We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a... more We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a mesh adaptation process, namely, a sequence of local modifications performed on a copy of the original mesh, while referring to the original mesh geometry. The algorithm has three stages. In the first stage the required number or vertices are generated by iterative simplification or refinement. The second stage performs an initial vertex partition using an area-based relaxation method. The third stage achieves precise isotropic vertex sampling prescribed by a given density function on the mesh. We use a modification of Lloyd's relaxation method to construct a weighted centroidal Voronoi tessellation of the mesh. We apply these iterations locally on small patches of the mesh that are parameterized into the 2D plane. This allows us to handle arbitrary complex meshes with any genus and any number of boundaries. The efficiency and the accuracy of the remeshing process is achieved using ...
With the advent of cheap, but relatively low-resolution, video sensors, the importance of automat... more With the advent of cheap, but relatively low-resolution, video sensors, the importance of automatically mosaicing many small video images to one large image has increased. This is due mainly to the many useful applications that may be based on such technology, such as hand-held mobile scanning, multi-resolution imaging, panoramic spreads and video compression. The process of creating a mosaiced image consists of first finding the geometric registration of each small image from the sequence to a global image plane, and then combining all the registered images into one smooth, pleasing image. We review two existing methods for finding the registration: sequential and canvas mosaicing, and discuss the advantages and disadvantages of each of those algorithms. After suggesting two methods to improve the reliability and the accuracy of the basic sequential algorithm, we present our algorithm, which combines and enhances the sequential and canvas methods. We demonstrate how our algorithm o...
In the age of real-time online traffic information and GPS-enabled devices, fastest-path computat... more In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a "travel time" value, are becoming a standard feature of many navigation-related applications. To support this, very efficient computation of these paths in very large road networks is critical. Fastest paths may be computed as minimal-cost paths in a weighted directed graph, but traditional minimal-cost path algorithms based on variants of the classic Dijkstra algorithm do not scale well, as in the worst case they may traverse the entire graph. A common improvement, which can dramatically reduce the number of traversed graph vertices, is the A* algorithm, which requires a good heuristic lower bound on the minimal cost. We introduce a simple, but very effective, heuristic function based on a small number of values assigned to each graph vertex. The values are based on...
Path planning is an important problem in robotics. One way to plan a path between two points $x,y... more Path planning is an important problem in robotics. One way to plan a path between two points $x,y$ within a (not necessarily simply-connected) planar domain $\Omega$, is to define a non-negative distance function $d(x,y)$ on $\Omega\times\Omega$ such that following the (descending) gradient of this distance function traces such a path. This presents two equally important challenges: A mathematical challenge -- to define $d$ such that $d(x,y)$ has a single minimum for any fixed $y$ (and this is when $x=y$), since a local minimum is in effect a "dead end", A computational challenge -- to define $d$ such that it may be computed efficiently. In this paper, given a description of $\Omega$, we show how to assign coordinates to each point of $\Omega$ and define a family of distance functions between points using these coordinates, such that both the mathematical and the computational challenges are met. This is done using the concepts of \emph{harmonic measure} and \emph{$f$-dive...
ABSTRACT We present a general framework for post-processing and optimizing surface meshes with re... more ABSTRACT We present a general framework for post-processing and optimizing surface meshes with respect to various target criteria. On the one hand, the framework allows us to control the shapes of the mesh triangles by applying simple averaging operations; on the other hand we can control the Hausdorff distance to some reference geometry by minimizing a quadratic energy. Due to the simplicity of this setup, the framework is efficient and easy to implement, yet it also constitutes an effective and versatile tool with a variety of possible applications. In particular, we use it to reduce the texture distortion in animated mesh sequences, to improve the results of cross-parameterizations, and to minimize the distance between meshes and their remeshes.
Proceedings of the eighteenth annual symposium on Computational geometry - SCG '02, 2002
ABSTRACT This video describes a simple automatic method for visually tracking activity on a 3D me... more ABSTRACT This video describes a simple automatic method for visually tracking activity on a 3D mesh surface. Such a method is useful in interactive algorithm visualization. Its operation is demonstrated on a sample visualization of Rossignac's Edgebreaker connectivity compression algorithm.
