A method of finding the precise ellipse of minimal area, enclosing a finite set of regular planar curves (and points), is presented. We start with a direct approach of prescribing the problem using a set of algebraic constraints and solving them. This approach turns out to be intractable using contemporary memory support and computing power and several improvements are presented to alleviate these difficulties: the number of degrees of freedom and constraints is limited and the search domain is restricted. As a result, an alternative set of algebraic constraints is created whose solution is found in a reasonable amount of memory size and/or computing time.

This paper presents a simple yet precise and efficient algorithm for collision prediction of two oriented bounding boxes under univariate (piecewise) rational motion. We present an analytic solution to the problem of finding the time of collision and the feature involved, or declaring that no collision should occur. Our solution can be applied to boxes of any size, under arbitrary rational rigid motion. The algorithm is based on the efficient examination of the Minkowski sum (MS) of the two boxes, using a spherical Gauss map dual representation, and a precise extraction of the collision time, if any, as a solution to a set of rational equations that are automatically derived

Computer-aided surgical simulation is a topic of increasingly extensive research. Computer graphics, geometric modeling and finite-element analysis all play major roles in these simulations. Furthermore, real-time response, interactivity and accuracy are crucial components in any such simulation system. A major effort has been invested in recent years to find ways to improve the performance, accuracy and realism of existing systems.In this paper, we extend the work of [Sela et al. 2004], in which we used Discontinuous Free Form Deformations (DFFD) to artificially simulate real-time surgical operations. The presented scheme now uses accurate data from a Finite-Element Model (FEM), which simulates the motion response of the tissue around the scalpel, during incision. The data is then encoded once into the DFFD, representing the simulation over time. In real-time, The DFFD is applied to the vertices of the surface mesh at the actual incision location and time. The presented scheme encapsulates and takes advantage of both the speed of the DFFD application, and the accuracy of a FEM. In addition, the presented system uses a haptic force feedback device in order to improve realism and ease of use.