Conic section is one of the geometric elements most commonly used for shape expression and mechanical accessory cartography. A rational quadratic Bézier curve is just a conic section. It cannot represent an elliptic segment whose center angle is not less than . However, conics represented in rational quartic format when compared to rational quadratic format, enjoy better properties such as bein...

H. J. Kong Jin Choi J. S. Shin S. W. Yi B. G. Jeon Korea Advanced Institute of Science and Technology Department of Physics Daejeon 305-701, Korea E-mail: [email protected] Abstract. By numerical simulations, it has been shown that a conventional cylindrical rod can be used as a hollow conic beam generator by illuminating a parallel laser beam inclined to the axis of the rod. Half of the conic...

We consider the problem of computing a restricted nonnegative matrix factorization (NMF) of an m × n matrix X . Specifically, we seek a factorization X ≈ BC, where the k columns of B are a subset of those from X and C ∈ Rk×n ≥0 . Equivalently, given the matrix X , consider the problem of finding a small subset, S, of the columns of X such that the conic hull of S ε-approximates the conic hull o...

Catadioptric systems consist of the combination of lenses and mirrors. From them, central panoramic systems stand out because they provide a unique effective viewpoint, leading to the well-known unifying theory for central catadioptric systems. This paper considers catadioptric systems consisting of a conic mirror and a projective camera. Although a system with conic mirror does not possess a s...

We study convex conic optimization problems in which the right-hand side and the cost vectors vary linearly as a function of a scalar parameter. We present a unifying geometric framework that subsumes the concept of the optimal partition in linear programming (LP) and semidefinite programming (SDP) and extends it to conic optimization. Similar to the optimal partition approach to sensitivity an...

The rational Bézier form has become a standard in CAD-CAM packages and data exchange formats, because it encompasses both conic segments (in the quadratic case) and general free-form geometry. We present several results on the relationship between the quadratic rational Bézier form and the classical definition of conics in terms of their characteristics, such as foci, centre, axis and eccentric...