### Abstract

Accurate theoretical characterization of radiation fields is a valuable tool in the design of complex systems, such as linac heads and intracavitary applicators, and for generation of basic dose calculation data that is inaccessible to experimental measurement. Both Monte Carlo and deterministic solutions to such problems require a system for accurately modeling complex 3-D geometries that supports ray tracing, point and segment classification, and 2-D graphical representation. Previous combinatorial approaches to solid modeling, which involve describing complex structures as set-theoretic combinations of simple objects, are limited in their ease of use and place unrealistic constraints on the geometric relations between objects such as excluding common boundaries. A new approach to volume-based solid modeling has been developed which is based upon topologically consistent definitions of boundary, interior, and exterior of a region. From these definitions, FORTRAN union, intersection, and difference routines have been developed that allow involuted and deeply nested structures to be described as set-theoretic combinations of ellipsoids, elliptic cylinders, prisms, cones, and planes that accommodate shared boundaries. Line segments between adjacent intersections on a trajectory are assigned to the appropriate region by a novel sorting algorithm that generalizes upon Siddon’s approach. Two 2-D graphic display tools are developed to help the debugging of a given geometric model. In this paper, the mathematical basis of our system is described, it is contrasted to other approaches, and examples are discussed.

Original language | English |
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Pages (from-to) | 667-677 |

Number of pages | 11 |

Journal | Medical physics |

Volume | 19 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1992 |

### Keywords

- point-set topology Geometric modeling Monte Carlo simulation radiation transport calculation

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## Cite this

*Medical physics*,

*19*(3), 667-677. https://doi.org/10.1118/1.596810