This paper presents a brief instructions to nd geodesics equa-tions on two dimensional surfaces in R3. The resulting geodesic equations are solved numerically using Computer Program Matlab, the geodesics are dis-played through Figures.

Given a hyperbolic 3-manifold containing an embedded geodesic, we estimate the volume of a complete hyperbolic metric after drilling the geodesic from the manifold in terms of the radius of an embedded tube about the geodesic.

This paper presents a geodesic voting method to segment tree structures, such as retinal or cardiac blood vessels. Many authors have used minimal cost paths, or similarly geodesics relative to a weight potential P, to find a vessel between two end points. Our goal focuses on the use of a set of such geodesic paths for finding a tubular tree structures, using minimal interaction. This work adapt...

in this paper, multi-stage optimum design of composite pressure vessels is presented. the design variables for composite vessels include the head shape, the winding angle, the layer thickness, the number of layers, and the stacking sequence. a parameter called modified shape factor is introduced as an objective function. this parameter takes into account the effects of the internal pressure and...

Geodesic regression generalizes linear regression to general Riemannian manifolds. Applied to images, it allows for a compact approximation of an image time-series through an initial image and an initial momentum. Geodesic regression requires the definition of a squared residual (squared distance) between the regression geodesic and the measurement images. In principle, this squared distance sh...

If we start with Einstein’s beautiful hypothesis that test particles in gravitational field move along geodesic lines of some Riemannian spaces V4, it is natural to expect that the differential equations for finding the metric tensor gαβ(x) for a given distribution of matter also should be invariant under any transformations at which the geodesic equations remain invariant. However, the geodesi...

Let X be a geodesic metric space. Gromov proved that there exists ε0 > 0 such that if every sufficiently large triangle ∆ satisfies the Rips condition with constant ε0 · pr(∆), where pr(∆) is the perimeter ∆, then X is hyperbolic. We give an elementary proof of this fact, also giving an estimate for ε0. We also show that if all the triangles ∆ ⊆ X satisfy the Rips condition with constant ε0 · p...

In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in R. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.

We discuss the enumeration of planar graphs using bijections with suitably decorated trees, which allow for keeping track of the geodesic distances between faces of the graph. The corresponding generating functions obey non-linear recursion relations on the geodesic distance. These are solved by use of stationary multi-soliton tau-functions of suitable reductions of the KP hierarchy. We obtain ...

For a polygonal domain with h holes and a total of n vertices, we present algorithms that compute the L1 geodesic diameter in O(n2 + h4) time and the L1 geodesic center in O((n4 + n2h4)α(n)) time, respectively, where α(·) denotes the inverse Ackermann function. No algorithms were known for these problems before. For the Euclidean counterpart, the best algorithms compute the geodesic diameter in...