Structure Preserving Manipulation and Interpolation for Multi‐element 2D Shapes

This paper presents a method that generates natural and intuitive deformations via direct manipulation and smooth interpolation for multi‐element 2D shapes. Observing that the structural relationships between different parts of a multi‐element 2D shape are important for capturing its feature semantics, we introduce a simple structure called a feature frame to represent such relationships. A constrained optimization is solved for shape manipulation to find optimal deformed shapes under user‐specified handle constraints. Based on the feature frame, local feature preservation and structural relationship maintenance are directly encoded into the objective function. Beyond deforming a given multi‐element 2D shape into a new one at each key frame, our method can automatically generate a sequence of natural intermediate deformations by interpolating the shapes between the key frames. The method is computationally efficient, allowing real‐time manipulation and interpolation, as well as generating natural and visually plausible results.     

Direct shape optimization for strengthening 3D printable objects

Recently there has been an increasing demand for software that can help designers create functional 3D objects with required physical strength. We introduce a generic and extensible method that directly optimizes a shape subject to physical and geometric constraints. Given an input shape, our method optimizes directly its input mesh representation until it can withstand specified external forces, while remaining similar to the original shape. Our method performs physics simulation and shape optimization together in a unified framework, where the physics simulator is an integral part of the optimizer. We employ geometric constraints to preserve surface details and shape symmetry, and adapt a second‐order method with analytic gradients to improve convergence and computation time. Our method provides several advantages over previous work, including the ability to handle general shape deformations, preservation of surface details, and incorporation of user‐defined constraints. We demonstrate the effectiveness of our method on a variety of prinTable 3D objects through detailed simulations as well as physical validations.     

Data‐Driven Sparse Priors of 3D Shapes

We present a sparse optimization framework for extracting sparse shape priors from a collection of 3D models. Shape priors are defined as point‐set neighborhoods sampled from shape surfaces which convey important information encompassing normals and local shape characterization. A 3D shape model can be considered to be formed with a set of 3D local shape priors, while most of them are likely to have similar geometry. Our key observation is that the local priors extracted from a family of 3D shapes lie in a very low‐dimensional manifold. Consequently, a compact and informative subset of priors can be learned to efficiently encode all shapes of the same family. A comprehensive library of local shape priors is first built with the given collection of 3D models of the same family. We then formulate a global, sparse optimization problem which enforces selecting representative priors while minimizing the reconstruction error. To solve the optimization problem, we design an efficient solver based on the Augmented Lagrangian Multipliers method (ALM). Extensive experiments exhibit the power of our data‐driven sparse priors in elegantly solving several high‐level shape analysis applications and geometry processing tasks, such as shape retrieval, style analysis and symmetry detection.     

Consistent quadrangulation for shape collections via feature line co-extraction

This paper presents a method that takes a collection of 3D surface shapes, and produces a consistent and individually feature preserving quadrangulation of each shape. By exploring the correspondence among shapes within a collection, we coherently extract a set of representative feature lines as the key characteristics for the given shapes. Then we compute a smooth cross-field interpolating sparsely distributed directional constraints induced from the feature lines and apply the mixed-integer quadrangulation to generate the quad meshes. We develop a greedy algorithm to extract aligned cut graphs across the shape collection so that the meshes can be aligned in a common parametric domain. Computational results demonstrate that our approach not only produces consistent quad meshes across the entire collection with significant geometry variation but also achieves a trade-off between global structural simplicity for the collection and local geometry fidelity for each shape.     

Projective Feature Learning for 3D Shapes with Multi‐View Depth Images

Feature learning for 3D shapes is challenging due to the lack of natural paramterization for 3D surface models. We adopt the multi‐view depth image representation and propose Multi‐View Deep Extreme Learning Machine (MVD‐ELM) to achieve fast and quality projective feature learning for 3D shapes. In contrast to existing multi‐view learning approaches, our method ensures the feature maps learned for different views are mutually dependent via shared weights and in each layer, their unprojections together form a valid 3D reconstruction of the input 3D shape through using normalized convolution kernels. These lead to a more accurate 3D feature learning as shown by the encouraging results in several applications. Moreover, the 3D reconstruction property enables clear visualization of the learned features, which further demonstrates the meaningfulness of our feature learning.     

