We develop a new method for placing a given context-free grammar into Greibach normal form with only polynomial increase of its size. Starting with an arbitrary "-free context-free grammar G, we transform G into an equivalent context-free grammar H in extended Greibach normal form; i.e., in addition to rules, fulllling the Greibach normal form properties, the grammar can have chain rules. The s...

We show a simple and efficient way for rendering arbitrary views from so-called free-form light fields, employing a convex free form camera surface and a set of arbitrarily oriented camera planes. This way directionally varying real-world imagery can be displayed without intermediate resampling steps, and yet rendering of free form light fields can be performed as efficiently as for two-planepa...

Given two sculptured objects, described b y a collection of rational Bkzier patches, we propose an algorithm that provides the distance between them i f the objects are not intersecting, or a measure of penetration otherwise. The algorithm extends the upper-lower bound subdivision approach to the computation of the nearest points by considering the relative orientations between the subdivided p...

A deformable registration approach for medical images of same dimensionality is proposed. The popular free-form deformations (FFD) setting is utilized to characterize deformations based on a grid of control points. B-splines serve the purpose of interpolating the dense deformation field from a given control point configuration. The central idea is to combine the FFD method with well-understood ...

A family of free-form lenses for intensity control is designed. The lens can shape an incident collimated beam with a given intensity distribution I1 into a new collimated beam with intensity distribution I2. No symmetry is assumed for the two intensity profiles. The key idea is that the lens design problem can be formulated and solved in terms of an optimization process involving a specific ac...

In this paper we prove a conjecture stated in an earlier paper [ A-L]]. The conjecture states that with respect to a rather natural operation, the set of N -dimensional magic cubes forms a free monoid for every integer N > 1. A consequence of this conjecture is a certain identity of formal Dirichlet series. These series and the associated power series are shown to diverge. Generalizations of th...

With the advent of sketch-based methods for shape construction, there is a new degree of power availablecreating several models.

Freeform features (FFF) manipulation is an emerging research area in geometric modelling field, which aims to develop innovative shape modification paradigms, more focused on global shape than on local curve modification. A major hindrance to FFF is given by locality properties of spline curves features representation, which forces designers to apply a direct control points manipulation, where ...

The problem of deforming a given spatial shape is treated. There are many examples of applications in visual computing: tting surfaces to sampled data points in space, correction of distortions in tomographic imaging, modeling of free form geometric shapes, and animating metamorphoses of geometric objects. Our solution warps the space surrounding the given shape with the eeect of deforming the ...