For well-composed (manifold) objects in the 3D cubical grid, the Euler characteristic is equal to half of the Euler characteristic of the object boundary, which in turn is equal to the number of boundary vertices minus the number of boundary faces. We extend this formula to arbitrary objects, not necessarily well-composed, by adjusting the count of boundary cells both for vertex- and for face-adjacency

In this paper, we present a technique that maps 2D plots to a spherical surface. We project 2D plots as large as possible while minimizing distortions. To accomplish this projection, we employ elliptical grid mapping, which maps points on a cube to those on a sphere. To determine the largest projection from points on the 2D plot to the cube, we find the largest projection inside an unfolded cube pattern

Using barycentric coordinates for thickness interpolation, we present a novel polygonal skeleton based convolution surface approximation method with varying radii. Given the prescribed radii of an arbitrary planar polygonal skeleton, we first employ a smooth interior mean value coordinate interpolation approach to calculate the thickness at each projection position in the polygonal plane. Then a local

3D object reconstruction from single view image is a challenge task. Due to the fact that the information contained in one isolated image is not sufficient for reasonable 3D shape reconstruction, the existing methods on single-view 3D reconstruction always lack marginal voxels and miss obvious semantic information. To tackle these problem, we propose Semantic Autoencoder-Attention Network (SAAN) for

Traffic simulation has become an efficient tool, with the assistance of computer visualizing techniques, to solve traffic issues such as traffic congestion, network design, and similar problems. Properly controlling simulated traffic flow and modeling each vehicle’s irregular behaviors are key issues in the traffic simulation field. In this paper, we introduce real vehicle trajectories as a data-driven

Generalization of 2D city layouts is a relevant operation common to Computer Graphics and GIS, whose goal is to generate simplified representations of street networks. However, most of the contributions in this area belong to the GIS literature, which we intend to bring closer to the CG community. In this paper we propose a threefold characterization of the algorithms dedicated to generic generalization

A surface of revolution with moving axes and angles is a rational tensor product surface generated from two rational space curves by rotating one curve (the directrix) around vectors and angles generated by the other curve (the director). Here we introduce these new kinds of rational generalized surfaces of revolution, provide some interesting examples, and investigate their algebraic and geometric

In this paper, a non-stationary Catmull–Clark subdivision scheme is presented which enables the user to change the shape of the surface obtained from a given initial mesh. Such a non-stationary subdivision scheme is constructed by taking tensor product of a properly modified cubic exponential B-spline scheme in the regular mesh and giving suitable rules in the neighborhoods of extraordinary points

The geometry image representation is a remeshing of an irregular triangle surface mesh onto a rectangular grid of points and facilitates the processing of surface geometry. Its connectivity is commonly generated by splitting each rectangular quad of grid points along the shorter diagonal. However, this simple approach typically yields skinny triangles on the surface when the underlying local surface

This paper presents a subdivision scheme for unstructured quadrilateral meshes with improved convergence rates in extraordinary regions for isogeometric analysis compared with that of Catmull–Clark and related tuned subdivision schemes. The new subdivision stencils are first constructed to ensure C1 continuity with bounded curvature at extraordinary positions. The eigenbasis functions corresponding

This paper deals with some techniques that can be used to improve quality and geometric consistency of data driven 3D city models. It focuses on two practical tasks with respect to roof polygons: finding better edges and planarization. To increase the quality of edges, models are merged with true orthophotos and cadastral data. With mixed integer linear programs, the number of right angles and symmetry

Analysis-suitable T-splines form a practically useful subset of T-splines. They maintain the design flexibility of T-splines with an efficient and highly localized refinement capability, while preserving the important analysis-suitable mathematical properties of the NURBS basis. The present paper proposes a new evaluation algorithm for analysis-suitable T-splines. The algorithm is based on the control

We present a curve-skeleton extraction method in the form of curve-skeleton transfer from the source shape to the target. The shapes we deal with need to be in correspondence. They are discretized as meshes embedded in 3D and are not necessarily watertight. They can even be in arbitrary topology, and furthermore be disconnected point clouds. Our method associates the source skeleton with the source

Relightable images have been widely used as a valuable tool in Cultural Heritage (CH) artifacts, including coins, bas-reliefs, paintings, and epigraphs. Reflection Transformation Imaging (RTI), a commonly used type of relightable images, consists of a per-pixel function which encodes the reflection behavior, estimated from a set of digital photographs acquired from a fixed view. Web visualisation tools

The use of Building Information Modeling (BIM) for Facility Management (FM) in the Operation and Maintenance (O&M) stages of the building life-cycle is intended to bridge the gap between operations and digital data, but lacks the functionality of assessing the state of the built environment due to non-automated generation of associated semantics. 3D point clouds can be used to capture the physical

In this paper, we focus on the two tasks of 3D shape abstraction and semantic analysis. This is in contrast to current methods, which focus solely on either 3D shape abstraction or semantic analysis. In addition, previous methods have had difficulty producing instance-level semantic results, which has limited their application. We present a novel method for the joint estimation of a 3D shape abstraction

