Articulating Space : Geometric Algebra for Parametric Design - Symmetry, Kinematics, and Curvature
- Degree Grantor:
- University of California, Santa Barbara. Media Arts and Technology
- Degree Supervisor:
- Marko Peljhan
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2016
- Issued Date:
- 2016
- Topics:
- Design, Applied mathematics, and Computer science
- Keywords:
- Differential Geometry,
Geometric Algebra,
Crystallographic Space Groups,
Deployable Structures,
Cyclidic Nets, and
Robotics - Genres:
- Online resources and Dissertations, Academic
- 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
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:10103561
- ARK:
- ark:/48907/f3668d0q
- ISBN:
- 9781339671277
- Catalog System Number:
- 990046534250203776
- Copyright:
- Pablo Colapinto, 2015
- Rights:
- In Copyright
- Copyright Holder:
- Pablo Colapinto
File | Description |
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Access: Public access | |
Colapinto_ucsb_0035D_12884.pdf | pdf (Portable Document Format) |