Abstract
In this paper, we present a new graph-based approach to geometric constraint solving. Geometric primitives (points, lines, circles, planes, etc.) possess intrinsic degrees of freedom in their embedding space. Constraints reduce the degrees of freedom of a set of objects. A constraint graph represents the objects and geometric relations between them. A graph algorithm which transforms the undirected constraint graph into a directed acyclic dependency graph is developed. The dependency graph is used to derive a sequence of construction operations as a symbolic solution to the constraint problem. The approach is based on a dimension independent degree-of-freedom analysis, which, among other things, allows for a uniform handling of 2-D and 3-D constraints as well as algebraic equations between parameters. The approach handles completely constrained, as well as under- and over constrained definitions with a worst-case time complexity of O(n), where n is the number of geometric elements.
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© 1997 Springer-Verlag Berlin Heidelberg
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Hsu, CY., Brüderlin, B. (1997). A Degree-of-Freedom Graph Approach. In: Strasser, W., Klein, R., Rau, R. (eds) Geometric Modeling: Theory and Practice. Focus on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60607-6_10
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DOI: https://doi.org/10.1007/978-3-642-60607-6_10
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