Abstract
Coordinate transformations and coordinate systems are introduced as an object class. Finite point sets are considered as objects with internal constraints, communicating through point identifications. A geometric approximation algorithm for curve intersection based on a generic nearest-point method for curves is explored. The method is guaranteed to find an intersection point or nearest approach, depending on the starting point and specified precision. Convergence properties of the algorithm have been proved, and demonstrated in implementation. Intersection problems are thus made independent of object type, without the need for explicit algebraic solutions.
This chapter combines work towards a Ph.D. by Burns with practical results by both authors.
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© 1991 EUROGRAPHICS The European Association for Computer Graphics
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Rankin, J.R., Burns, J. (1991). Coordinate Frames and Geometric Approximation in Graphics Object Oriented Programming. In: Blake, E.H., Wisskirchen, P. (eds) Advances in Object-Oriented Graphics I. EurographicSeminars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76303-8_8
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DOI: https://doi.org/10.1007/978-3-642-76303-8_8
Publisher Name: Springer, Berlin, Heidelberg
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