3D model deformation has been an active research topic in geometric processing. Due to its efficiency, linear blend skinning (LBS) and its follow-up methods are widely used in practical applications as an efficient method for deforming vector images, geometric models and animated characters. LBS needs to determine the control handles and specify their influence weights, which requires expertise and

3D point cloud technology facilitates the automated and highly detailed acquisition of real-world environments such as assets, sites, and countries. We present a web-based system for the interactive exploration and inspection of arbitrary large 3D point clouds. Our approach is able to render 3D point clouds with billions of points using spatial data structures and level-of-detail representations. Point-based

In 3D printing, it is critical to use as few as possible supporting materials for efficiency and material saving. Multiple model decomposition methods and multi-DOF (degrees of freedom) 3D printers have been developed to address this issue. However, most systems utilize model decomposition and multi-DOF independently. Only a few existing approaches combine the two, i.e. partitioning the models for

Physics-based skin deformation methods can greatly improve the realism of character animation, but require non-trivial training, intensive manual intervention, and heavy numerical calculations. Due to these limitations, it is generally time-consuming to implement them, and difficult to achieve a high runtime efficiency. In order to tackle the above limitations caused by numerical calculations of physics-based

This paper presents a deep CNN approach for point-based semantic scene labeling. This is challenging because 3D point clouds do not have a canonical domain and can have complex geometry and substantial variation of sampling densities. We propose a novel framework where the convolution operator is defined on depth maps around sampled points, which captures characteristics of local surface regions. We

Registration and visualization of surfaces play a significant role in the engineering and medical fields. Especially in virtual colonoscopy (VC), an efficient and robust registration method between supine and prone computed tomography (CT) scans is highly desirable, due to the fact that it helps improve polyp detection rates. However, supine and prone colon registration is still a challenging task

In this paper we propose a single image-based 3D model retrieval and pose estimation method for indoor scenes. By simulating the scene context of the input image, our method is able to handle several challenging scenarios featuring cluttered backgrounds and severe occlusions. To use our system, the user only needs to drag a few semantic bounding boxes for the query objects. The proposed approach then

In this paper we introduce a 2D convolutional neural network (CNN) which exploits the additive depth map, a minimal representation of volume, for reconstructing occluded portions of objects captured using commodity depth sensors. The additive depth map represents the amount of depth needed to transform the input into the “back” depth map taken with a sensor exactly opposite of the input camera. A union

Generating natural textures is a challenging task in graphics and virtual reality. Leaf texture is an important part of natural textures. Different from many other textures with repetitive and random patterns, leaves are closely related to its botanic structures, especially veins. Appearing in forms of foliages in the wild, the variety of leaf textures produces the realism of virtual scenes. In this

Liquid-solid interaction produces a characteristic sound which is different from the sound of bubbly water flows. This paper explores liquid-solid interaction sound (LSIS) synthesis. The resulting LSIS consists of two components: bubble sound and impact sound, which corresponding to liquid-liquid collision and liquid-solid collision, respectively. To improve the quality of LSIS, we propose a novel

This paper presents an architecture for large-scale distributed AR services and an experimental evaluation of the main component – Semantic Augmented Reality Middleware. The architecture is based on a client-server design, which supports semantic modeling and building contextual AR presentations for a large number of users. The architecture is based on the Service Oriented Architecture (SOA) paradigm

Most of the methods for digital bas-reliefs modeling are based on images or 3D models. In this paper, we propose a novel approach to construct bas-reliefs surface with isogeometric analysis from sketch curves provided by the users. Our modeling system allows the users to input the boundary sketch of a planar domain and the feature constraints of bas-relief surface, then the bas-relief is generated

In this paper, we establish the connection between exponential representation of curve (surface) and the classical linear differential system. That is, a curve (surface) can be described by a vector-valued function X(t)=eAtX0(t) (X(s,t)=eAtX0(s,t)), which can be viewed as a solution of the ordinary (partial) linear differential system X˙(t)=AX(t)+f(t) (∂X(s,t)∂t=AX(s,t)+f(s,t)). Further, we propose

We extend the gradient mesh vector graphics primitive with procedural noise functions. Specifically, we couple Perlin, Worley and Gabor noise to the gradient mesh. We allow local parameters controlling the noise functions to be defined at the vertices of the mesh. The parameters are interpolated along with the geometry similarly to how colour is interpolated in an ordinary gradient mesh, allowing for

We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial complexes, and we define an efficient encoding for the discrete Morse gradient on the most compact of such representations. We theoretically compare methods based on reductions

This paper presents how freeform surface properties can be estimated through bounding, rather than sampling. Bounding surface positions using the control mesh, and bounding surface normals using normal cones, are both well known procedures. In this paper, we add to these, a procedure to bound the normal curvature values of a surface. We then show how collision free 5-axis tool-paths for CNC machining

Graphs are widely used to conceptually represent objects and their relations in several applications. Time-evolving graphs, usually referred to as temporal or dynamic graphs, have been used to encode how objects and their relations change over time. In this paper, we introduce a new image-based representation, named Graph Visual Rhythm (GVR), proposed to encode visually temporal network changes. GVR