Hierarchical object representations play an important role in performing efficient collision handling. Many different geometric primitives have been used to construct these representations, which allow areas of interaction to be localized quickly. For time-critical algorithms, there are distinct advantages to using hierarchies of spheres, known as sphere-trees, for object representation. This paper presents a novel algorithm for the construction of sphere-trees. The algorithm presented approximates objects, both convex and non-convex, with a higher degree of fit than existing algorithms. In the lower levels of the representations, there is almost an order of magnitude decrease in the number of spheres required to represent the objects to a given accuracy.

Collision handling is very computationally expensive, especially in large scale interactive animations. Hierarchical object representations play an important role in performing efficient collision handling. Many different geometric primitives have been used to construct these representations, which allow areas of interaction to be localised quickly. For time-critical algorithms, such as interruptible collision detection, there are distinct advantages to using hierarchies of spheres, known as sphere-trees. This paper presents a novel algorithm for the construction of sphere-trees. The algorithm presented approximates objects, both convex and non-convex, with a higher degree of fit than existing algorithms. In the lower levels of the representations, there is almost an order of magnitude decrease in the number of spheres required to represent the objects to a given accuracy.

Collision handling is very computationally expensive, especially in large scale interactive animations. Hierarchical object representations play an important role in performing efficient collision handling. Many different geometric primitives have been used to construct these representations, which allow areas of interaction to be localised quickly. For time-critical algorithms, such as interruptible collision detection, there are distinct advantages to using hierarchies of spheres, known as sphere-trees. This paper presents a novel algorithm for the construction of sphere-trees. The algorithm presented approximates objects, both convex and non-convex, with a higher degree of fit than existing algorithms. In the lower levels of the representations, there is almost an order of magnitude decrease in the number of spheres required to represent the objects to a given accuracy.

Cross-sectional pmfiles of medieval mouldings are often considered to be a vital form of data to Art Historians. Mouldings were often used to highlight salient areas of buildings, and they provide a wealth of information. To date little use of computer technology has been made in their acquisition, storage and analysis. This paper presents a representation for such planar curves, and an algorithm for its extraction from planar curves. The representation uses geometric primitives specificalh line and arc segments, which allows the curves to be represented in a compact form, approximating the circular sections more eflectively than using linear segments alone. These idealised models provide templates which provide a means for the identification of specific features, within profiles, which can then serve as characteristics for use in case-based reasoning.

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