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Articulating Space : Geometric Algebra for Parametric Design - Symmetry, Kinematics, and Curvature

Author:
Colapinto, Pablo
Degree Supervisor:
Marko Peljhan
Place of Publication:
[Santa Barbara, Calif.]
Publisher:
University of California, Santa Barbara
Creation Date:
2016
Issued Date:
2016
Topics:
Applied mathematics, Computer science, and Design
Keywords:
Crystallographic Space Groups
Cyclidic Nets
Deployable Structures
Differential Geometry
Geometric Algebra
Robotics
Genres:
Online resources and Dissertations, Academic
Degree Grantor:
University of California, Santa Barbara. Media Arts and Technology
Dissertation:
Ph.D.--University of California, Santa Barbara, 2016
Description:

To advance the use of geometric algebra in practice, we develop computational methods for parameterizing spatial structures with the conformal model. Three discrete parameterizations -- symmetric, kinematic, and curvilinear -- are employed to generate space groups, linkage mechanisms, and rationalized surfaces. In the process we illustrate techniques that directly benefit from the underlying mathematics, and demonstrate how they might be applied to various scenarios. Each technique engages the versor -- as opposed to matrix -- representation of transformations, which allows for structure-preserving operations on geometric primitives. This covariant methodology facilitates constructive design through geometric reasoning: incidence and movement are expressed in terms of spatial variables such as lines, circles and spheres. In addition to providing a toolset for generating forms and transformations in computer graphics, the resulting expressions could be used in the design and fabrication of machine parts, tensegrity systems, robot manipulators, deployable structures, and freeform architectures. Building upon existing algorithms, these methods participate in the advancement of geometric thinking, developing an intuitive spatial articulation that can be creatively applied across disciplines, ranging from time-based media to mechanical and structural engineering, or reformulated in higher dimensions.

Physical Description:
1 online resource (222 pages)
Format:
Text
Collection(s):
UCSB electronic theses and dissertations
ARK:
ark:/48907/f3668d0q
ISBN:
9781339671277
Catalog System Number:
004653425
Rights:
In Copyright
File (Download) Description
Access: Public access
Pdf 32x Colapinto_ucsb_0035D_12884.pdf (29.6 MB) Full-text thesis or dissertation