Zhonggui Chen

Curved folding

Fascinating and elegant shapes may be folded from a single planar sheet of material without stretching, tearing or cutting, if one incorporates curved folds into the design. We present an optimization-based computational framework for design and digital reconstruction of surfaces which can be produced by curved folding. Our work not only contributes to applications in architecture and industrial design, but it also provides a new way to study the complex and largely unexplored phenomena arising in curved folding.

Easy Mesh Cutting

We present Easy Mesh Cutting, an intuitive and easy‐to‐use mesh cutout tool. Users can cut meaningful components from meshes by simply drawing freehand sketches on the mesh. Our system provides instant visual feedback to obtain the cutting results based on an improved region growing algorithm using a feature sensitive metric. The cutting boundary can be automatically optimized or easily edited by users. Extensive experimentation shows that our approach produces good cutting results while requiring little skill or effort from the user and provides a good user experience. Based on the easy mesh cutting framework, we introduce two applications including sketch‐based mesh editing and mesh merging for geometry processing.

Variational Blue Noise Sampling

Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including nonphotorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces.

Revisiting optimal Delaunay triangulation for 3D graded mesh generation

NSFC [61100107, 61100105, 61272019, 61332015]; Natural Science Foundation of Fujian Province of China [2012J01291, 2011J05007]; National Basic Research Program of China [2011CB302400]; Research Grant Council of Hong Kong [718209, 718010, 718311, 717012]; NSF [61222206]; Chinese Academy of Sciences

Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh

We develop a novel isotropic remeshing method based on constrained centroidal Delaunay mesh (CCDM), a generalization of centroidal patch triangulation from 2D to mesh surface. Our method starts with resampling an input mesh with a vertex distribution according to a user‐defined density function. The initial remeshing result is then progressively optimized by alternatively recovering the Delaunay mesh and moving each vertex to the centroid of its 1‐ring neighborhood. The key to making such simple iterations work is an efficient optimization framework that combines both local and global optimization methods. Our method is parameterization‐free, thus avoiding the metric distortion introduced by parameterization, and generating more well‐shaped triangles. Our method guarantees that the topology of surface is preserved without requiring geodesic information. We conduct various experiments to demonstrate the simplicity, efficacy, and robustness of the presented method.

Spherical DCB-Spline Surfaces with Hierarchical and Adaptive Knot Insertion

This paper develops a novel surface fitting scheme for automatically reconstructing a genus-0 object into a continuous parametric spline surface. A key contribution for making such a fitting method both practical and accurate is our spherical generalization of the Delaunay configuration B-spline (DCB-spline), a new non-tensor-product spline. In this framework, we efficiently compute Delaunay configurations on sphere by the union of two planar Delaunay configurations. Also, we develop a hierarchical and adaptive method that progressively improves the fitting quality by new knot-insertion strategies guided by surface geometry and fitting error. Within our framework, a genus-0 model can be converted to a single spherical spline representation whose root mean square error is tightly bounded within a user-specified tolerance. The reconstructed continuous representation has many attractive properties such as global smoothness and no auxiliary knots. We conduct several experiments to demonstrate the efficacy of our new approach for reverse engineering and shape modeling.

B-spline surface fitting with knot position optimization

In linear least squares fitting of B-spline surfaces, the choice of knot vector is essentially important to the quality of the approximating surface. In this paper, a heuristic criterion for optimal knot positions in the fitting problem is formulated as an optimization problem according to the geometric feature distribution of the input data. Then, the coordinate descent algorithm is used for the optimal knot computation. Based on knot position optimization, an iterative surface fitting framework is developed, which adaptively introduces more knot isolines passing through the regions with more complex geometry or large fitting errors. Hence, the approximation quality of the reconstructed surface is progressively improved up to a pre-specified threshold. We test several models to demonstrate the efficacy of our method in fitting surface with distinct geometric features. Different from the knot placement technique (NKTP method) proposed in Piegl and Tiller 1 and the dominant-column-based fitting method (DOM-based method) (Park 2) which require input data in semi-grid or grid form, our algorithm takes more general data points as input, i.e., any scattered data sets with parameterization. Comparing to NKTP method and DOM-based method, our method efficiently produces more accurate results by using the same number of knots. Graphical abstractDisplay Omitted HighlightsA heuristic criterion is proposed for optimizing knots in the B-spline surface fitting problem.The iterative surface fitting framework can well preserve geometric features.Our method is more efficient and yields more accurate results than DOM-based method.

Surface parameterization via aligning optimal local flattening

This paper presents a novel parameterization method for a non-closed triangular mesh. For every flattened 1-ring neighbors, we choose a local coordinate frame, and the local geometry structure is represented as local parametric coordinates. Then the global optimal parametric coordinates are attained by aligning all the local parametric planes while preserving the local structure as much as possible. The boundary conditions are not necessary in our method, thus no high distortion appears around the boundary, and distortion is uniformly distributed over parametric domain. In addition, our method can operate directly on mesh surface which has holes without any preprocessing of surface partition. Furthermore, linear constraints are allowed in the parameterization in a least squares sense.

An intrinsic algorithm for computing geodesic distance fields on triangle meshes with holes

As a fundamental concept, geodesics play an important role in many geometric modeling applications. However, geodesics are highly sensitive to topological changes; a small topological shortcut may result in a significantly large change of geodesic distance and path. Most of the existing discrete geodesic algorithms can only be applied to noise-free meshes. In this paper, we present a new algorithm to compute the meaningful approximate geodesics on polygonal meshes with holes. Without the explicit hole filling, our algorithm is completely intrinsic and independent of the embedding space; thus, it has the potential for isometrically deforming objects as well as meshes in high dimensional space. Furthermore, our method can guarantee the exact solution if the surface is developable. We demonstrate the efficacy of our algorithm in both real-world and synthetic models.

Centroidal power diagrams with capacity constraints: computation, applications, and extension

This article presents a new method to optimally partition a geometric domain with capacity constraints on the partitioned regions. It is an important problem in many fields, ranging from engineering to economics. It is known that a capacity-constrained partition can be obtained as a power diagram with the squared L2 metric. We present a method with super-linear convergence for computing optimal partition with capacity constraints that outperforms the state-of-the-art in an order of magnitude. We demonstrate the efficiency of our method in the context of three different applications in computer graphics and geometric processing: displacement interpolation of function distribution, blue-noise point sampling, and optimal convex decomposition of 2D domains. Furthermore, the proposed method is extended to capacity-constrained optimal partition with respect to general cost functions beyond the squared Euclidean distance.