Buoyancy Optimization for Computational Fabrication

This paper introduces a design and fabrication pipeline for creating floating forms. Our method optimizes for buoyant equilibrium and stability of complex 3D shapes, applying a voxel‐carving technique to control the mass distribution. The resulting objects achieve a desired floating pose defined by a user‐specified waterline height and orientation. In order to enlarge the feasible design space, we explore novel ways to load the interior of a design using prefabricated components and casting techniques. 3D printing is employed for high‐precision fabrication. For larger scale designs we introduce a method for stacking lasercut planar pieces to create 3D objects in a quick and economic manner. We demonstrate fabricated designs of complex shape in a variety of floating poses.     

Learning Part Generation and Assembly for Sketching Man‐Made Objects

Modeling 3D objects on existing software usually requires a heavy amount of interactions, especially for users who lack basic knowledge of 3D geometry. Sketch‐based modeling is a solution to ease the modelling procedure and thus has been researched for decades. However, modelling a man‐made shape with complex structures remains challenging. Existing methods adopt advanced deep learning techniques to map holistic sketches to 3D shapes. They are still bottlenecked to deal with complicated topologies. In this paper, we decouple the task of sketch2shape into a part generation module and a part assembling module, where deep learning methods are leveraged for the implementation of both modules. By changing the focus from holistic shapes to individual parts, it eases the learning process of the shape generator and guarantees high‐quality outputs. With the learned automated part assembler, users only need a little manual tuning to obtain a desired layout. Extensive experiments and user studies demonstrate the usefulness of our proposed system.     

Stable Region Correspondences Between Non‐Isometric Shapes

We consider the problem of finding meaningful correspondences between 3D models that are related but not necessarily very similar. When the shapes are quite different, a point‐to‐point map is not always appropriate, so our focus in this paper is a method to build a set of correspondences between shape regions or parts. The proposed approach exploits a variety of feature functions on the shapes and makes use of the key observation that points in matching parts have similar ranks in the sorting of the corresponding feature values. Our algorithm proceeds in two steps. We first build an affinity matrix between points on the two shapes, based on feature rank similarity over many feature functions. We then define a notion of stability of a pair of regions, with respect to this affinity matrix, obtained as a fixed point of a nonlinear operator. Our method yields a family of corresponding maximally stable regions between the two shapes that can be used to define shape parts. We observe that this is an instance of the biclustering problem and that it is related to solving a constrained maximal eigenvalue problem. We provide an algorithm to solve this problem that mimics the power method. We show the robustness of its output to noisy input features as well its convergence properties. The obtained part correspondences are shown to be almost perfect matches in the isometric case, and also semantically appropriate even in non‐isometric cases. We provide numerous examples and applications of this technique, for example to sharpening correspondences in traditional shape matching algorithms.     

Single‐View Modeling of Layered Origami with Plausible Outer Shape

Modeling 3D origami pieces using conventional software is laborious due to the geometric constraints imposed by the complicated layered structure. Targeting origami models used in visual content such as CG illustrations and movies, we propose an interactive system that dramatically simplifies the modeling of 3D origami pieces with plausible outer shapes, while omitting accurate inner structures. By focusing on flat origami models with a front‐and‐back symmetry commonly found in traditional artworks, our system realizes easy and quick modeling via single‐view interface; given a reference image of the target origami piece, the user draws polygons of planar faces onto the image, and assigns annotations indicating the types of folding operations. Our system automatically rectifies the manually‐specified polygons, infers the folded structures that should yield the user‐specified polygons with reference to the depth order of layered polygons, and generates a plausible 3D model while accounting for gaps between layers. Our system is versatile enough for modeling pseudo‐origami models that are not realizable by folding a single sheet of paper. Our user study demonstrates that even novice users without the specialized knowledge and experience on origami and 3D modeling can create plausible origami models quickly.     

