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Fast exact and approximate geodesics on meshes
 ACM Trans. Graph
, 2005
"... The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of th ..."
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Cited by 71 (0 self)
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The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of the exact “single source, all destination ” algorithm presented by Mitchell, Mount, and Papadimitriou (MMP). We show that the algorithm runs much faster in practice than suggested by worst case analysis. Next, we extend the algorithm with a merging operation to obtain computationally efficient and accurate approximations with bounded error. Finally, to compute the shortest path between two given points, we use a lowerbound property of our approximate geodesic algorithm to efficiently prune the frontier of the MMP algorithm, thereby obtaining an exact solution even more quickly.
Three dimensional receding horizon control for UAVs
 AIAA Guidance, Navigation, and Control Conference and Exhibit
, 2004
"... This paper presents a receding horizon controller (RHC) that can be used to design trajectories for an aerial vehicle flying through a three dimensional terrain with obstacles and nofly zones. To avoid exposure to threats, the paths are chosen to stay as close to the terrain as possible, but the ve ..."
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Cited by 15 (2 self)
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This paper presents a receding horizon controller (RHC) that can be used to design trajectories for an aerial vehicle flying through a three dimensional terrain with obstacles and nofly zones. To avoid exposure to threats, the paths are chosen to stay as close to the terrain as possible, but the vehicle can choose to popup over the obstacles if necessary. The approach is similar to our previous twodimensional algorithms that construct a coarse cost map to provide approximate paths from a sparse set of nodes to the goal and then use Mixedinteger Linear Programming (MILP) optimization to design a detailed trajectory. The main contribution of this paper is to extend this approach to 3D, in particular providing a new algorithm for connecting the cost map and the detailed path in the MILP. This connection is done by introducing a new costtogo function that includes an altitude penalty and accounts for the vehicle dynamics. Initial guess for MILP RHC is constructed from the previous solution and is shown to reduce the solution time. Several simulation results are presented to show that the path planning algorithm yields good overall performance and is computationally tractable in a complex environment.
Multiresolution Interpolation Meshes
 In Proc. Pacific Graphics
, 2001
"... In this paper, we propose a new multiresolutionbased shape representation for 3D mesh morphing. Our approach does not use combination operations that caused some serious problems in the previous approaches for mesh morphing. Therefore, we can calculate a hierarchical interpolation mesh robustly usi ..."
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Cited by 15 (0 self)
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In this paper, we propose a new multiresolutionbased shape representation for 3D mesh morphing. Our approach does not use combination operations that caused some serious problems in the previous approaches for mesh morphing. Therefore, we can calculate a hierarchical interpolation mesh robustly using two types of subdivision fitting schemes. Our new representation has a hierarchical semiregular mesh structure based on subdivision connectivity. This leads to various advantages including efficient data storage, and easy acquisition of an interpolation mesh with arbitrary subdivision level. We also demonstrate several new features for 3D morphing using multiresolution interpolation meshes.
Segmenting reliefs on triangle meshes
 Proc. ACM Symp. Solid and Physical Modeling
, 2006
"... Sculptural reliefs are widely used in various industries for purposes such as applying brands to packaging and decorating porcelain. In order to easily apply reliefs to CAD models, it is often desirable to reverseengineer previously designed and manufactured reliefs. 3D scanners can generate triang ..."
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Cited by 10 (5 self)
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Sculptural reliefs are widely used in various industries for purposes such as applying brands to packaging and decorating porcelain. In order to easily apply reliefs to CAD models, it is often desirable to reverseengineer previously designed and manufactured reliefs. 3D scanners can generate triangle meshes from objects with reliefs; however, previous mesh segmentation work has not considered the particular problem of separation of reliefs from background. We consider here the specific case of segmenting a simple relief delimited by a single outer contour, which lies on a smooth, slowly varying background. Generally, such reliefs meet the surrounding surface in a small step, enabling us to devise a specific method for such relief segmentation. We find the boundary between the background and the relief using an adaptive snake. It starts at a simple userdrawn contour, and is driven inwards by a collapsing force until it matches the relief's boundary. Our method is insensitive to the choice of the initial contour. The snake's limiting position is controlled by a feature energy term designed to find a step. A refinement strategy is then used to drive the snake into concavities of the relief contour. We demonstrate operation of our algorithm using real scanned models with different relief contour shapes and triangle meshes with different resolutions.
