### Abstract

Interpolation of two-dimensional shapes described by iterated function systems is explored. Iterated function systems define shapes using self-transformations, and interpolation of these shapes requires interpolation of these transformations. Polar decomposition is used to avoid singular intermediate transformations and to better simulate articulated motion. Unlike some other representations, such as polygons, shaped described by iterated function systems can become totally disconnected. A new, fast and image-based technique for determining the connectedness of an iterated function system attractor is introduced. For each shape interpolation, a two parameter family of iterated function systems is defined, and a connectedness locus for these shapes is plotted, to maintain connectedness during the interpolation.

Original language | English (US) |
---|---|

Pages (from-to) | 155-162 |

Number of pages | 8 |

Journal | Proceedings - Graphics Interface |

State | Published - Dec 1 1997 |

Externally published | Yes |

Event | Proceedings of the 1997 Graphics Interface Conference - Kelowna, Can Duration: May 21 1997 → May 23 1997 |

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### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design

### Cite this

*Proceedings - Graphics Interface*, 155-162.

**Linear fractal shape interpolation.** / Burch, Brandon; Hart, John C.

Research output: Contribution to journal › Conference article

*Proceedings - Graphics Interface*, pp. 155-162.

}

TY - JOUR

T1 - Linear fractal shape interpolation

AU - Burch, Brandon

AU - Hart, John C.

PY - 1997/12/1

Y1 - 1997/12/1

N2 - Interpolation of two-dimensional shapes described by iterated function systems is explored. Iterated function systems define shapes using self-transformations, and interpolation of these shapes requires interpolation of these transformations. Polar decomposition is used to avoid singular intermediate transformations and to better simulate articulated motion. Unlike some other representations, such as polygons, shaped described by iterated function systems can become totally disconnected. A new, fast and image-based technique for determining the connectedness of an iterated function system attractor is introduced. For each shape interpolation, a two parameter family of iterated function systems is defined, and a connectedness locus for these shapes is plotted, to maintain connectedness during the interpolation.

AB - Interpolation of two-dimensional shapes described by iterated function systems is explored. Iterated function systems define shapes using self-transformations, and interpolation of these shapes requires interpolation of these transformations. Polar decomposition is used to avoid singular intermediate transformations and to better simulate articulated motion. Unlike some other representations, such as polygons, shaped described by iterated function systems can become totally disconnected. A new, fast and image-based technique for determining the connectedness of an iterated function system attractor is introduced. For each shape interpolation, a two parameter family of iterated function systems is defined, and a connectedness locus for these shapes is plotted, to maintain connectedness during the interpolation.

UR - http://www.scopus.com/inward/record.url?scp=0031370305&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031370305&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0031370305

SP - 155

EP - 162

JO - Proceedings - Graphics Interface

JF - Proceedings - Graphics Interface

SN - 0713-5424

ER -