Abstract Shape Synthesis From Linear Combinations of Clelia Curves

Putnam, Lance; Todd, Stephen and Latham, William. 2019. 'Abstract Shape Synthesis From Linear Combinations of Clelia Curves'. In: ACM/EG Expressive Symposium 2019. Genoa, Italy 5-6 May 2019. [Conference or Workshop Item]

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Abstract or Description

This article outlines several families of shapes that can be produced from a linear combination of Clelia curves. We present parameters required to generate a single curve that traces out a large variety of shapes with controllable axial symmetries. Several families of shapes emerge from the equation that provide a productive means by which to explore the parameter space. The mathematics involves only arithmetic and trigonometry making it accessible to those with only the most basic mathematical background. We outline formulas for producing basic shapes, such as cones, cylinders, and tori, as well as more complex families of shapes having non-trivial symmetries. This work is of interest to computational artists and designers as the curves can be constrained to exhibit specific types of shape motifs while still permitting a liberal amount of room for exploring variations on those shapes.

Item Type:

Conference or Workshop Item (Paper)

Identification Number (DOI):



Computing methodologies, Parametric curve and surface models, Applied computing, Media art

Departments, Centres and Research Units:



21 March 2019Accepted
5 May 2019Published

Event Location:

Genoa, Italy

Date range:

5-6 May 2019

Item ID:


Date Deposited:

20 Nov 2019 13:32

Last Modified:

18 Jun 2021 05:04



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