Shi-Qing Xin

Making burr puzzles from 3D models

A 3D burr puzzle is a 3D model that consists of interlocking pieces with a single-key property. That is, when the puzzle is assembled, all the pieces are notched except one single key component which remains mobile. The intriguing property of the assembled burr puzzle is that it is stable, perfectly interlocked, without glue or screws, etc. Moreover, a burr puzzle consisting of a small number of pieces is still rather difficult to solve since the assembly must follow certain orders while the combinatorial complexity of the puzzles piece arrangements is extremely high. In this paper, we generalize the 6-piece orthogonal burr puzzle (a knot) to design and model burr puzzles from 3D models. Given a 3D input model, we first interactively embed a network of knots into the 3D shape. Our method automatically optimizes and arranges the orientation of each knot, and modifies pieces of adjacent knots with an appropriate connection type. Then, following the geometry of the embedded pieces, the entire 3D model is partitioned by splitting the solid while respecting the assembly motion of embedded pieces. The main technical challenge is to enforce the single-key property and ensure the assembly/disassembly remains feasible, as the puzzle pieces in a network of knots are highly interlocked. Lastly, we also present an automated approach to generate the visualizations of the puzzle assembly process.

Editable polycube map for GPU-based subdivision surfaces

In this paper we propose an editable polycube mapping method that, given an arbitrary high-resolution polygonal mesh and a simple polycube representation plus optional sketched features indicating relevant correspondences between the two, provides a uniform, regular and artist-controllable quads-only mesh with a parameterized subdivision scheme. The method introduces a global parameterization, based on a divide and conquer strategy, which allows to create polycube-maps with a much smaller number of patches, and gives much more control over the quality of the induced subdivision surface. All this makes it practical for real-time rendering on modern hardware (e.g. OGL 4.1 and D3D11 tessellation hardware). By sketching these correspondence features, processing large-scale models with complex geometry and topology is now feasible. This is crucial for obtaining watertight displaced Catmull-Clark subdivision surfaces and high-quality texturing on real-time applications.

Parallel chen-han (PCH) algorithm for discrete geodesics

In many graphics applications, the computation of exact geodesic distance is very important. However, the high computational cost of existing geodesic algorithms means that they are not practical for large-scale models or time-critical applications. To tackle this challenge, we propose the Parallel Chen-Han (or PCH) algorithm, which extends the classic Chen-Han (CH) discrete geodesic algorithm to the parallel setting. The original CH algorithm and its variant both lack a parallel solution because the windows (a key data structure that carries the shortest distance in the wavefront propagation) are maintained in a strict order or a tightly coupled manner, which means that only one window is processed at a time. We propose dividing the CHs sequential algorithm into four phases, window selection, window propagation, data organization, and events processing so that there is no data dependence or conflicts in each phase and the operations within each phase can be carried out in parallel. The proposed PCH algorithm is able to propagate a large number of windows simultaneously and independently. We also adopt a simple yet effective strategy to control the total number of windows. We implement the PCH algorithm on modern GPUs (such as Nvidia GTX 580) and analyze the performance in detail. The performance improvement (compared to the sequential algorithms) is highly consistent with GPU double-precision performance (GFLOPS). Extensive experiments on real-world models demonstrate an order of magnitude improvement in execution time compared to the state-of-the-art.

Unsupervised 3D shape segmentation and co-segmentation via deep learning

In this paper, we propose a novel unsupervised algorithm for automatically segmenting a single 3D shape or co-segmenting a family of 3D shapes using deep learning. The algorithm consists of three stages. In the first stage, we pre-decompose each 3D shape of interest into primitive patches to generate over-segmentation and compute various signatures as low-level shape features. In the second stage, high-level features are learned, in an unsupervised style, from the low-level ones based on deep learning. Finally, either segmentation or co-segmentation results can be quickly reported by patch clustering in the high-level feature space. The experimental results on the Princeton Segmentation Benchmark and the Shape COSEG Dataset exhibit superior segmentation performance of the proposed method over the previous state-of-the-art approaches. We propose a novel segmentation and co-segmentation approach for 3D shapes.We introduce deep learning into 3D shape segmentation and co-segmentation.Our method is data-driven but does not need a tedious labeling process.Our algorithm achieves better or comparable performance when compared with the state-of-the-art methods.

Constant-time O (1) all pairs geodesic distance query on triangle meshes

Geodesic plays an important role in geometric computation and analysis. Rather than the widely studied <i>single source all destination</i> discrete geodesic problem, very little work has been reported on the <i>all pairs</i> geodesic distance query So far, the best known result is due to Cook IV and Wenk [2009], who pre-computed the pairwise geodesic between any two mesh vertices in <i>O</i>(<i>n</i>⁵2^α(<i>n</i>) log<i>n</i>) time complexity and <i>O</i>(<i>n</i>⁴) space complexity, where <i>n</i> is the number of mesh vertices and α(<i>n</i>) the inverse Ackermann function. Then the geodesic distance between any pair of points on the mesh edges can be computed in <i>O</i>(<i>m</i> + log<i>n</i>) time, where <i>m</i> is the number of edges crossed by the geodesic path. Although Cook IV and Wenks algorithm is able to compute the <i>exact</i> geodesic the high computational cost limits its applications to real-world models which usually contain thousands of vertices.