Parametric 3D modeling of young women's lower bodies based on shape classification

Three-dimensional (3D) human body modeling is an important research direction in the field of clothing virtual design. On the basis of 3D human body scanning, this paper studied a method to build a 3D parametric lower body model according to body classification. The research includes three main parts. (1) Anthropometry and body shape classification. We randomly selected 333 young women ages 18–25 years old in Northeast China as the experimental sample. Then we divided the lower body shape into three categories using principal component analysis and K-means clustering. (2) Determination of feature cross sections and points, and reconstruction of feature curves. According to the average values of each body type, we obtained the mean reference body by Euclidean distance method. We determined feature cross sections and points, and extracted the 3D coordinates of the feature points of the mean reference body to reconstruct the feature curves. (3) The surface lofting and establishment of parametric 3D lower body model. According to the shape characteristics of the lower body, we constructed the guiding lines for the crotch and lower limbs, and established parametric lower body models for three body types.Relevance to industry3D human modeling is an important part of garment industry digitization. This research provides an effective way to construct a parametric 3D lower body model. The method offers a reference for the parametric virtual human modeling and virtual fitting of trousers.     

Soft Folding

We introduce soft folding, a new interactive method for designing and exploring thin‐plate forms. A user specifies sharp and soft folds as two‐dimensional(2D) curves on a flat sheet, along with the fold magnitude and sharpness of each. Then, based on the soft folds, the system computes the three‐dimensional(3D) folded shape. Internally, the system first computes a fold field, which defines local folding operations on a flat sheet. A fold field is a generalization of a discrete fold graph in origami, replacing a graph with sharp folds with a continuous field with soft folds. Next, local patches are folded independently according to the fold field. Finally, a globally folded 3D shape is obtained by assembling the locally folded patches. This algorithm computes an approximation of 3D developable surfaces with user‐defined soft folds at an interactive speed. The user can later apply nonlinear physical simulation to generate more realistic results. Experimental results demonstrated that soft folding is effective for producing complex folded shapes with controllable sharpness.     

An Algorithm for Random Fractal Filling of Space

Computational experiments with a simple algorithm show that it is possible to fill any spatial region with a random fractalization of any shape, with a continuous range of pre‐specified fractal dimensions D. The algorithm is presented here in 1, 2 or 3 physical dimensions. The size power‐law exponent c or the fractal dimension D can be specified ab initio over a substantial range. The method creates an infinite set of shapes whose areas (lengths, volumes) obey a power law and sum to the area (length and volume) to be filled. The algorithm begins by randomly placing the largest shape and continues using random search to place each smaller shape where it does not overlap or touch any previously placed shape. The resulting gasket is a single connected object.     

High Reliefs from 3D Scenes

We present a method for synthesizing high reliefs, a sculpting technique that attaches 3D objects onto a 2D surface within a limited depth range. The main challenges are the preservation of distinct scene parts by preserving depth discontinuities, the fine details of the shape, and the overall continuity of the scene. Bas relief depth compression methods such as gradient compression and depth range compression are not applicable for high relief production. Instead, our method is based on differential coordinates to bring scene elements to the relief plane while preserving depth discontinuities and surface details of the scene. We select a user‐defined number of attenuation points within the scene, attenuate these points towards the relief plane and recompute the positions of all scene elements by preserving the differential coordinates. Finally, if the desired depth range is not achieved we apply a range compression. High relief synthesis is semi‐automatic and can be controlled by user‐defined parameters to adjust the depth range, as well as the placement of the scene elements with respect to the relief plane.     

Game level layout from design specification

The design of video game environments, or levels, aims to control gameplay by steering the player through a sequence of designer‐controlled steps, while simultaneously providing a visually engaging experience. Traditionally these levels are painstakingly designed by hand, often from pre‐existing building blocks, or space templates. In this paper, we propose an algorithmic approach for automatically laying out game levels from user‐specified blocks. Our method allows designers to retain control of the gameplay flow via user‐specified level connectivity graphs, while relieving them from the tedious task of manually assembling the building blocks into a valid, plausible layout. Our method produces sequences of diverse layouts for the same input connectivity, allowing for repeated replay of a given level within a visually different, new environment. We support complex graph connectivities and various building block shapes, and are able to compute complex layouts in seconds. The two key components of our algorithm are the use of configuration spaces defining feasible relative positions of building blocks within a layout and a graph‐decomposition based layout strategy that leverages graph connectivity to speed up convergence and avoid local minima. Together these two tools quickly steer the solution toward feasible layouts. We demonstrate our method on a variety of real‐life inputs, and generate appealing layouts conforming to user specifications.     

