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17
Cacheoblivious mesh layouts
 ACM Trans. Graph
, 2005
"... ACM acknowledges that this contribution was authored or coauthored by a contractor of affiliate of the U.S. Government. As such, the Government retains a nonexclusive, royaltyfree right to publish or reproduce this article, or to allow others to do so, for Government purposes only. ..."
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Cited by 38 (7 self)
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ACM acknowledges that this contribution was authored or coauthored by a contractor of affiliate of the U.S. Government. As such, the Government retains a nonexclusive, royaltyfree right to publish or reproduce this article, or to allow others to do so, for Government purposes only.
Constrained Strip Generation and Management for Efficient Interactive 3D Rendering
 In Proc. of Computer Graphics International Conference
, 2005
"... Representing a triangulated two manifold using a single triangle strip is an NPcomplete problem. By introducing a few Steiner vertices, recent works find such a singlestrip and hence a linear ordering of edgeconnected triangles of the entire triangulation. In this paper, we highlight and exploit ..."
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Cited by 9 (6 self)
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Representing a triangulated two manifold using a single triangle strip is an NPcomplete problem. By introducing a few Steiner vertices, recent works find such a singlestrip and hence a linear ordering of edgeconnected triangles of the entire triangulation. In this paper, we highlight and exploit this linear order in efficient trianglestrip management for highperformance rendering. We present new algorithms to generate weighted singlestrip representations that respect different constraintbased clustering of triangles. These functional constraints can be application dependent; for example, normalbased constraints for efficient visibility culling or spatial constraints for highly coherent vertexcaching. We also present a hierarchical singlestripmanagement strategy for highperformance interactive 3D rendering.
Stripification of FreeForm Surfaces with Global Error Bounds for Developable Approximation
"... Abstract—Developable surfaces have many desired properties in manufacturing process. Since most existing CAD systems utilize tensorproduct parametric surfaces including Bsplines as design primitives, there is a great demand in industry to convert a general freeform parametric surface within a pre ..."
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Cited by 6 (1 self)
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Abstract—Developable surfaces have many desired properties in manufacturing process. Since most existing CAD systems utilize tensorproduct parametric surfaces including Bsplines as design primitives, there is a great demand in industry to convert a general freeform parametric surface within a prescribed global error bound into developable patches. In this work we propose a practical and efficient solution to approximate a rectangular parametric surface with a small set of C 0joint developable strips. The key contribution of the proposed algorithm is that, several optimization problems are elegantly solved in a sequence that offers a controllable global error bound on the developable surface approximation. Experimental results are presented to demonstrate the effectiveness and stability of the proposed algorithm. Note to Practitioners—This paper was motivated by a joint industrial project which uses CATIA V5R16 as the design platform. The shape of product was modeled by freeform parametric patches including NURBS in the CATIA system. For efficient manufacturing, the parametric surfaces are required to convert into developable patches with controllable global error bounds. Given a small tolerance, if this cannot be achieved, then cut the surface into pieces, each of which is developable. However, the CATIA system does not provide such a functionality. With the development of this project, we design an efficient algorithm which is presented in the paper to achieve this goal. We also build the algorithm into a plugin module in CATIA using CAA V5. Index Terms—Developable surface approximation, freeform parametric surfaces, geometric optimization, triangle strip. I.
LR: compact connectivity representation for triangle meshes
 in ACM SIGGRAPH 2011 papers, SIGGRAPH ’11
, 2011
"... Figure 1: The ring (black loop) delineates two corridors of triangles. Normal T1 triangles (cream/orange) have one ring edge, deadend T2 triangles (blue) have two ring edges, and T0 triangles (green) comprising bifurcations have no ring edges. Adjacent T0 (gray/red) and T2 triangles (left) are repr ..."
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Cited by 4 (2 self)
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Figure 1: The ring (black loop) delineates two corridors of triangles. Normal T1 triangles (cream/orange) have one ring edge, deadend T2 triangles (blue) have two ring edges, and T0 triangles (green) comprising bifurcations have no ring edges. Adjacent T0 (gray/red) and T2 triangles (left) are represented internally as inexpensive T1 triangles (right), thereby significantly reducing storage. Our LR representation supports random access to connectivity, storing on average only 1.08 references or 26.2 bits per triangle. We propose LR (Laced Ring)—a simple data structure for representing the connectivity of manifold triangle meshes. LR provides the option to store on average either 1.08 references per triangle or 26.2 bits per triangle. Its construction, from an input mesh that supports constanttime adjacency queries, has linear space and time complexity, and involves ordering most vertices along a nearlyHamiltonian cycle. LR is best suited for applications that process meshes with fixed connectivity, as any changes to the connectivity require the data structure to be rebuilt. We provide an implementation of the set of standard randomaccess, constanttime operators for traversing a mesh, and show that LR often saves both space and traversal time over competing representations.
