Myung-Soo Kim

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We present a new approach to building a solver for a set of geometric constraints represented by multivariate rational functions. The constraints are formulated using inequalities as well as equalities. When the solution set has dimension larger than zero, we approximate it by fitting a hypersurface to discrete solution points. We also consider a variety of(More)
This paper proposes a new class of unit quaternion curves inSO(3). A general method is developed that transforms a curve in R (defined as a weighted sum of basis functions) into its unit quaternion analogue in SO(3). Applying the method to well-known spline curves (such as Bézier, Hermite, and B-spline curves), we are able to construct various unit(More)
Offset curves have diverse engineering applications, which have consequently motivated extensive research concerning various offset techniques. Offset research in the early 1980s focused on approximation techniques to solve immediate application problems in practice. This trend continued until 1988, when Hoschek [1, 2] applied non-linear optimization(More)
An algorithm is presented to approximate planar offset curves within an arbitrary tolerance > 0. Given a planar parametric curve C(t) and an offset radius r, the circle of radius r is first approximated by piecewise quadratic Bézier curve segments within the tolerance . The exact offset curve Cr(t) is then approximated by the convolution of C(t) with the(More)
Given two planar curves, their convolution curve is defined as the set of all vector sums generated by all pairs of curve points which have the same curve normal direction. The Minkowski sum of two planar objects is closely related to the convolution curve of the two object boundary curves. That is, the convolution curve is a superset of the Minkowski sum(More)
We present an algorithm that computes the convex hull of multiple rational curves in the plane. The problem is reformulated as one of nding the zero-sets of polynomial equations in one or two variables; using these zero-sets we characterize curve segments that belong to the boundary of the convex hull. We also present a preprocessing step that can eliminate(More)
This paper presents a simple and robust method for computing the bisector of two planar rational curves. We represent the correspondence between the foot points on two planar rational curves C1(t) and C2(r) as an implicit curve F(t; r) = 0, where F(t; r) is a bivariate polynomial B-spline function. Given two rational curves of degree m in the xy-plane, the(More)
This paper presents an algorithm to compute an approximation to the general sweep boundary of a 2D curved moving object which changes its shape dynamically while traversing a trajectory. In eeect, we make polygonal approximations to the trajectory and to the object shape at every appropriate instance along the trajectory so that the approximated polygonal(More)