Jiongxin Jin

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We present an approximation algorithm for the shortest descending path problem. Given a source s and a destination t on a terrain, a shortest descending path from s to t is a path of minimum Euclidean length on the terrain subject to the constraint that the height decreases monotonically as we traverse that path from s to t. Given any ε ∈ (0, 1), our(More)
Let P be a path between two points s and t in a polygonal subdivision T with obstacles and weighted regions. Given a relative error tolerance ε ∈ (0, 1), we present the first algorithm to compute a path between s and t that can be deformed to P without passing over any obstacle and the path cost is within a factor 1+ ε of the optimum. The running time is O((More)
We present an algorithm for surface reconstruction from a point cloud. It runs in <i>O</i>(<i>n</i>log <i>n</i>) time, where <i>n</i> is the number of sample points, and this is optimal in the pointer machine model. The only existing <i>O</i>(<i>n</i>log <i>n</i>)-time algorithm is due to Funke and Ramos, and it uses some sophisticated data structures. The(More)
Let T be a planar subdivision with n vertices. Each face of T has a weight from [1, ρ] ∪ {∞}. A path inside a face has cost equal to the product of its length and the face weight. In general, the cost of a path is the sum of the subpath costs in the faces intersected by the path. For any ε ∈ (0, 1), we present a fully polynomial-time approximation scheme(More)
We propose an algorithm for finding a (1 + ε)-approximate shortest path through a weighted 3D simplicial complex T . The weights are integers from the range [1,W ] and the vertices have integral coordinates. Let N be the largest vertex coordinate magnitude, and let n be the number of tetrahedra in T . Let ρ be some arbitrary constant. Let κ be the size of(More)
We study edge flips in a surface mesh and the maintenance of a deforming surface mesh. If the vertices are dense with respect to the local feature size and the triangles have angles at least a constant, we can flip edges in linear time such that all triangles have almost empty diametric balls. For a planar triangulation with a constant angle lower bound, we(More)
Let P be a path between two points s and t in a polygonal subdivision T with obstacles and weighted regions. Given a relative error tolerance ε ∈ (0, 1), we present the first algorithm to compute a path between s and t that can be deformed to P without passing over any obstacle and the path cost is within a factor 1 + ε of the optimum. The running time is(More)
Little theoretical work has been done on edge flips in surface meshes despite their popular usage in graphics and solid modeling to improve mesh equality. We propose the class of (ε, α)-meshes of a surface that satisfy several properties: the vertex set is an ε-sample of the surface, the triangle angles are no smaller than a constant α, some triangle has a(More)
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