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Article The Brush-Trajectory Approach to Figure Specification: Some Algebraic-Solutions

Author(s): Pijush K. Ghosh, S. P. Mudur.
Article: ACM Transactions on Graphics, Vol. 3, No. 2, pp. 110--134, April, 1984.
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The brush-trajectory method, a very natural scheme for describing two-dimensional shapes used in graphic arts and typesetting applications, has been used in only a few systems largely owing to the computational complexity involved in transforming such descriptions into raster bit maps. This paper addresses the problem. For some specific brushes and trajectories we derive algebraic solutions for describing the resulting outlines. The result of dynamic transformations on the brush as it moves along the trajectory is also studied. A special closed, smooth, convex brush defined by a fourth-order parametric equation is introduced to describe more complex shapes. An algorithmic solution to determining the outlines for an unconstrained brush is then presented. Finally, we present some ideas on a canonical brush and its use in solving the inverse problem, that is, determininl, the brushtrajectory description from given outlines.

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