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- Ching-Kuang Shene, John K. Johnstone
- ACM Trans. Graph.
- 1994

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)

- Rida T. Farouki, John K. Johnstone
- Computer Aided Geometric Design
- 1994

- Joon-Kyung Seong, Gershon Elber, John K. Johnstone, Myung-Soo Kim
- Computing
- 2004

We present an algorithm for computing the convex hull of freeform rational surfaces. The convex hull problem is reformulated as one of finding the zero-sets of polynomial equations; using these zero-sets we characterize developable surface patches and planar patches that belong to the boundary of the convex hull.

- Rida T. Farouki, John K. Johnstone
- IMA Conference on the Mathematics of Surfaces
- 1992

- John K. Johnstone
- Computer Aided Geometric Design
- 1993

- John K. Johnstone, Ching-Kuang Shene
- Computers & Graphics
- 1992

- John K. Johnstone, Kenneth R. Sloan
- IEEE Visualization
- 1995

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)

- Ching-Kuang Shene, John K. Johnstone
- Symposium on Solid Modeling and Applications
- 1991

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)

- John K. Johnstone
- Shape Modeling International
- 2001

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)

- John K. Johnstone, Chandrajit L. Bajaj
- SIAM J. Comput.
- 1990