### Abstract

A testing algorithm takes a model and produces a set of points that can be used to test whether or not an unknown object is sufficiently similar to the model. A testing algorithm performs a complementary task to that performed by a learning algorithm, which takes a set of examples and builds a model that succinctly describes them. Testing can also be viewed as a type of geometric probing that uses point probes (i.e. test points) to verify that an unknown geometric object is similar to a given model. In this paper we examine the problem of verifying orthogonal shapes using test points. In particular, we give testing algorithms for sets of disjoint rectangles in two and higher dimensions and for general orthogonal shapes in 2-D and 3-D. This work is a first step towards developing efficient testing algorithms for objects with more general shapes, including those with non-orthogonal and curved surfaces.

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

Pages (from-to) | 33-49 |

Number of pages | 17 |

Journal | Computational Geometry: Theory and Applications |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - 1995 |

### Fingerprint

### Keywords

- Helpful teacher learning
- Probing
- Testing

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mathematics
- Control and Optimization
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*5*(1), 33-49. https://doi.org/10.1016/0925-7721(94)00016-O

**Testing orthogonal shapes.** / Romanik, Kathleen; Salzberg, Steven L.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 5, no. 1, pp. 33-49. https://doi.org/10.1016/0925-7721(94)00016-O

}

TY - JOUR

T1 - Testing orthogonal shapes

AU - Romanik, Kathleen

AU - Salzberg, Steven L

PY - 1995

Y1 - 1995

N2 - A testing algorithm takes a model and produces a set of points that can be used to test whether or not an unknown object is sufficiently similar to the model. A testing algorithm performs a complementary task to that performed by a learning algorithm, which takes a set of examples and builds a model that succinctly describes them. Testing can also be viewed as a type of geometric probing that uses point probes (i.e. test points) to verify that an unknown geometric object is similar to a given model. In this paper we examine the problem of verifying orthogonal shapes using test points. In particular, we give testing algorithms for sets of disjoint rectangles in two and higher dimensions and for general orthogonal shapes in 2-D and 3-D. This work is a first step towards developing efficient testing algorithms for objects with more general shapes, including those with non-orthogonal and curved surfaces.

AB - A testing algorithm takes a model and produces a set of points that can be used to test whether or not an unknown object is sufficiently similar to the model. A testing algorithm performs a complementary task to that performed by a learning algorithm, which takes a set of examples and builds a model that succinctly describes them. Testing can also be viewed as a type of geometric probing that uses point probes (i.e. test points) to verify that an unknown geometric object is similar to a given model. In this paper we examine the problem of verifying orthogonal shapes using test points. In particular, we give testing algorithms for sets of disjoint rectangles in two and higher dimensions and for general orthogonal shapes in 2-D and 3-D. This work is a first step towards developing efficient testing algorithms for objects with more general shapes, including those with non-orthogonal and curved surfaces.

KW - Helpful teacher learning

KW - Probing

KW - Testing

UR - http://www.scopus.com/inward/record.url?scp=0347671431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0347671431&partnerID=8YFLogxK

U2 - 10.1016/0925-7721(94)00016-O

DO - 10.1016/0925-7721(94)00016-O

M3 - Article

AN - SCOPUS:0347671431

VL - 5

SP - 33

EP - 49

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 1

ER -