Not being (super)thin or solid is hard: A study of grid Hamiltonicity
, 2008
"... We give a systematic study of Hamiltonicity of grids—the graphs induced by finite subsets of vertices of the tilings of the plane with congruent regular convex polygons (triangles, squares, or hexagons). Summarizing and extending existing classification of the usual, “square”, grids, we give a compr ..."
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Cited by 1 (0 self)
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We give a systematic study of Hamiltonicity of grids—the graphs induced by finite subsets of vertices of the tilings of the plane with congruent regular convex polygons (triangles, squares, or hexagons). Summarizing and extending existing classification of the usual, “square”, grids, we give a comprehensive taxonomy of the grid graphs. For many classes of grid graphs we resolve the computational complexity of the Hamiltonian cycle problem. For graphs for which there exists a polynomialtime algorithm we give efficient algorithms to find a Hamiltonian cycle. We also establish, for any g ≥ 6, a onetoone correspondence between Hamiltonian cycles in planar bipartite maximumdegree3 graphs and Hamiltonian cycles in the class Cg of girthg planar maximumdegree3 graphs. As applications of the correspondence, we show that for graphs in Cg the Hamiltonian cycle problem is NPcomplete and that for any N ≥ 5 there exist graphs in Cg that have exactly N Hamiltonian cycles. We also prove that for the graphs in Cg, a Chinese Postman tour gives a (1 + 8 g)approximation to TSP, improving thereby the Christofides ratio when g> 16. We show further that, on any graph, the tour obtained by Christofides ’ algorithm is not longer than a Chinese Postman tour.
FlowBased Automatic Generation of Hybrid Picture Mazes
"... A method for automatically generating a picture maze from two different images is introduced throughout this paper. The process begins with the extraction of salient contours and edge tangent flow information from the primary image in order to build the overall maze. Thus, mazes with passages flowin ..."
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A method for automatically generating a picture maze from two different images is introduced throughout this paper. The process begins with the extraction of salient contours and edge tangent flow information from the primary image in order to build the overall maze. Thus, mazes with passages flowing in the main edge directions and walls that effectively represent an abstract version of the primary image can be successfully created. Furthermore, our proposed approach makes possible the use of their solution path as a means of illustrating the main features of the secondary image, while attempting to keep its image motif concealed until the maze has been finally solved. The contour features and intensity of the secondary image are also incorporated into our method in order to determine the areas of the maze to be shaded by allowing the solution path to go through them. Moreover, an experiment has been conducted to confirm that solution paths can be successfully hidden from the participants in the mazes generated using our method. Categories and Subject Descriptors (according to ACM CCS): I.3.8 [Computer Graphics]: Applications—J.5 [Computer Applications]: Arts and Humanities—
Optimized Topological Surgery for Unfolding 3D Meshes
"... Constructing a 3D papercraft model from its unfolding has been fun for both children and adults since we can reproduce virtual 3D models in the real world. However, facilitating the papercraft construction process is still a challenging problem, especially when the shape of the input model is comple ..."
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Constructing a 3D papercraft model from its unfolding has been fun for both children and adults since we can reproduce virtual 3D models in the real world. However, facilitating the papercraft construction process is still a challenging problem, especially when the shape of the input model is complex in the sense that it has large variation in its surface curvature. This paper presents a new heuristic approach to unfolding 3D triangular meshes without any shape distortions, so that we can construct the 3D papercraft models through simple atomic operations for gluing boundary edges around the 2D unfoldings. Our approach is inspired by the concept of topological surgery, where the appearance of boundary edges of the unfolded closed surface can be encoded using a symbolic representation. To fully simplify the papercraft construction process, we developed a geneticbased algorithm for unfolding the 3D mesh into a single connected patch in general, while optimizing the usage of the paper sheet and balance in the shape of that patch. Several examples together with user studies are included to demonstrate that the proposed approach works well for a broad range of 3D triangular meshes. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems mesh unfolding, topological surgery, genetic algorithms, papercraft models 1.
Interactive Visualization and Collision Detection using Dynamic Simplification and CacheCoherent Layouts
, 2006
"... Recent advances in model acquisition, computeraided design, and simulation technologies have resulted in massive databases of complex geometric models consisting of more than tens or hundreds of millions of triangles. In spite of the rapid progress in the performance of CPUs and graphics processing ..."
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Recent advances in model acquisition, computeraided design, and simulation technologies have resulted in massive databases of complex geometric models consisting of more than tens or hundreds of millions of triangles. In spite of the rapid progress in the performance of CPUs and graphics processing units (GPUs), it may not be possible to visualize or perform collision detection between massive models at interactive rates on commodity hardware. In this thesis, we present dynamic simplification and cachecoherent layout algorithms for interactive visualization and collision detection between large models, in order to bridge the gap between the performance of commodity hardware and high model complexity. Firstly, we present a novel dynamic simplification algorithm that efficiently handles massive models for viewdependent rendering while alleviating discontinuity problems