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Abstract: In this paper, we derive the bounds on the magnitude of lth order derivatives of rational Bézier curves, estimate the error, in the norm sense, for the hybrid polynomial approximation of the lth order derivatives of rational Bézier curves. We then prove that when the hybrid polynomial approximation converges to a given rational Bézier curve, the lth derivatives of the hybrid polynomial approximation curve also uniformly converge to the corresponding derivatives of the rational curve. These results are useful for designing simpler algorithms for computing tangent vector, curvature vector and torsion vector of rational Bézier curves. [Copyright &y& Elsevier]

This paper presents a global optimization operator for arbitrary meshes. The global optimization operator is composed of two main terms, one part is the global Laplacian operator of the mesh which keeps the fairness and another is the constraint condition which reserves the fidelity to the mesh. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Our global mesh optimization approach can be effectively used in at least three applications: smoothing the noisy mesh, improving the simplified mesh, and geometric modeling with subdivision-connectivity. Many experimental results are presented to show the applicability and flexibility of the approach. [Copyright &y& Elsevier]

Abstract: Current methods for recognition and interpretation of architectural drawings are limited to either low-level analysis of paper drawings or interpretation of electronic drawings that depicts only high-level design entities. In this paper, we propose a Self-Incremental Axis-Net-based Hierarchical Recognition (SINEHIR) model for automatic recognition and interpretation of real-life complex electronic construction structural drawings. We design and implement a series of integrated algorithms for recognizing dimensions, coordinate systems and structural components. We tested our approach on more than 200 real-life drawings. The results show that the average recognition rate of structural components is about 90%, and the computation time is significantly shorter than manual estimation time. [Copyright &y& Elsevier]

This paper presents a new interpolation method that enables the construction of C2 cubic polynomial spline curves without solving a global system of equations, while providing slackness/continuity control and convexity preserving ability. The basic idea is to blend a cubic B-spline curve with a singularly parametrized sequence of connected line segments. A global slackness parameter controls the tautness, specifically the distance between the interpolating curve and the linear interpolant. The order of continuity at each knot is controlled via multiple knot insertions so that cusps and straight-line segments can be conveniently prescribed. In addition, a method for selecting local slackness values to produce G1 convexity preserving curve is presented. With the low-degree polynomials and direct computation of control vertices, this local method is computationally simple and is useful for interactive shape design and computer graphics applications. [Copyright &y& Elsevier]

This paper presents an algorithm for reconstructing a triangle mesh surface from a given point cloud. Starting with a seed triangle, the algorithm grows a partially reconstructed triangle mesh by selecting a new point based on an intrinsic property of the point cloud, namely, the sampling uniformity degree. The reconstructed mesh is essentially an approximate minimum-weight triangulation to the point cloud constrained to be on a two-dimensional manifold. Thus, the reconstructed surface has only small topological difference from the surface of the sampled object. Topological correct reconstruction can be guaranteed by adding a post-processing step. [Copyright &y& Elsevier]

Most existing handle-based mesh deformation methods require costly re-computation for every handle set updating, namely, adding or removing of handles on the mesh surface. In this paper, we propose a reduced deformation model that is independent of handle configuration, allowing users to dynamically update the handle set without noticeable waiting time. We represent the deformation space of a mesh as propagation fields defined by only the mesh geometry, independent of the handle set. We define the propagation fields as selected eigenvectors of the Laplacian operator and adopt the transformations of isolines sampled from the fields as the deformation descriptors. In this way, the deformation descriptors are pre-computed before handle specification. During interactive manipulation, constraints generated from the handles are incorporated into the deformation system in real time. Our method therefore supports incremental mesh editing where the user can freely define different handle sets to edit different parts of the shape without waiting for long re-computation. Our reduced model is scalable since the updating time per iteration is independent of the mesh size and the number of handles. We demonstrate the effectiveness of the proposed deformation method and compare its performance with related reduced deformation models. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of constructing a family of surfaces from a given spatial geodesic curve. We derive a parametric representation for a surface pencil whose members share the same geodesic curve as an isoparametric curve. By utilizing the Frenet trihedron frame along the given geodesic, we express the surface pencil as a linear combination of the components of this local coordinate frame, and derive the necessary and sufficient conditions for the coefficients to satisfy both the geodesic and the isoparametric requirements. We illustrate and verify the method by finding exact surface pencil formulations for some simple surfaces, such as surfaces of revolution and ruled surfaces. Finally, we demonstrate the use of this method in a garment design application. [Copyright &y& Elsevier]

