We present a method for extracting iso-surfaces and their intersections in 4D. Our work is a signiicant extension of the 3D Marching Lines algorithm with new orientation and implementation considerations. As a practical tool, it can be applied to track eeciently space curves, de-ned by diierential invariants, across increasing scale.

In this paper we study the exact contours of a piecewise trilinear scalar field. We show how to represent these contours exactly as trimmed surfaces of triangular rational cubic Bézier patches. As part of this, we introduce an extension of the marching cubes algorithm which gives a topologically exact triangular approximation of the contours for any case. Finally, we modify the exact contours t...

The main motivation of this work is the problem of compute intersection curve between two surface. The surface/surface intersection, is a fundamental problem in computational geometry and geometric modelling of complex shapes. In general surface intersections, the most commonly used methods include subdivision and marching. Marching-based algorithms begin by finding a starting point on the inte...

We present a new algorithm to compute a geodesic path over a triangulated surface. Based on Sethian’s Fast Marching Method and Polthier’s straightest geodesics theory, we are able to generate an iterative process to obtain a good discrete geodesic approximation. It can handle both convex and non-convex surfaces. r 2005 Elsevier Ltd. All rights reserved.

This paper presents a new method to quickly extract geodesic paths on images and 3D meshes. We use a heuristic to drive the front propagation procedure of the classical Fast Marching. This results in a modification of the Fast Marching algorithm that is similar to the A∗ algorithm used in artificial intelligence. In order to find very quickly geodesic paths between any given pair of points, two...

We consider two different non-autonomous anisotropic time-optimal control problems. For the min-time-from-boundary problem, we show that the value function is recovered as a viscosity solution of a static Hamilton–Jacobi–Bellman partial differential equation H(∇u(x), u(x),x) = 1. We demonstrate that the space-marching Ordered Upwind Methods (introduced in [29] for the autonomous control) can be...

Several participating media rendering algorithms are based on ray marching: they integrate the variations of radiance along the volume covered by the participating media by splitting the path of light into segments and sampling light contribution at each of those segments. This paper revisits the concept of ray marching not as an integration technique, but as the application of a numerical meth...

Integration of surface normal vectors is a vital component in many shape reconstruction algorithms that require integrating surface normals to produce their final outputs, the depth values. In this paper, we introduce a fast and efficient method for computing the depth values from surface normal vectors. The method is based on solving the Eikonal equation using Fast Marching Method. We introduc...