John K. Johnstone

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In general, two quadric surface intersect in a space quartic curve. However, the intersection frequently degenerates to a collection of plane curves. Degenerate cases are frequent in geometric/solid modeling because degeneracies are often required by design. Their detection is important because degenerate intersections can be computed more easily and allow(More)
We present a method for constructing tensor product Bezier surfaces from contour (cross-section) data. Minimal area triangulations are used to guide the surface construction , and the final surface reflects the optimality of the triangulation. The resulting surface differs from the initial triangulation in two important ways: it is smooth (as opposed to the(More)
In general, two quadric surfaces intersect in a space quartic curve. However, the intersection curve frequently degenerates to a collection of plane curves. These degenerate cases introduce problems into the general intersection algorithms and are difficult to implement in a reliable way. In this paper, we investigate this problem for natural quadrics.(More)
We develop an efficient algorithm for the construction of common tangents between a set of Bezier curves. Common tangents are important in visibility, lighting, robot motion, and convex hulls. Common tangency is reduced to the intersection of parametric curves in a dual space, rather than the traditional intersection of implicit curves. We show how to(More)