dc.contributor.authorCheng, Peng
dc.identifier.citationCheng, P. (2016). Initial value problem of discrete geodesics and its application. Doctoral thesis, Nanyang Technological University, Singapore.
dc.description.abstractThe 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.en_US
dc.format.extent110 p.en_US
dc.subjectDRNTU::Engineering::Computer science and engineeringen_US
dc.titleInitial value problem of discrete geodesics and its applicationen_US
dc.contributor.schoolSchool of Computer Engineeringen_US
dc.contributor.supervisorNadia Magnenat-Thalmann
dc.contributor.supervisorMiao Chun Yanen_US
dc.description.degreeDOCTOR OF PHILOSOPHY (SCE)en_US

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