Abstract
A technique referred to as Bézier clipping is presented. This technique forms the basis of algorithm for computing the points at which two curves intersect, and also an algorithm for robustly and quickly computing points of tangency between two curves. Bézier clipping behaves like an intelligent interval Newton method, in which geometric insight is used to identify regions of the parameter domain which exclude the solution set. Implementation tests suggest that the curve intersection algorithm is marginally slower than an algorithm based on implicitization (though faster than other algorithms) for curves of degree four and less, and is faster than the implicitization algorithm for higher degrees.
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