Point Cloud Surfaces using Geometric Proximity Graphs
, 2004
"... We present a new definition of an implicit surface over a noisy point cloud, based on the weighted least squares approach. It can be evaluated very fast, but artifacts are significantly reduced. We propose to use a different... ..."
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Cited by 8 (0 self)
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We present a new definition of an implicit surface over a noisy point cloud, based on the weighted least squares approach. It can be evaluated very fast, but artifacts are significantly reduced. We propose to use a different...
Expansionbased algorithms for finding single pair shortest path on surface
 Proc. of W2GIS
, 2004
"... Abstract. Finding single pair shortest paths on surface is a fundamental problem in various domains, like Geographic Information Systems (GIS) 3D applications, robotic path planning system, and surface nearest neighbor query in spatial database, etc. Currently, to solve the problem, existing algorit ..."
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Cited by 5 (2 self)
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Abstract. Finding single pair shortest paths on surface is a fundamental problem in various domains, like Geographic Information Systems (GIS) 3D applications, robotic path planning system, and surface nearest neighbor query in spatial database, etc. Currently, to solve the problem, existing algorithms must traverse the entire polyhedral surface. With the rapid advance in areas like Global Positioning System (GPS), Computer Aided Design (CAD) systems and laser range scanner, surface models are becoming more and more complex. It is not uncommon that a surface model contains millions of polygons. The single pair shortest path problem is getting harder and harder to solve. Based on the observation that the single pair shortest path is in the locality, we investigate in this paper efficient methods by excluding part of the surface model without considering them in the search process. Three novel expansionbased algorithms are proposed, namely, Naïve algorithm, Rectanglebased Algorithm and Ellipsebased Algorithm. Each algorithm uses a twostep approach to find the shortest path. (1) compute an initial local path. (2) use the value of this initial path to select a search region, in which the global shortest path exists. The search process terminates once the global optimum criteria are satisfied. By reducing the searching region, the performance is improved dramatically in most cases. 1
Surface kNN Query Processing
"... A kNN query finds the k nearestneighbors of a given point from a point database. When it is sufficient to measure object distance using the Euclidian distance, the key to efficient kNN query processing is to fetch and check the distances of a minimum number of points from the database. For many a ..."
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Cited by 5 (2 self)
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A kNN query finds the k nearestneighbors of a given point from a point database. When it is sufficient to measure object distance using the Euclidian distance, the key to efficient kNN query processing is to fetch and check the distances of a minimum number of points from the database. For many applications, such as vehicle movement along road networks or rover and animal movement along terrain surfaces, the distance is only meaningful when it is along a valid movement path. For this type of kNN queries, the focus of efficient query processing is to minimize the cost of computing distances using the environment data (such as the road network data and the terrain data), which can be several orders of magnitude larger than that of the point data. Efficient processing of kNN queries based on the Euclidian distance or the road network distance has been investigated extensively in the past. In this paper, we investigate the problem of surface kNN query processing, where the distance is calculated from the shortest path along a terrain surface. This problem is very challenging, as the terrain data can be very large and the computational cost of finding shortest paths is very high. We propose an efficient solution based on multiresolution terrain models. Our approach eliminates the need of costly process of finding shortest paths by ranking objects using estimated lower and upper bounds of distance on multiresolution terrain models. 1.
A multiresolution surface distance model for kNN query processing
 THE VLDB JOURNAL
, 2008
"... A spatial kNN query returns k nearest points in a point dataset to a given query point. To measure the distance between two points, most of the literature focuses on the Euclidean distance or the network distance. For many applications, such as wildlife movement, it is necessary to consider the sur ..."
