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DesignDriven Quadrangulation of Closed 3D Curves
"... (a) input curve network (c) pairing and iterative refinement (f) design rendering (b) initial segmentation (d) final quadrangulation and quadmesh (e) designdriven quadrangulation Figure 1: Steps to quadrangulating a design network of closed 3D curves (a) : Closed curves are independently segmented ..."
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Cited by 11 (4 self)
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(a) input curve network (c) pairing and iterative refinement (f) design rendering (b) initial segmentation (d) final quadrangulation and quadmesh (e) designdriven quadrangulation Figure 1: Steps to quadrangulating a design network of closed 3D curves (a) : Closed curves are independently segmented (b) and iteratively paired and refined to capture dominant flowlines as well as overall flowline quality (c); final quadrangulation in green and dense quadmesh (d); quadrangulations are aligned across adjacent cycles to generate a single densely sampled mesh (e), suitable for design rendering and downstream applications (f). We propose a novel, designdriven, approach to quadrangulation of closed 3D curves created by sketchbased or other curve modeling systems. Unlike the multitude of approaches for quadremeshing of existing surfaces, we rely solely on the input curves to both conceive and construct the quadmesh of an artist imagined surface bounded by them. We observe that viewers complete the intended shape by envisioning a dense network of smooth, gradually changing, flowlines that interpolates the input curves. Components of the network bridge pairs of input curve segments with similar orientation and shape. Our algorithm mimics this behavior. It first segments the input closed curves into pairs of matching segments, defining dominant flow line sequences across the surface. It then interpolates the input curves by a network of quadrilateral cycles whose isolines define the desired flow line network. We proceed to interpolate these networks with allquad meshes that convey designer intent. We evaluate our results by showing convincing quadrangulations of complex and diverse curve networks with concave, nonplanar cycles, and validate our approach by comparing our results to artist generated interpolating meshes. 1
Interval assignment for volumes with holes
 International Journal for Numerical Methods in Engineering 2000
, 2000
"... This paper presents a new technique for automatically detecting interval constraints for swept volumes with holes. The technique finds true volume constraints that are not necessarily imposed by the surfaces of the volume. A graphing algorithm finds independent, parallel paths of edges from source s ..."
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Cited by 6 (2 self)
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This paper presents a new technique for automatically detecting interval constraints for swept volumes with holes. The technique finds true volume constraints that are not necessarily imposed by the surfaces of the volume. A graphing algorithm finds independent, parallel paths of edges from source surfaces to target surfaces. The number of intervals on two paths between a given source and target surface must be equal; in general, the collection of paths determine a set of linear constraints. Linear programming techniques solve the interval assignment problem for the surface and volume constraints simultaneously.
A DivideandConquer Approach to Quad Remeshing
"... Abstract—Many natural and manmade objects consist of simple primitives, similar components, and various symmetry structures. This paper presents a divideandconquer quadrangulation approach that exploits such global structural information. Given a model represented in triangular mesh, we first seg ..."
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Abstract—Many natural and manmade objects consist of simple primitives, similar components, and various symmetry structures. This paper presents a divideandconquer quadrangulation approach that exploits such global structural information. Given a model represented in triangular mesh, we first segment it into a set of submeshes, and compare them with some predefined quad mesh templates. For the submeshes that are similar to a predefined template, we remesh them as the template up to a number of subdivisions. For the others, we adopt the wavebased quadrangulation technique to remesh them with extensions to preserve symmetric structure and generate compatible quad mesh boundary. To ensure that the individually remeshed submeshes can be seamlessly stitched together, we formulate a mixedinteger optimization problem and design a heuristic solver to optimize the subdivision numbers and the size fields on the submesh boundaries. With this dividerandconquer quadrangulation framework, we are able to process very large models that are very difficult for the previous techniques. Since the submeshes can be remeshed individually in any order, the remeshing procedure can run in parallel. Experimental results showed that the proposed method can preserve the highlevel structures, and process large complex surfaces robustly and efficiently. Index Terms—Quad remeshing, divideandconquer, segmentation, mixedinteger optimization Ç
Meshing complexity: predicting meshing . . .
, 2005
"... This paper proposes a method for predicting the complexity of meshing computer aided design (CAD) geometries with unstructured, hexahedral, finite elements. Meshing complexity refers to the relative level of e#ort required to generate a valid finite element mesh on a given CAD geometry. A function i ..."