In this article, we study the problem of multi-view sketch correspondence, where we take as input multiple freehand sketches with different views of the same object and predict as output the semantic correspondence among the sketches. This problem is challenging since the visual features of corresponding points at different views can be very different. To this end, we take a deep learning approach and learn a novel local sketch descriptor from data. We contribute a training dataset by generating the pixel-level correspondence for the multi-view line drawings synthesized from 3D shapes. To handle the sparsity and ambiguity of sketches, we design a novel multi-branch neural network that integrates a patch-based representation and a multi-scale strategy to learn the pixel-level correspondence among multi-view sketches. We demonstrate the effectiveness of our proposed approach with extensive experiments on hand-drawn sketches and multi-view line drawings rendered from multiple 3D shape datasets. [ABSTRACT FROM AUTHOR]

Videos are an accessible form of media for analyzing sports postures and providing feedback to athletes. Existing sport-specific systems embed bespoke human pose attributes and thus can be hard to scale for new attributes, especially for users without programming experiences. Some systems retain scalability by directly showing the differences between two poses, but they might not clearly visualize the key differences that viewers would like to pursue. Besides, video-based coaching systems often present feedback on the correctness of poses by augmenting videos with visual markers or reference poses. However, previewing and augmenting videos limit the analysis and visualization of human poses due to the fixed viewpoints in videos, which confine the observation of captured human movements and cause ambiguity in the augmented feedback. To address these issues, we study customizable human pose data analysis and visualization in the context of running pose attributes, such as joint angles and step distances. Based on existing literature and a formative study, we have designed and implemented a system, PoseCoach, to provide feedback on running poses for amateurs by comparing the running poses between a novice and an expert. PoseCoach adopts a customizable data analysis model to allow users' controllability in defining pose attributes of their interests through our interface. To avoid the influence of viewpoint differences and provide intuitive feedback, PoseCoach visualizes the pose differences as part-based 3D animations on a human model to imitate the demonstration of a human coach. We conduct a user study to verify our design components and conduct expert interviews to evaluate the usefulness of the system.

In recent years, sparse voxel-based methods have become the state-of-the-arts for 3D semantic segmentation of indoor scenes, thanks to the powerful 3D CNNs. Nevertheless, being oblivious to the underlying geometry, voxel-based methods suffer from ambiguous features on spatially close objects and struggle with handling complex and irregular geometries due to the lack of geodesic information. In view of this, we present Voxel-Mesh Network (VMNet), a novel 3D deep architecture that operates on the voxel and mesh representations leveraging both the Euclidean and geodesic information. Intuitively, the Euclidean information extracted from voxels can offer contextual cues representing interactions between nearby objects, while the geodesic information extracted from meshes can help separate objects that are spatially close but have disconnected surfaces. To incorporate such information from the two domains, we design an intra-domain attentive module for effective feature aggregation and an inter-domain attentive module for adaptive feature fusion. Experimental results validate the effectiveness of VMNet: specifically, on the challenging ScanNet dataset for large-scale segmentation of indoor scenes, it outperforms the state-of-the-art SparseConvNet and MinkowskiNet (74.6% vs 72.5% and 73.6% in mIoU) with a simpler network structure (17M vs 30M and 38M parameters).

Sketches in existing large-scale datasets like the recent QuickDraw collection are often stored in a vector format, with strokes consisting of sequentially sampled points. However, most existing sketch recognition methods rasterize vector sketches as binary images and then adopt image classification techniques. In this article, we propose a novel end-to-end single-branch network architecture RNN-Rasterization-CNN (Sketch-R2CNN for short) to fully leverage the vector format of sketches for recognition. Sketch-R2CNN takes a vector sketch as input and uses an RNN for extracting per-point features in the vector space. We then develop a neural line rasterization module to convert the vector sketch and the per-point features to multi-channel point feature maps, which are subsequently fed to a CNN for extracting convolutional features in the pixel space. Our neural line rasterization module is designed in a differentiable way for end-to-end learning. We perform experiments on existing large-scale sketch recognition datasets and show that the RNN-Rasterization design brings consistent improvement over CNN baselines and that Sketch-R2CNN substantially outperforms the state-of-the-art methods.