We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a... more We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a mesh adaptation process, namely, a sequence of local modifications performed on a copy of the original mesh, while referring to the original mesh geometry. The algorithm has three stages. In the first stage the required number or vertices are generated by iterative simplification or refinement. The second stage performs an initial vertex partition using an area-based relaxation method. The third stage achieves precise isotropic vertex sampling prescribed by a given density function on the mesh. We use a modification of Lloyd's relaxation method to construct a weighted centroidal Voronoi tessellation of the mesh. We apply these iterations locally on small patches of the mesh that are parameterized into the 2D plane. This allows us to handle arbitrary complex meshes with any genus and any number of boundaries. The efficiency and the accuracy of the remeshing process is achieved using ...
With the advent of cheap, but relatively low-resolution, video sensors, the importance of automat... more With the advent of cheap, but relatively low-resolution, video sensors, the importance of automatically mosaicing many small video images to one large image has increased. This is due mainly to the many useful applications that may be based on such technology, such as hand-held mobile scanning, multi-resolution imaging, panoramic spreads and video compression. The process of creating a mosaiced image consists of first finding the geometric registration of each small image from the sequence to a global image plane, and then combining all the registered images into one smooth, pleasing image. We review two existing methods for finding the registration: sequential and canvas mosaicing, and discuss the advantages and disadvantages of each of those algorithms. After suggesting two methods to improve the reliability and the accuracy of the basic sequential algorithm, we present our algorithm, which combines and enhances the sequential and canvas methods. We demonstrate how our algorithm o...
In the age of real-time online traffic information and GPS-enabled devices, fastest-path computat... more In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a "travel time" value, are becoming a standard feature of many navigation-related applications. To support this, very efficient computation of these paths in very large road networks is critical. Fastest paths may be computed as minimal-cost paths in a weighted directed graph, but traditional minimal-cost path algorithms based on variants of the classic Dijkstra algorithm do not scale well, as in the worst case they may traverse the entire graph. A common improvement, which can dramatically reduce the number of traversed graph vertices, is the A* algorithm, which requires a good heuristic lower bound on the minimal cost. We introduce a simple, but very effective, heuristic function based on a small number of values assigned to each graph vertex. The values are based on...
Path planning is an important problem in robotics. One way to plan a path between two points $x,y... more Path planning is an important problem in robotics. One way to plan a path between two points $x,y$ within a (not necessarily simply-connected) planar domain $\Omega$, is to define a non-negative distance function $d(x,y)$ on $\Omega\times\Omega$ such that following the (descending) gradient of this distance function traces such a path. This presents two equally important challenges: A mathematical challenge -- to define $d$ such that $d(x,y)$ has a single minimum for any fixed $y$ (and this is when $x=y$), since a local minimum is in effect a "dead end", A computational challenge -- to define $d$ such that it may be computed efficiently. In this paper, given a description of $\Omega$, we show how to assign coordinates to each point of $\Omega$ and define a family of distance functions between points using these coordinates, such that both the mathematical and the computational challenges are met. This is done using the concepts of \emph{harmonic measure} and \emph{$f$-dive...
ABSTRACT We present a general framework for post-processing and optimizing surface meshes with re... more ABSTRACT We present a general framework for post-processing and optimizing surface meshes with respect to various target criteria. On the one hand, the framework allows us to control the shapes of the mesh triangles by applying simple averaging operations; on the other hand we can control the Hausdorff distance to some reference geometry by minimizing a quadratic energy. Due to the simplicity of this setup, the framework is efficient and easy to implement, yet it also constitutes an effective and versatile tool with a variety of possible applications. In particular, we use it to reduce the texture distortion in animated mesh sequences, to improve the results of cross-parameterizations, and to minimize the distance between meshes and their remeshes.
Proceedings of the eighteenth annual symposium on Computational geometry - SCG '02, 2002
ABSTRACT This video describes a simple automatic method for visually tracking activity on a 3D me... more ABSTRACT This video describes a simple automatic method for visually tracking activity on a 3D mesh surface. Such a method is useful in interactive algorithm visualization. Its operation is demonstrated on a sample visualization of Rossignac's Edgebreaker connectivity compression algorithm.
Uploads