Abstract
A method is described for performing a symbolic analysis of planar drawings. The method takes input in the form of a dimensioned (i.e. labeled) drawing and determines whether the coordinates of all of the points in the drawing can be uniquely written in terms of the specified labels. If it is possible to determine the coordinates of the points (i.e. the drawing is consistently dimensioned), then they are calculated. Otherwise the algorithm returns a flag specifying whether the drawing is underdimensioned or over-dimensioned. The method employes standard constructions from geometry such as the construction of a line from two distinct points or the construction of a line from a given line, a point and an angle. In order to determine whether some sequence of given constructions can be used to calculate the coordinates of each point we construct and analyse an undirected graph called the dimension graph of the drawing. If such a sequence exists, then the calculations are performed by calling symbolic routines which correspond to the various constructions. An implementation is described and examples are given.
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© 1989 Springer-Verlag Berlin Heidelberg
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Todd, P.H., Cherry, G.W. (1989). Symbolic analysis of planar drawings. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_33
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DOI: https://doi.org/10.1007/3-540-51084-2_33
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