### Abstract

Given two non-intersecting simple polylines in the plane, we study the problem of continuously transforming or morphing one polyline into the other. Our morphing strategies have the desirable property that every intermediate polyline is also simple. We also guarantee that no portion of the polylines to be morphed is stretched or compressed by more than a user-defined parameter during the entire morphing. Our algorithms are based on the morphing width, a new metric we have developed for measuring the similarity between two polylines. We develop an algorithm that computes the morphing width of the two polylines and constructs a corresponding morphing strategy in &Ogr;(n^{2} log ^{2} n) time using &Ogr;(n^{2}) space, where n is the total number of vertices in the polylines. We describe another algorithm that computes a factor-2 approximation of the morphing width and a corresponding morphing scheme in &Ogr;(n log n) time.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 680-689 |

Number of pages | 10 |

State | Published - 2001 |

Event | 2001 Operating Section Proceedings, American Gas Association - Dallas, TX, United States Duration: Apr 30 2001 → May 1 2001 |

### Other

Other | 2001 Operating Section Proceedings, American Gas Association |
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Country | United States |

City | Dallas, TX |

Period | 4/30/01 → 5/1/01 |

### Fingerprint

### Keywords

- Algorithms
- Design
- Measurement
- Performance
- Theory
- Verification

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 680-689)

**Morphing between polylines.** / Efrat, Alon; Har-Peled, Sariel; Guibas, Leonidas J.; Murali, T. M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.*pp. 680-689, 2001 Operating Section Proceedings, American Gas Association, Dallas, TX, United States, 4/30/01.

}

TY - GEN

T1 - Morphing between polylines

AU - Efrat, Alon

AU - Har-Peled, Sariel

AU - Guibas, Leonidas J.

AU - Murali, T. M.

PY - 2001

Y1 - 2001

N2 - Given two non-intersecting simple polylines in the plane, we study the problem of continuously transforming or morphing one polyline into the other. Our morphing strategies have the desirable property that every intermediate polyline is also simple. We also guarantee that no portion of the polylines to be morphed is stretched or compressed by more than a user-defined parameter during the entire morphing. Our algorithms are based on the morphing width, a new metric we have developed for measuring the similarity between two polylines. We develop an algorithm that computes the morphing width of the two polylines and constructs a corresponding morphing strategy in &Ogr;(n2 log 2 n) time using &Ogr;(n2) space, where n is the total number of vertices in the polylines. We describe another algorithm that computes a factor-2 approximation of the morphing width and a corresponding morphing scheme in &Ogr;(n log n) time.

AB - Given two non-intersecting simple polylines in the plane, we study the problem of continuously transforming or morphing one polyline into the other. Our morphing strategies have the desirable property that every intermediate polyline is also simple. We also guarantee that no portion of the polylines to be morphed is stretched or compressed by more than a user-defined parameter during the entire morphing. Our algorithms are based on the morphing width, a new metric we have developed for measuring the similarity between two polylines. We develop an algorithm that computes the morphing width of the two polylines and constructs a corresponding morphing strategy in &Ogr;(n2 log 2 n) time using &Ogr;(n2) space, where n is the total number of vertices in the polylines. We describe another algorithm that computes a factor-2 approximation of the morphing width and a corresponding morphing scheme in &Ogr;(n log n) time.

KW - Algorithms

KW - Design

KW - Measurement

KW - Performance

KW - Theory

KW - Verification

UR - http://www.scopus.com/inward/record.url?scp=0005507893&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0005507893&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0898714907

SP - 680

EP - 689

BT - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

ER -