Changhe Tu

Build-to-last: strength to weight 3D printed objects

The emergence of low-cost 3D printers steers the investigation of new geometric problems that control the quality of the fabricated object. In this paper, we present a method to reduce the material cost and weight of a given object while providing a durable printed model that is resistant to impact and external forces. We introduce a hollowing optimization algorithm based on the concept of honeycomb-cells structure. Honeycombs structures are known to be of minimal material cost while providing strength in tension. We utilize the Voronoi diagram to compute irregular honeycomb-like volume tessellations which define the inner structure. We formulate our problem as a strength--to--weight optimization and cast it as mutually finding an optimal interior tessellation and its maximal hollowing subject to relieve the interior stress. Thus, our system allows to build-to-last 3D printed objects with large control over their strength-to-weight ratio and easily model various interior structures. We demonstrate our method on a collection of 3D objects from different categories. Furthermore, we evaluate our method by printing our hollowed models and measure their stress and weights.

Synthesizing Training Images for Boosting Human 3D Pose Estimation

Human 3D pose estimation from a single image is a challenging task with numerous applications. Convolutional Neural Networks (CNNs) have recently achieved superior performance on the task of 2D pose estimation from a single image, by training on images with 2D annotations collected by crowd sourcing. This suggests that similar success could be achieved for direct estimation of 3D poses. However, 3D poses are much harder to annotate, and the lack of suitable annotated training images hinders attempts towards end-to-end solutions. To address this issue, we opt to automatically synthesize training images with ground truth pose annotations. Our work is a systematic study along this road. We find that pose space coverage and texture diversity are the key ingredients for the effectiveness of synthetic training data. We present a fully automatic, scalable approach that samples the human pose space for guiding the synthesis procedure and extracts clothing textures from real images. Furthermore, we explore domain adaptation for bridging the gap between our synthetic training images and real testing photos. We demonstrate that CNNs trained with our synthetic images out-perform those trained with real photos on 3D pose estimation tasks.

Medial axis tree-an internal supporting structure for 3D printing

Saving material and improving strength are two important but conflicting requirements in 3D printing. We propose a novel method for designing the internal supporting frame structures of 3D objects based on their medial axis such that the objects are fabricated with minimal amount of material but can still withstand specified external load. Our method is inspired by the observation that the medial axis, being the skeleton of an object, serves as a natural backbone structure of the object to improve its resistance to external loads. A hexagon-dominant framework beneath the boundary surface is constructed and a set of tree-like branching bars are designed to connect this framework to the medial axis. The internal supporting structure is further optimized to minimize the material cost subject to strength constraints. Models fabricated with our method are intended to withstand external loads from various directions, other than just from a particular direction as considered in some other existing methods. Experimental results show that our method is capable of processing various kinds of input models and producing stronger and lighter 3D printed objects than those produced with other existing methods.

Enhancing Levin's method for computing quadric-surface intersections

Levins method produces a parameterization of the intersection curve of two quadrics in the form p(u) = a(u) ± d(u) √s(u), where a(u) and d(u) are vector valued polynomials, and s(u) is a quartic polynomial. This method, however, is incapable of classifying the morphology of the intersection curve, in terms of reducibility, singularity, and the number of connected components, which is critical structural information required by solid modeling applications. We study the theoretical foundation of Levins method, as well as the parameterization p(u) it produces. The following contributions are presented in this paper: (1) It is shown how the roots of s(u) can be used to classify the morphology of an irreducible intersection curve of two quadric surfaces. (2) An enhanced version of Levins method is proposed that, besides classifying the morphology of the intersection curve of two quadrics, produces a rational parameterization of the curve if the curve is singular. (3) A simple geometric proof is given for the existence of a real ruled quadric in any quadric pencil, which is the key result on which Levins method is based. These results enhance the capability of Levins method in processing the intersection curve of two general quadrics within its own self-contained framework.

