We present a framework for generating street networks and parcel layouts. Our goal is the generation of high-quality layouts that can be used for urban planning and virtual environments. We propose a solution based on hierarchical domain splitting using two splitting types: streamline-based splitting, which splits a region along one or multiple streamlines of a cross field, and template-based splitting, which warps pre-designed templates to a region and uses the interior geometry of the template as the splitting lines. We combine these two splitting approaches into a hierarchical framework, providing automatic and interactive tools to explore the design space.

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For the purpose of isogeometric analysis, one of the most common ways is to construct structured hexahedral meshes, which have regular tensor product structure, and fit them by volumetric T-Splines. This theoretic work proposes a novel surface quadrilateral meshing method, colorable quad-mesh, which leads to the structured hexahedral mesh of the enclosed volume for high genus surfaces. The work proves the equivalence relations among colorable quad-meshes, finite measured foliations and Strebel differentials on surfaces. This trinity theorem lays down the theoretic foundation for quadrilateral/hexahedral mesh generation, and leads to practical, automatic algorithms. The work proposes the following algorithm: the user inputs a set of disjoint, simple loops on a high genus surface, and specifies a height parameter for each loop; a unique Strebel differential is computed with the combinatorial type and the heights prescribed by the user’s input; the Strebel differential assigns a flat metric on the surface and decomposes the surface into cylinders; a colorable quad-mesh is generated by splitting each cylinder into two quadrilaterals, followed by subdivision; the surface cylindrical decomposition is extended inward to produce a solid cylindrical decomposition of the volume; the hexadhedral meshing is generated for each volumetric cylinder and then glued together to form a globally consistent hex-mesh. The method is rigorous, geometric, automatic and conformal to the geometry. This work focuses on the theoretic aspects of the framework, the algorithmic details and practical evaluations will be given in the future expositions.

Ricci flow deformsthe Riemannian metric proportionallyto the curvature, such that the curvatureevolves accordingto a heat diffusion process and eventually becomes constant everywhere. Ricci flow has demonstrated its great potential by solving various problems in many fields, which can be hardly handled by alternative methods so far. This work introduces the unified theoretic framework for discrete Surface Ricci Flow, including all the common schemes: Tangential Circle Packing, Thurston’s Circle Packing, Inversive Distance Circle Packing and Discrete Yamabe Flow. Furthermore, this work also introduces a novel schemes, Virtual Radius Circle Packing and the Mixed Type schemes, under the unified framework. This work gives explicit geometric interpretation to the discrete Ricci energies for all the schemes with all back ground geometries, and the corresponding Hessian matrices. The unified frame work deepens our understanding to the the discrete surface Ricci flow theory, and has inspired us to discover the new schemes, improved the flexibility and robustness of the algorithms, greatly simplified the implementation and improved the efficiency. Experimental results show the unified surface Ricci flow algorithms can handle general surfaces with different topologies, and is robust to meshes with different qualities, and is effective for solving real problems.

3D scene modeling has long been a fundamental problem in computer graphics and computer vision. With the popularity of consumer-level RGB-D cameras, there is a growing interest in digitizing real-world indoor 3D scenes. However, modeling indoor 3D scenes remains a challenging problem because of the complex structure of interior objects and poor quality of RGB-D data acquired by consumer-level sensors. Various methods have been proposed to tackle these challenges. In this survey, we provide an overview of recent advances in indoor scene modeling techniques, as well as public datasets and code libraries which can facilitate experiments and evaluation.

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The goal of urban building mesh simplification is to generate a compact representation of a building from a given mesh. Local smoothness and sharp contours of urban buildings are important features for converting unstructured data into solid models, which should be preserved during the simplification. In this paper, we present a general method to filter and simplify 3D building mesh models, capable of preserving piecewise planar structures and sharp features. Given a building mesh model, a mesh filtering technique is firstly designed to yield piecewise planar regions and extract crease contours. The planar regions are used to constrain the simplification of the mesh. Mesh decimation is achieved through a series of edge collapse operations, which uses regional structural constraints and local geometric error metrics to handle planar and non-planar areas respectively. The proposed method preserves the mesh structure with meaningful levels of detail while reducing the number of faces. The effectiveness of this method is evaluated on various building models generated from different observation scales, and the performance is validated by extensive comparisons to state-of-the-art techniques.

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We present the first computational tool to help ordinary users create transforming pop-up books. In each transforming pop-up, when the user pulls a tab, an initial flat 2D pattern, i.e. a 2D shape with a superimposed picture, such as an airplane, turns into a new 2D pattern, such as a robot, standing up from the page. Given the two 2D patterns, our approach automatically computes a 3D pop-up mechanism that transforms one pattern into the other; it also outputs a design blueprint, allowing the user to easily make the final model. We also present a theoretical analysis of basic transformation mechanisms; combining these basic mechanisms allows more flexibility of final designs. Using our approach, inexperienced users can create models in a short time; previously, even experienced artists often took weeks to manually create them. We demonstrate our method on a variety of real world examples.

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Non-rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non-rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an l2-norm regularization on the local transformation differences. However, the l2-norm regularization tends to bias the solution towards outliers and noise with heavy-tailed distribution, which is verified by the poor goodness- of-fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non-rigid registration (SNR) method with an l1-norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi-resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large-scale deformations as well as outliers and noise.