An Intrinsic Algorithm for Parallel Poisson Disk Sampling on Arbitrary Surfaces

Poisson disk sampling has excellent spatial and spectral properties, and plays an important role in a variety of visual computing. Although many promising algorithms have been proposed for multidimensional sampling in euclidean space, very few studies have been reported with regard to the problem of generating Poisson disks on surfaces due to the complicated nature of the surface. This paper presents an intrinsic algorithm for parallel Poisson disk sampling on arbitrary surfaces. In sharp contrast to the conventional parallel approaches, our method neither partitions the given surface into small patches nor uses any spatial data structure to maintain the voids in the sampling domain. Instead, our approach assigns each sample candidate a random and unique priority that is unbiased with regard to the distribution. Hence, multiple threads can process the candidates simultaneously and resolve conflicts by checking the given priority values. Our algorithm guarantees that the generated Poisson disks are uniformly and randomly distributed without bias. It is worth noting that our method is intrinsic and independent of the embedding space. This intrinsic feature allows us to generate Poisson disk patterns on arbitrary surfaces in IRn. To our knowledge, this is the first intrinsic, parallel, and accurate algorithm for surface Poisson disk sampling. Furthermore, by manipulating the spatially varying density function, we can obtain adaptive sampling easily.

Efficiently Computing Exact Geodesic Loops within Finite Steps

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

Synthesis of filigrees for digital fabrication

Filigrees are thin patterns found in jewelry, ornaments and lace fabrics. They are often formed of repeated base elements manually composed into larger, delicate patterns. Digital fabrication simplifies the process of turning a virtual model of a filigree into a physical object. However, designing a virtual model of a filigree remains a time consuming and challenging task. The difficulty lies in tightly packing together the base elements while covering a target surface. In addition, the filigree has to be well connected and sufficiently robust to be fabricated. We propose a novel approach automating this task. Our technique covers a target surface with a set of input base elements, forming a filigree strong enough to be fabricated. We exploit two properties of filigrees to make this possible. First, as filigrees form delicate traceries they are well captured by their skeleton. This affords for a simpler definition of operators such as matching and deformation. Second, instead of seeking for a perfect packing of the base elements we relax the problem by allowing appearance preserving partial overlaps. We optimize a filigree by a stochastic search, further improved by a novel boosting algorithm that records and reuses good configurations discovered during the process. We illustrate our technique on a number of challenging examples reproducing filigrees on large objects, which we manufacture by 3D printing. Our technique affords for several user controls, such as the scale and orientation of the elements.

Intrinsic computation of centroidal Voronoi tessellation (CVT) on meshes

Centroidal Voronoi tessellation (CVT) is a special type of Voronoi diagram such that the generating point of each Voronoi cell is also its center of mass. The CVT has broad applications in computer graphics, such as meshing, stippling, sampling, etc. The existing methods for computing CVTs on meshes either require a global parameterization or compute it in the restricted sense (that is, intersecting a 3D CVT with the surface). Therefore, these approaches often fail on models with complicated geometry and/or topology. This paper presents two intrinsic algorithms for computing CVT on triangle meshes. The first algorithm adopts the Lloyd framework, which iteratively moves the generator of each geodesic Voronoi diagram to its mass center. Based on the discrete exponential map, our method can efficiently compute the Riemannian center and the center of mass for any geodesic Voronoi diagram. The second algorithm uses the L-BFGS method to accelerate the intrinsic CVT computation. Thanks to the intrinsic feature, our methods are independent of the embedding space, and work well for models with arbitrary topology and complicated geometry, where the existing extrinsic approaches often fail. The promising experimental results show the advantages of our method. We propose two intrinsic methods for computing centroidal Voronoi tessellation (CVT) on triangle meshes.Thanks to their intrinsic nature, our methods compute CVT using metric only.Our results are independent of the embedding space.

LBDP: localized boundary detection and parametrization for 3-D sensor networks

Many applications of wireless sensor networks involve monitoring a time-variant event (e.g., radiation pollution in the air). In such applications, fast boundary detection is a crucial function, as it allows us to track the event variation in a timely fashion. However, the problem becomes very challenging as it demands a highly efficient algorithm to cope with the dynamics introduced by the evolving event. Moreover, as many physical events occupy volumes rather than surfaces (e.g., pollution again), the algorithm has to work for 3-D cases. Finally, as boundaries of a 3-D network can be complicated 2-manifolds, many network functionalities (e.g., routing) may fail in the face of such boundaries. To this end, we propose Localized Boundary Detection and Parametrization (LBDP) to tackle these challenges. The first component of LBDP is UNiform Fast On-Line boundary Detection (UNFOLD). It applies an inversion to node coordinates such that a “notched” surface is “unfolded” into a convex one, which in turn reduces boundary detection to a localized convexity test. We prove the correctness and efficiency of UNFOLD; we also use simulations and implementations to evaluate its performance, which demonstrates that UNFOLD is two orders of magnitude more time- and energy-efficient than the most up-to-date proposal. Another component of LBDP is Localized Boundary Sphericalization (LBS). Through purely localized operations, LBS maps an arbitrary genus-0 boundary to a unit sphere, which in turn supports functionalities such as distinguishing inter boundaries from external ones and distributed coordinations on a boundary. We implement LBS in TOSSIM and use simulations to show its effectiveness.