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Cited by 5 (0 self)
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A spatial kNN query returns k nearest points in a point dataset to a given query point. To measure the distance between two points, most of the literature focuses on the Euclidean distance or the network distance. For many applications, such as wildlife movement, it is necessary to consider the surface distance, which is computed from the shortest path along a terrain surface. In this paper, we investigate the problem of efficient surface kNN (skNN) query processing. This is an important yet highly challenging problem because the underlying environment data can be very large and the computational cost of finding the shortest path on a surface can be very high. To minimize the amount of surface data to be used and the cost of surface distance computation, a multiresolution surface distance model is proposed in this paper to take advantage of monotonic distance changes when the distances are computed at different resolution levels. Based on this
Indexing Land Surface for Efficient kNN Query
"... The class of k Nearest Neighbor (kNN) queries is frequently used in geospatial applications. Many studies focus on processing kNN in Euclidean and road network spaces. Meanwhile, with the recent advances in remote sensory devices that can acquire detailed elevation data, the new geospatial applicati ..."
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Cited by 4 (2 self)
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The class of k Nearest Neighbor (kNN) queries is frequently used in geospatial applications. Many studies focus on processing kNN in Euclidean and road network spaces. Meanwhile, with the recent advances in remote sensory devices that can acquire detailed elevation data, the new geospatial applications heavily operate on this third dimension, i.e., land surface. Hence, for the field of databases to stay relevant, it should be able to efficiently process spatial queries given this constrained third dimension. However, online processing of the surface k Nearest Neighbor (skNN) queries is quite challenging due to the huge size of land surface models which renders any accurate distance computation on the surface extremely slow. In this paper, for the first time, we propose an index structure on land surface that enables exact and fast responses to skNN queries. Two complementary indexing schemes, namely Tight Surface Index (TSI) and Loose Surface Index (LSI), are constructed and stored collectively on a single novel data structure called Surface Index Rtree (SIRtree). With those indexes, we can process skNN query efficiently by localizing the search and minimizing the invocation of the costly surface distance computation and hence incurring low I/O and computation costs. Our algorithm does not need to know the value of k a priori and can incrementally expand the search region using SIRtree and report the query result progressively. It also reports the exact shortest surface paths to the query results. We show through experiments with real world data sets that our algorithm has better performance than the competitors in both efficiency and accuracy. 1.
Improving Chen and Han’s Algorithm on the Discrete Geodesic Problem
"... The computation of geodesic distances or paths between two points on triangulated meshes is a common operation in many computer graphics applications. In this article, we present an exact algorithm for the singlesource allvertices shortest path problem. Mitchell et al. [1987] proposed an O(n2 log ..."
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Cited by 4 (1 self)
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The computation of geodesic distances or paths between two points on triangulated meshes is a common operation in many computer graphics applications. In this article, we present an exact algorithm for the singlesource allvertices shortest path problem. Mitchell et al. [1987] proposed an O(n2 log n) method (MMP), based on Dijkstra’s algorithm, where n is the complexity of the polyhedral surface. Then, Chen and Han [1990] (CH) improved the running time to O(n2). Interestingly Surazhsky et al. [2005] provided experimental evidence demonstrating that the MMP algorithm runs many times faster, in practice, than the CH algorithm. The CH algorithm encodes the structure of the set of shortest paths using a set of windows on the edges of the polyhedron. Our experiments showed that in many examples over 99 % of the windows created by the CH algorithm are of no use to define a shortest path. So this article proposes to improve the CH algorithm by two separate techniques. One is to filter out useless windows using the current estimates of the distances to the vertices, the other is to maintain a priority queue like that achieved in Dijkstra’s algorithm. Our experimental results suggest that the improved CH algorithm, in spite of an O(n2 log n) asymptotic time complexity, greatly outperforms the original CH algorithm in both time and space. Furthermore, it generally runs faster than the MMP algorithm and uses considerably less space.