Abstract Shape Synthesis From Linear Combinations of Clelia Curves

Putnam, Lance; Todd, Stephen; Latham, William

Abstract Shape Synthesis From Linear Combinations of Clelia Curves

Files

087-099.pdf (10.21 MB)

Date

2019

Authors

Putnam, Lance
Todd, Stephen
Latham, William

Publisher

The Eurographics Association

Abstract

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.

        @inproceedings{10.2312:exp.20191080
,
booktitle = {ACM/EG Expressive Symposium
},
editor = {Kaplan, Craig S. and Forbes, Angus and DiVerdi, Stephen
},
title = {{Abstract Shape Synthesis From Linear Combinations of Clelia Curves
}},
author = {Putnam, Lance and 
Todd, Stephen and 
Latham, William
},
year = {2019
},
publisher = {The Eurographics Association
},
ISBN = {978-3-03868-078-9
},
DOI = {10.2312/exp.20191080
}
}