Computing geodesics on triangular meshes

نویسندگان

  • Dimas Martínez Morera
  • Luiz Velho
  • Paulo Cezar Pinto Carvalho
چکیده

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.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Central WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes

We derive Godunov-type semidiscrete central schemes for Hamilton–Jacobi equations on triangular meshes. High-order schemes are then obtained by combining our new numerical fluxes with high-order WENO reconstructions on triangular meshes. The numerical fluxes are shown to be monotone in certain cases. The accuracy and high-resolution properties of our scheme are demonstrated in a variety of nume...

متن کامل

Subdivision Curves on Triangular Meshes

Subdivision curves have great importance for many CAD/CAM applications. In this paper we propose a simple method to define subdivision schemes on triangulations. It works by translating to the triangulation a perturbation of a planar binary subdivision. To reproduce this perturbation in the surface we use both, shortest and straightest geodesics, so we call this strategy intrinsic projection me...

متن کامل

Multiresolution Techniques for the Simplification of Triangular and Tetrahedral Meshes

We study the simplification of triangular and tetrahedral meshes using techniques based on successive edge collapses, as well as the exploitation of the generated multiple levels of detail for the effective processing of the models. Regarding triangular meshes, we present a method for the construction of progressive hulls, by suitable edge collapses; we use the generated hulls for the accelerat...

متن کامل

Discrete Conservation Laws on Curved Surfaces

In this paper we shall introduce a simple, effective numerical method to compute differential operators for scalar and vector-valued functions on regular surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute directly partial derivatives of functions defined on triangular meshes which are the discretizations of regular surfaces under consideration. Most im...

متن کامل

Fast Exact and Approximate Geodesic Paths on Meshes

In this paper, we develop simple and numerically stable family of algorithms for computing geodesic paths on meshes. The exact version of the algorithm is based on the interval propagation idea introduced by Mitchell, Mount, and Papadimitriou, and has the same O(n2 log n) worst case time complexity. The fastest approximate version works in roughly O(n log n) time and still guarantees computing ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Computers & Graphics

دوره 29  شماره 

صفحات  -

تاریخ انتشار 2005