016-0677-7

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  • DOI: https://doi.org/10.1007/s00006-016-0677-7

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