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Title: Initial value problem of discrete geodesics and its application
Authors: Cheng, Peng
Keywords: DRNTU::Engineering::Computer science and engineering
Issue Date: 2016
Source: Cheng, P. (2016). Initial value problem of discrete geodesics and its application. Doctoral thesis, Nanyang Technological University, Singapore.
Abstract: The commonly used shortest geodesic paths neither simulate properties of geodesics on smooth surface nor provide a unique solution on triangle meshes. We focus on the initial value problem, i.e., finding a uniquely determined geodesic path from a given point in any direction. Firstly, we propose a first-order tangent ODE method. Our method is different from the conventional methods of directly solving the geodesic equation (i.e., a second-order ODE of the position) on piecewise smooth surfaces, which is difficult to implement due to complicated representation of the geodesic equation involving Christoffel symbols. Our method is particularly useful for computing geodesic paths on low-resolution meshes which may have large and/or skinny triangles. Moreover, we employ the initial value problem geodesic to solve the constrained texture mapping problem. The proposed method provides a valid one-to-one mapping, which not only satisfies user-defined constraints but also preserves the metric structure of the original mesh.
DOI: 10.32657/10356/67025
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SCSE Theses

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