Specifying precise relationships among graphic elements is often a time-consuming process with traditional alignment tools. Automatic beautification of roughly designed layouts can provide a more efficient solution but often lead to undesired results due to ambiguity problems. To facilitate ambiguity resolution in layout beautification, we present a novel user interface for visualizing and editing inferred relationships through an automatic global layout beautification process. First, our interface provides a preview of the beautified layout with inferred constraints without directly modifying an input layout. In this way, the user can easily keep refining beautification results by interactively repositioning and/or resizing elements in the input layout. Second, we present a gestural interface for editing automatically inferred constraints by directly interacting with the visualized constraints via simple gestures. Our technique is applicable to both 2D and 3D global layout beautification, supported by efficient system implementation that provides instant user feedback. Our user study validates that our tool is capable of creating, editing, and refining layouts of graphic elements, and is significantly faster than the standard snap-dragging or command-based alignment tools for both 2D and 3D layout tasks.

This paper presents a simple and efficient automatic mesh segmentation algorithm that solely exploits the shape concavity information. The method locates concave creases and seams using a set of concavity-sensitive scalar fields. These fields are computed by solving a Laplacian system with a novel concavity-sensitive weighting scheme. Isolines sampled from the concavity-aware fields naturally gather at concave seams, serving as good cutting boundary candidates. In addition, the fields provide sufficient information allowing efficient evaluation of the candidate cuts. We perform a summarization of all field gradient magnitudes to define a score for each isoline and employ a score-based greedy algorithm to select the best cuts. Extensive experiments and quantitative analysis have shown that the quality of our segmentations are better than or comparable with existing state-of-the-art more complex approaches.

We present a novel knowledge-based system to automatically convert real-life engineering drawings to content-oriented high-level descriptions. The proposed method essentially turns the complex interpretation process into two parts: knowledge representation and knowledge-based interpretation. We propose a new hierarchical descriptor-based knowledge representation method to organize the various types of engineering objects and their complex high-level relations. The descriptors are defined using an Extended Backus Naur Form (EBNF), facilitating modification and maintenance. When interpreting a set of related engineering drawings, the knowledge-based interpretation system first constructs an EBNF-tree from the knowledge representation file, then searches for potential engineering objects guided by a depth-first order of the nodes in the EBNF-tree. Experimental results and comparisons with other interpretation systems demonstrate that our knowledge-based system is accurate and robust for high-level interpretation of complex real-life engineering projects.

The need to examine and manipulate large surface models is commonly found in many science, engineering, and medical applications. On a desktop monitor, however, seeing the whole model in detail is not possible. In this paper, we present a new, interactive Focus+Context method for visualizing large surface models. Our method, based on an energy optimization model, allows the user to magnify an area of interest to see it in detail while deforming the rest of the area without perceivable distortion. The rest of the surface area is essentially shrunk to use as little of the screen space as possible in order to keep the entire model displayed on screen. We demonstrate the efficacy and robustness of our method with a variety of models.

This paper presents a novel basis function, called spherical piecewise constant basis function (SPCBF), for precomputed radiance transfer. SPCBFs have several desirable properties: rotatability, ability to represent all-frequency signals, and support for efficient multiple product. By smartly partitioning the illumination sphere into a set of subregions, and associating each subregion with an SPCBF valued 1 inside the region and 0 elsewhere, we precompute the light coefficients using the resulting SPCBFs. Efficient rotation of the light representation in SPCBFs is achieved by rotating the domain of SPCBFs. We run-time approximate the BRDF and visibility coefficients using the set of SPCBFs for light, possibly rotated, through fast lookup of summed-area-table (SAT) and visibility distance table (VDT), respectively. SPCBFs enable new effects such as object rotation in all-frequency rendering of dynamic scenes and on-the-fly BRDF editing under rotating environment lighting. With graphics hardware acceleration, our method achieves real-time frame rates.

Recently, differential information as local intrinsic feature descriptors has been used for mesh editing. Given certain user input as constraints, a deformed mesh is reconstructed by minimizing the changes in the differential information. Since the differential information is encoded in a global coordinate system, it must somehow be transformed to fit the orientations of details in the deformed surface, otherwise distortion will appear. We observe that visually pleasing deformed meshes should preserve both local parameterization and geometry details. We propose to encode these two types of information in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Both sets of information are nondirectional and nonlinearly dependent on the vertex positions. Thus, we present a novel editing framework that iteratively updates both the primal vertex positions and the dual Laplacian coordinates to progressively reduce distortion in parametrization and geometry. Unlike previous related work, our method can produce visually pleasing deformations with simple user interaction, requiring only the handle positions, not local frames at the handles.