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This paper proposes a method for predicting the complexity of meshing computer aided design (CAD) geometries with unstructured, hexahedral, finite elements. Meshing complexity refers to the relative level of e#ort required to generate a valid finite element mesh on a given CAD geometry. A function is proposed to approximate the meshing complexity for single part CAD models. The function is dependent on a user defined element size as well as on data extracted from the geometry and topology of the CAD part. Several geometry and topology measures are proposed, which both characterize the shape of the CAD part and detect configurations that complicate mesh generation. Based on a test suite of CAD models, the function is demonstrated to be accurate within a certain range of error. The solution proposed here is intended to provide managers and users of meshing software a method of predicting the difficulty in meshing a CAD model. This will enable them to make decisions about model simplification and analysis approaches prior to mesh generation.
Simple and Fast Interval Assignment Using Nonlinear and Piecewise Linear Objectives
"... Summary. Interval Assignment (IA) is the problem of assigning an integer number of mesh edges, intervals, to each curve so that the assigned value is close to the goal value, and all containing surfaces and volumes may be meshed independently and compatibly. Sumeven constraints are modeled by an in ..."
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Summary. Interval Assignment (IA) is the problem of assigning an integer number of mesh edges, intervals, to each curve so that the assigned value is close to the goal value, and all containing surfaces and volumes may be meshed independently and compatibly. Sumeven constraints are modeled by an integer variable with no goal. My new method NLIA solves IA more quickly than the prior lexicographic minmax approach. A problem with one thousand faces and ten thousand curves can be solved in one second. I still achieve good compromises when the assigned intervals must deviate a large amount from their goals. The constraints are the same as in prior approaches, but I define a new objective function, the sum of cubes of the weighted deviations from the goals. I solve the relaxed (noninteger) problem with this cubic objective. I adaptively bend the objective into a piecewise linear function, which has a nearby mostlyinteger optimum. I randomize and rescale weights. For variables stuck at noninteger values, I tilt their objective. As a last resort, I introduce wavelike nonlinear constraints to force integrality. In short, I relax, bend, tilt, and wave.
Quantized Global Parametrization
"... Figure 1: Left: Global parametrization with continuous rigid transitions; notice the mismatch of the depicted isolines across the red cuts. Right: Global parametrization with quantized (or integral) transitions computed robustly and efficiently by our method. Global surface parametrization often req ..."
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Figure 1: Left: Global parametrization with continuous rigid transitions; notice the mismatch of the depicted isolines across the red cuts. Right: Global parametrization with quantized (or integral) transitions computed robustly and efficiently by our method. Global surface parametrization often requires the use of cuts or charts due to nontrivial topology. In recent years a focus has been on socalled seamless parametrizations, where the transition functions across the cuts are rigid transformations with a rotation about some multiple of 90◦. Of particular interest, e.g. for quadrilateral meshing, paneling, or texturing, are those instances where in addition the translational part of these transitions is integral (or more generally: quantized). We show that finding not even the optimal, but just an arbitrary valid quantization (one that does not imply parametric degeneracies), is a complex combinatorial problem. We present a novel method that allows us to solve it, i.e. to find valid as well as good quality quantizations. It is based on an original approach to quickly construct solutions to linear Diophantine equation systems, exploiting the specific geometric nature of the parametrization problem. We thereby largely outperform the stateoftheart, sometimes by several orders of magnitude.
1Volumetric Mapping of Genus Zero Objects via Mass Preservation
"... Abstract—In this work, we present a technique to map any genus zero solid object onto a hexahedral decomposition of a solid cube. This problem appears in many applications ranging from finite element methods to visual tracking. From this, one can then hopefully utilize the proposed technique for sha ..."
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Abstract—In this work, we present a technique to map any genus zero solid object onto a hexahedral decomposition of a solid cube. This problem appears in many applications ranging from finite element methods to visual tracking. From this, one can then hopefully utilize the proposed technique for shape analysis, registration, as well as other related computer graphics tasks. More importantly, given that we seek to establish a onetoone correspondence of an input volume to that of a solid cube, our algorithm can naturally generate a quality hexahedral mesh as an output. In addition, we constrain the mapping itself to be volume preserving allowing for the possibility of further mesh simplification. We demonstrate our method both qualitatively and quantitatively on various 3D solid models.