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We introduce an interactive technique for manipulating simple 3D shapes based on extracting them from a single photograph. Such extraction requires understanding of the components of the shape, their projections, and relations. These simple cognitive tasks for humans are particularly difficult for automatic algorithms. Thus, our approach combines the cognitive abilities of humans with the computational accuracy of the machine to solve this problem. Our technique provides the user the means to quickly create editable 3D parts¡ª human assistance implicitly segments a complex object into its components, and positions them in space. In our interface, three strokes are used to generate a 3D component that snaps to the shape¡¯s outline in the photograph, where each stroke defines one dimension of the component. The computer reshapes the component to fit the image of the object in the photograph as well as to satisfy various inferred geometric constraints imposed by its global 3D structure. We show that with this intelligent interactive modeling tool, the daunting task of object extraction is made simple. Once the 3D object has been extracted, it can be quickly edited and placed back into photos or 3D scenes, permitting object-driven photo editing tasks which are impossible to perform in image-space.

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We present a novel solution to automatic semantic modeling of indoor scenes from a sparse set of low-quality RGB-D images. Such data presents challenges due to noise, low resolution, occlusion and missing depth information. We exploit the knowledge in a scene database containing 100s of indoor scenes with over 10,000 manually segmented and labeled mesh models of objects. In seconds, we output a visually plausible 3D scene, adapting these models and their parts to fit the input scans. Contextual relationships learned from the database are used to constrain reconstruction, ensuring semantic compatibility between both object models and parts. Small objects and objects with incomplete depth information which are difficult to recover reliably are processed with a two-stage approach. Major objects are recognized first, providing a known scene structure. 2D contour-based model retrieval is then used to recover smaller objects. Evaluations using our own data and two public datasets show that our approach can model typical real-world indoor scenes efficiently and robustly.

Intrinsic Delaunay triangulation (IDT) naturally generalizes Delaunay triangulation from R^2 to curved surfaces. Due to many favorable properties, the IDT whose vertex set includes all mesh vertices is of particular interest in polygonal mesh processing. To date, the only way for constructing such IDT is the edge-flipping algorithm, which iteratively flips non-Delaunay edges to become locally Delaunay. Although this algorithm is conceptually simple and guarantees to terminate in finite steps, it has no known time complexity and may also produce triangulations containing faces with only two edges. This article develops a new method to obtain proper IDTs on manifold triangle meshes.We first compute a geodesic Voronoi diagram (GVD) by taking all mesh vertices as generators and then find its dual graph. The sufficient condition for the dual graph to be a proper triangulation is that all Voronoi cells satisfy the so-called closed ball property. To guarantee the closed ball property everywhere, a certain sampling criterion is required. For Voronoi cells that violate the closed ball property, we fix them by computing topologically safe regions, inwhich auxiliary sites can be addedwithout changing the topology of theVoronoi diagram beyond them.Given a meshwith n vertices, we prove that by adding at most O(n) auxiliary sites, the computed GVD satisfies the closed ball property, and hence its dual graph is a proper IDT. Our method has a theoretical worst-case time complexity O(n^2 + tn log n), where t is the number of obtuse angles in the mesh. Computational results show that it empirically runs in linear time on real-world models.

We present a general computational framework to locally characterize any shape space of meshes implicitly prescribed by a collection of non-linear constraints. We computationally access such manifolds, typically of high dimension and co-dimension, through first and second order approximants, namely tangent spaces and quadratically parameterized osculant surfaces. Exploration and navigation of desirable subspaces of the shape space with regard to application specific quality measures are enabled using approximants that are intrinsic to the underlying manifold and directly computable in the parameter space of the osculant surface. We demonstrate our framework on shape spaces of planar quad (PQ) meshes, where each mesh face is constrained to be (nearly) planar, and circular meshes, where each face has a circumcircle. We evaluate our framework for navigation and design exploration on a variety of inputs, while keeping context specific properties such as fairness, proximity to a reference surface, etc.

In this paper, we introduce a surface reconstruction method that can perform gracefully with non-uniformly-distributed, noisy, and even sparse data. We reconstruct the surface by estimating an implicit function and then obtain a triangle mesh by extracting an iso-surface from it. Our implicit function takes advantage of both the indicator function and the signed distance function. It is dominated by the indicator function at the regions away from the surface and approximates (up to scaling) the signed distance function near the surface. On one hand, it is well defined over the entire space so that the extracted iso-surface must lie near the underlying true surface and is free of spurious sheets. On the other hand, thanks to the nice properties of the signed distance function, a smooth iso-surface can be extracted using the approach of marching cubes with simple linear interpolations. More importantly, our implicit function can be estimated directly from an explicit integral formula without solving any linear system. This direct approach leads to a simple, accurate and robust reconstruction method, which can be paralleled with little overhead. We call our reconstruction method Gauss surface reconstruction. We apply our method to both synthetic and real-world scanned data and demonstrate the accuracy, robustness and efficiency of our method. The performance of Gauss surface reconstruction is also compared with that of several state-of-the-art methods.

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In this paper, we tackle the problem of tiling a domain with a set of deformable templates. A valid solution to this problem completely covers the domain with templates such that the templates do not overlap. We generalize existing specialized solutions and formulate a general layout problem by modeling important constraints and admissible template deformations. Our main idea is to break the layout algorithm into two steps: a discrete step to lay out the approximate template positions and a continuous step to refine the template shapes. Our approach is suitable for a large class of applications, including floorplans, urban layouts, and arts and design.

We present a novel remeshing algorithm that avoids triangles with small (acute) angles and those with large (obtuse) angles. Our solution is based on an extension of Centroidal Voronoi Tesselation (CVT).We augment the original CVT formulation with a penalty term that penalizes short Voronoi edges, while the CVT term helps to avoid small angles. Our results show significant improvements in remeshing quality over the state of the art.