CustomCut: On‐demand Extraction of Customized 3D Parts with 2D Sketches

Several applications in shape modeling and exploration require identification and extraction of a 3D shape part matching a 2D sketch. We present CustomCut, an on‐demand part extraction algorithm. Given a sketched query, CustomCut automatically retrieves partially matching shapes from a database, identifies the region optimally matching the query in each shape, and extracts this region to produce a customized part that can be used in various modeling applications. In contrast to earlier work on sketch‐based retrieval of predefined parts, our approach can extract arbitrary parts from input shapes and does not rely on a prior segmentation into semantic components. The method is based on a novel data structure for fast retrieval of partial matches: the randomized compound k‐NN graph built on multi‐view shape projections. We also employ a coarse‐to‐fine strategy to progressively refine part boundaries down to the level of individual faces. Experimental results indicate that our approach provides an intuitive and easy means to extract customized parts from a shape database, and significantly expands the design space for the user. We demonstrate several applications of our method to shape design and exploration.     

Learning Detail Transfer based on Geometric Features

The visual richness of computer graphics applications is frequently limited by the difficulty of obtaining high‐quality, detailed 3D models. This paper proposes a method for realistically transferring details (specifically, displacement maps) from existing high‐quality 3D models to simple shapes that may be created with easy‐to‐learn modeling tools. Our key insight is to use metric learning to find a combination of geometric features that successfully predicts detail‐map similarities on the source mesh; we use the learned feature combination to drive the detail transfer. The latter uses a variant of multi‐resolution non‐parametric texture synthesis, augmented by a high‐frequency detail transfer step in texture space. We demonstrate that our technique can successfully transfer details among a variety of shapes including furniture and clothing.     

采用草绘轮廓的3维人脸建模方法

为方便用户进行3维人脸形状设计,提出一种基于手绘轮廓的3维人脸建模方法。该方法的主要特点在于,一方面,引用姿态估计技术对人脸草图进行解析,将用户绘制的侧视人脸草图转换成对应的正视人脸草图,可支持用户选择多个视角绘制人脸;另一方面,采用多层映射机制建立人脸草图特征点与3维人脸特征点之间的一一对应关系,由对应特征点之间的形变量来控制生成3维人脸,保证草图笔画的几何形状信息能有效映射到3维模型中。实验结果表明,文中方法能快速生成形状新颖的特定人脸,可有效支持用户进行3维人脸形状的手绘建模。     

Temporally Coherent and Artistically Intended Stylization of Feature Lines Extracted from 3D Models

In this paper, we propose a method to maintain the temporal coherence of stylized feature lines extracted from 3D models and preserve an artistically intended stylization provided by the user. We formally define the problem of combining spatio‐temporal continuity and artistic intention as a weighted energy minimization problem of competing constraints. The proposed method updates the style properties to provide real‐time smooth transitions from current to goal stylization, by assuring first‐ and second‐order temporal continuity, as well as spatial continuity along each stroke. The proposed weighting scheme guarantees that the stylization of strokes maintains motion coherence with respect to the apparent motion of the underlying surface in consecutive frames. This weighting scheme emphasizes temporal continuity for small apparent motions where the human vision system is able to keep track of the scene, and prioritizes the artistic intention for large apparent motions where temporal coherence is not expected. The proposed method produces temporally coherent and visually pleasing animations without the flickering artifacts of previous methods, while also maintaining the artistic intention of a goal stylization provided by the user.     

Geometry curves: A compact representation for 3D shapes

We propose a novel compact surface representation, namely geometry curves, which record the essence of shape geometry and topology. The geometry curves mainly contain two parts: the interior and boundary lines. The interior lines, which correspond to the feature lines, record the geometry information of the 3D shapes; the boundary lines, which correspond to the boundary or fundamental polygons, record the topology information of the 3D shapes. As a vector representation, geometry curves can depict highly complex geometry details. The concept of geometry curves can be utilized in many potential applications, e.g., mesh compression, shape modeling and editing, animation, and level of details. Furthermore, we develop a procedure for automatically constructing geometry curves which obtain an excellent approximation to the original mesh.