Dong-Ming Yan

On centroidal voronoi tessellation—energy smoothness and fast computation

Centroidal Voronoi tessellation (CVT) is a particular type of Voronoi tessellation that has many applications in computational sciences and engineering, including computer graphics. The prevailing method for computing CVT is Lloyds method, which has linear convergence and is inefficient in practice. We develop new efficient methods for CVT computation and demonstrate the fast convergence of these methods. Specifically, we show that the CVT energy function has 2nd order smoothness for convex domains with smooth density, as well as in most situations encountered in optimization. Due to the 2nd order smoothness, it is possible to minimize the CVT energy functions using Newton-like optimization methods and expect fast convergence. We propose a quasi-Newton method to compute CVT and demonstrate its faster convergence than Lloyds method with various numerical examples. It is also significantly faster and more robust than the Lloyd-Newton method, a previous attempt to accelerate CVT. We also demonstrate surface remeshing as a possible application.

Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram

We propose a new isotropic remeshing method, based on Centroidal Voronoi Tessellation (CVT). Constructing CVT requires to repeatedly compute Restricted Voronoi Diagram (RVD), defined as the intersection between a 3D Voronoi diagram and an input mesh surface. Existing methods use some approximations of RVD. In this paper, we introduce an efficient algorithm that computes RVD exactly and robustly. As a consequence, we achieve better remeshing quality than approximation‐based approaches, without sacrificing efficiency. Our method for RVD computation uses a simple procedure and a kd‐tree to quickly identify and compute the intersection of each triangle face with its incident Voronoi cells. Its time complexity is O(mlog n), where n is the number of seed points and m is the number of triangles of the input mesh. Fast convergence of CVT is achieved using a quasi‐Newton method, which proved much faster than Lloyds iteration. Examples are presented to demonstrate the better quality of remeshing results with our method than with the state‐of‐art approaches.

Acquiring 3D indoor environments with variability and repetition

Large-scale acquisition of exterior urban environments is by now a well-established technology, supporting many applications in search, navigation, and commerce. The same is, however, not the case for indoor environments, where access is often restricted and the spaces are cluttered. Further, such environments typically contain a high density of repeated objects (e.g., tables, chairs, monitors, etc.) in regular or non-regular arrangements with significant pose variations and articulations. In this paper, we exploit the special structure of indoor environments to accelerate their 3D acquisition and recognition with a low-end handheld scanner. Our approach runs in two phases: (i) a learning phase wherein we acquire 3D models of frequently occurring objects and capture their variability modes from only a few scans, and (ii) a recognition phase wherein from a single scan of a new area, we identify previously seen objects but in different poses and locations at an average recognition time of 200ms/model. We evaluate the robustness and limits of the proposed recognition system using a range of synthetic and real world scans under challenging settings.

Quadric surface extraction by variational shape approximation

Based on Lloyd iteration, we present a variational method for extracting general quadric surfaces from a 3D mesh surface. This work extends the previous variational methods that extract only planes or special types of quadrics, i.e., spheres and circular cylinders. Instead of using the exact L2 error metric, we use a new approximate L2 error metric to make our method more efficient for computing with general quadrics. Furthermore, a method based on graph cut is proposed to smooth irregular boundary curves between segmented regions, which greatly improves the final results.

Variational mesh segmentation via quadric surface fitting

We present a new variational method for mesh segmentation by fitting quadric surfaces. Each component of the resulting segmentation is represented by a general quadric surface (including plane as a special case). A novel energy function is defined to evaluate the quality of the segmentation, which combines both L^2 and L^2^,^1 metrics from a triangle to a quadric surface. The Lloyd iteration is used to minimize the energy function, which repeatedly interleaves between mesh partition and quadric surface fitting. We also integrate feature-based and simplification-based techniques in the segmentation framework, which greatly improve the performance. The advantages of our algorithm are demonstrated by comparing with the state-of-the-art methods.

Gap processing for adaptive maximal poisson-disk sampling

In this article, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or when their radii are changed. We build on the concepts of regular triangulations and the power diagram. Third, we show how our analysis contributes to the state-of-the-art in surface remeshing.

Generating and exploring good building layouts

Good building layouts are required to conform to regulatory guidelines, while meeting certain quality measures. While different methods can sample the space of such good layouts, there exists little support for a user to understand and systematically explore the samples. Starting from a discrete set of good layouts, we analytically characterize the local shape space of good layouts around each initial layout, compactly encode these spaces, and link them to support transitions across the different local spaces. We represent such transitions in the form of a portal graph. The user can then use the portal graph, along with the family of local shape spaces, to globally and locally explore the space of good building layouts. We use our framework on a variety of different test scenarios to showcase an intuitive design, navigation, and exploration interface.

Inverse procedural modeling of facade layouts

In this paper, we address the following research problem: How can we generate a meaningful split grammar that explains a given facade layout? To evaluate if a grammar is meaningful, we propose a cost function based on the description length and minimize this cost using an approximate dynamic programming framework. Our evaluation indicates that our framework extracts meaningful split grammars that are competitive with those of expert users, while some users and all competing automatic solutions are less successful.

Efficient computation of clipped Voronoi diagram for mesh generation

The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially outside of the domain, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm to compute the clipped Voronoi diagram for a set of sites with respect to a compact 2D region or a 3D volume. We also apply the proposed method to optimal mesh generation based on the centroidal Voronoi tessellation.

Efficient computation of 3d clipped voronoi diagram

The Voronoi diagram is a fundamental geometry structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact 3D domain (i.e. a finite 3D volume), some Voronoi cells of their Voronoi diagram are infinite, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm for computing the clipped Voronoi diagram for a set of sites with respect to a compact 3D volume, assuming that the volume is represented as a tetrahedral mesh. We also describe an application of the proposed method to implementing a fast method for optimal tetrahedral mesh generation based on the centroidal Voronoi tessellation.