The ray shooting problem arises in many different contexts and is a bottleneck of ray tracing in computer graphics. Unfortunately, theoretical solutions to the problem are not very practical, while practical methods offer few provable guarantees on performance. Attempting to combine practicality with theoretical soundness, we show how to provably measure the average performance of any ray-shoot...

In this paper we extend our previous result on reusing shooting paths when dealing with moving light sources in radiosity to the final gathering step algorithm, which combines a shooting solution and a gathering step. Paths are reused for each frame in both shooting and gathering steps, obtaining a noticeable reduction of cost in the computation of the solutions for every frame. Moreover, the c...

The spectral problem associated with the linearization about solitary waves of spinor systems or optical coupled mode equations supporting gap solitons is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to eigenvalues. These problems may exhibit oscillatory instabilities where eigenvalues detach from the edges of the continuous spectrum, so called e...

We present a new data structure for a set of n convex simply-shaped fat objects in the plane, and use it to obtain eecient and rather simple solutions to several problems including (i) vertical ray shooting | preprocess a set K of n non-intersecting convex simply-shaped at objects in 3-space, whose xy-projections are fat, for eecient vertical ray shooting queries, (ii) point enclosure | preproc...

This paper presents a fast geodesic shooting algorithm for diffeomorphic image registration. We first introduce a novel finite-dimensional Lie algebra structure on the space of bandlimited velocity fields. We then show that this space can effectively represent initial velocities for diffeomorphic image registration at much lower dimensions than typically used, with little to no loss in registra...