Using signature sequences to classify intersection curves of two quadrics

We present a method that uses signature sequences to classify the intersection curve of two quadrics (QSIC) or, equivalently, quadric pencils in PR^3 (3D real projective space), in terms of the shape, topological properties, and algebraic properties of the QSIC. Specifically, for a QSIC we consider its singularity, reducibility, the number of its components, and the degree of each irreducible component, etc. There are in total 35 different types of non-degenerate quadric pencils. For each of the 35 types of QSICs given by these non-degenerate pencils, through a detailed study of the eigenvalue curve and the index function jump we establish a characterizing algebraic condition expressed in terms of the Segre characteristics and the signature sequence of the quadric pencil. We show how to compute a signature sequence with rational arithmetic and use it to determine the type of the intersection curve of any two quadrics which form a non-degenerate pencil. As an example of application, we discuss how to apply our results to collision detection of cones in 3D affine space.

SMI 2011: Full Paper: Shape optimization of quad mesh elements

We study the problem of optimizing the face elements of a quad mesh surface, that is, re-sampling a given quad mesh to make it possess, as much as possible, face elements of some desired aspect ratio and size. Unlike previous quad mesh optimization/improvement methods based on local operations on a small group of elements, we adopt a global approach that does not introduce extra singularities and therefore preserves the original quad structure of the input mesh. Starting from a collection of quad patches extracted from an input quad mesh, two global operations, i.e. re-sampling and re-distribution, are performed to optimize the number and spacings of grid lines in each patch. Both operations are formulated as simple optimization problems with linear constraints.

Classifying the nonsingular intersection curve of two quadric surfaces

We present new results on classifying the morphology of the nonsingular intersection curve of two quadrics by studying the roots of the characteristic equation, or the discriminant, of the pencil spanned by the two quadrics. The morphology of a nonsingular algebraic curve means the structural (or topological) information about the curve, such as the number of disjoint connected components of the curve in P/spl Ropf//sup 3/ (the 3D real projective space), and whether a particular component is a compact set in any affine realization of P/spl Ropf//sup 3/. For example, we show that two quadrics intersect along a nonsingular space quartic curve in P/spl Ropf//sup 3/ with one connected component if and only if their characteristic equation has two distinct real roots and a pair of complex conjugate roots. Since the number of the real roots of the characteristic equation can be counted robustly with exact arithmetic, our results can be used to obtain structural information reliably before computing the parameterization of the intersection curve; thus errors in the subsequent computation that is most likely done using floating point arithmetic will not lead to erroneous topological classification of the intersection curve. The key technique used to prove our results is to reduce two quadrics into simple forms using a projective transformation, a technique equivalent to the simultaneous block diagonalization of two real symmetric matrices, a topic that has been studied in matrix algebra.

Hallucinating Stereoscopy from a Single Image

We introduce a novel method for enabling stereoscopic viewing of a scene from a single pre‐segmented image. Rather than attempting full 3D reconstruction or accurate depth map recovery, we hallucinate a rough approximation of the scenes 3D model using a number of simple depth and occlusion cues and shape priors. We begin by depth‐sorting the segments, each of which is assumed to represent a separate object in the scene, resulting in a collection of depth layers. The shapes and textures of the partially occluded segments are then completed using symmetry and convexity priors. Next, each completed segment is converted to a union of generalized cylinders yielding a rough 3D model for each object. Finally, the object depths are refined using an iterative ground fitting process. The hallucinated 3D model of the scene may then be used to generate a stereoscopic image pair, or to produce images from novel viewpoints within a small neighborhood of the original view. Despite the simplicity of our approach, we show that it compares favorably with state‐of‐the‐art depth ordering methods. A user study was conducted showing that our method produces more convincing stereoscopic images than existing semi‐interactive and automatic single image depth recovery methods.

A BPEL4WS-based Composite Service Modeling Solution in Manufacturing Grid

In Manufacturing Grid, a lot of applications and resources in manufacturing enterprises are encapsulated as web services and a cooperative work environment is provided. Applying web service composition and workflow technologies, services are integrated into a composite service to represent a cooperative business process. Therefore the enterprise cooperation can be implemented by executing and monitoring the composite service. According to the characteristics of Manufacturing, this paper presents a composite service modeling solution based on BPEL4WS and discusses how this solution support BPEL4WS during the whole modeling process. The solution includes dynamic service discovery and service selection to support a flexible binding with the partners? services. This paper also describes how to execute and monitor the composite service.

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.