Subdivision Surface based One-Piece Representation

Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject\u27s topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications

AlSub: Fully Parallel and Modular Subdivision

In recent years, mesh subdivision---the process of forging smooth free-form surfaces from coarse polygonal meshes---has become an indispensable production instrument. Although subdivision performance is crucial during simulation, animation and rendering, state-of-the-art approaches still rely on serial implementations for complex parts of the subdivision process. Therefore, they often fail to harness the power of modern parallel devices, like the graphics processing unit (GPU), for large parts of the algorithm and must resort to time-consuming serial preprocessing. In this paper, we show that a complete parallelization of the subdivision process for modern architectures is possible. Building on sparse matrix linear algebra, we show how to structure the complete subdivision process into a sequence of algebra operations. By restructuring and grouping these operations, we adapt the process for different use cases, such as regular subdivision of dynamic meshes, uniform subdivision for immutable topology, and feature-adaptive subdivision for efficient rendering of animated models. As the same machinery is used for all use cases, identical subdivision results are achieved in all parts of the production pipeline. As a second contribution, we show how these linear algebra formulations can effectively be translated into efficient GPU kernels. Applying our strategies to $\sqrt{3}$, Loop and Catmull-Clark subdivision shows significant speedups of our approach compared to state-of-the-art solutions, while we completely avoid serial preprocessing.Comment: Changed structure Added content Improved description

Conversion of trimmed NURBS surfaces to Catmull-Clark subdivision surfaces

This paper introduces a novel method to convert trimmed NURBS surfaces to untrimmed subdivision surfaces with Bézier edge conditions. We take a NURBS surface and its trimming curves as input, from this we automatically compute a base mesh, the limit surface of which fits the trimmed NURBS surface to a specified tolerance. We first construct the topology of the base mesh by performing a cross-field based decomposition in parameter space. The number and positions of extraordinary vertices required to represent the trimmed shape can be automatically identified by smoothing a cross field bounded by the parametric trimming curves. After the topology construction, the control point positions in the base mesh are calculated based on the limit stencils of the subdivision scheme and constraints to achieve tangential continuity across the boundary. Our method provides the user with either an editable base mesh or a fine mesh whose limit surface approximates the input within a certain tolerance. By integrating the trimming curve as part of the desired limit surface boundary, our conversion can produce gap-free models. Moreover, since we use tangential continuity across the boundary between adjacent surfaces as constraints, the converted surfaces join with G1 continuity. © 2014 The Authors.EPSRC, Chinese Government (PhD studentship) and Cambridge Trust

PARAMETRIZATION AND SHAPE RECONSTRUCTION TECHNIQUES FOR DOO-SABIN SUBDIVISION SURFACES

This thesis presents a new technique for the reconstruction of a smooth surface from a set of 3D data points. The reconstructed surface is represented by an everywhere -continuous subdivision surface which interpolates all the given data points. And the topological structure of the reconstructed surface is exactly the same as that of the data points. The new technique consists of two major steps. First, use an efficient surface reconstruction method to produce a polyhedral approximation to the given data points. Second, construct a Doo-Sabin subdivision surface that smoothly passes through all the data points in the given data set. A new technique is presented for the second step in this thesis. The new technique iteratively modifies the vertices of the polyhedral approximation 1CM until a new control meshM, whose Doo-Sabin subdivision surface interpolatesM, is reached. It is proved that, for any mesh M with any size and any topology, the iterative process is always convergent with Doo-Sabin subdivision scheme. The new technique has the advantages of both a local method and a global method, and the surface reconstruction process can reproduce special features such as edges and corners faithfully

Subdivision Surface-Based Geometric Modeling System

A method for surface modeling of images to produce realistic images or to provide simulations with accurate surface information is provided. More particularly, the present invention relates to a new subdivision depth computation technique and to an improved label-driven adaptive subdivision technique for use in Catmull-Clark subdivision surface modeling systems. The method comprises computing a subdivision depth to determine the number of recursive subdivisions which may be performed on a control mesh to generate a plurality of finer mesh elements while preserving a predetermined error tolerance, and using the computed subdivision depth to construct an adaptively refined mesh that is substantially similar to the control mesh within the predetermined error tolerance. Limit control surfaces with and without extraordinary vertices may be analysed using the method of the invention. In another aspect, a software program for accomplishing the method of the present invention is provided