Geometrically smooth spline surfaces, generalized to include n-sided facets or configurations of n≠4 quads, can exhibit a curious lack of additional degrees of freedom for modeling or engineering analysis when refined. This paper establishes a minimal polynomial degree for smooth constructions of multi-sided surfaces that guarantees more flexibility in all directions under refinement. Degree bi-4 is

Most previous methods of bas-relief generation run slow, or require tuning several important parameters. These issues seriously reduce the efficiency of bas-relief modeling. We introduce a fast generation method for high-quality bas-reliefs from 3D objects based on a deep learning technique. Unlike neural networks for image tasks, the proposed network for reliefs (ReliefNet) is elaborately designed

This paper introduces a flexible and easy to use method for designing complex composite heterogeneous materials. These materials feature two distinct phases called core and matrix that remain separate and distinct. Moreover, composite materials have an internal microarchitecture that have to be precisely modeled. All the microarchitecture examples that are shown in this paper have been modeled in the

Additive manufacturing processes enable the fabrication of the material with multiscale complexities. However, to efficiently model the material compositions and microstructures on multiple design scales is an issue for most existing heterogeneous object modeling methods. To solve this problem, a universal material template and its associated heterogeneous object model are developed in this paper.

The present research develops a direct multiscale topology optimization method for additive manufacturing (AM) of coated structures with nonperiodic infill by employing an adaptive mapping technique of adaptive geometric components (AGCs). The AGCs consist of a framework of macro-sandwich bars that represent the macrostructure with the solid coating and a network of micro-solid bars that represent

2.5D processes are ubiquitous in pocket machining of structural parts as well as layer based additive manufacturing. Modern manufacturing systems are mostly integrated with high-speed motion capacity, which conventionally generated tool path cannot fully exploit due to large path stepover variation and sharp turnings at degenerated corners. Advanced geometric approaches strived to increase the local

In this paper, we propose a normal estimation method for unstructured 3D point clouds. In this method, a feature constraint mechanism called Local Plane Features Constraint (LPFC) is used and then a multi-scale selection strategy is introduced. The LPFC can be used in a single-scale point network architecture for a more stable normal estimation of the unstructured 3D point clouds. In particular, it

A field (2-parameter family of similarities) S(x,y) is Tran-Similar (TS) if there exist similarities U and V such that S(x,y)=Ux⋅Vy and U⋅V=V⋅U. The recently proposed COTS map, M, is defined in terms of a planar TS field, S, as M(x,y)=S(x,y)⋅A and is Corner-Operated (CO), i.e., controlled by the images A, B, C, and D of the four corners of the unit-square in parameter space. The CO property enables

In pattern design of a 3D plush toy model, the key task is to draw seam lines on the 3D surface to divide it into surface patches to obtain 2D patterns. However, how to draw seam lines requires a lot of professional knowledge and skills of pattern design. In this paper, we present a new method that can guide and assist users to create 2D patterns of a 3D toy model efficiently. Based on a component-based

Describing data, obtained by various instruments, with an analytic function is one of the tasks that people often face in a wide variety of applications such as virtual reality, CAD design, reverse engineering, data visualization, medical imaging, and cultural relic restoration and so on. Moreover, non-uniform B-spline is an extensively-used tool for interpolation which is an effective means of describing

Functionally graded conformal lattice structures (FGCLSs) are a particular type of lattice structure in which lattice unit cells are populated following structural boundaries and the density of the lattice unit cells is optimally distributed. Additionally, additively manufactured parts are reported to have anisotropic mechanical properties that highly depend on the part build orientations. This is

The parametrization of triangle meshes, in particular by means of computing a map onto the plane, is a key operation in computer graphics. Typically, a piecewise linear setting is assumed, i.e., the map is linear per triangle. We present a method for the efficient computation and optimization of piecewise nonlinear parametrizations, with higher-order polynomial maps per triangle. We describe how recent

We present a novel curvature-aware modeling technique for interactively designing shapes. The basic principle we used is that an intrinsic metric of a mesh determines the Euclidean edge lengths and the angles, thereby defining the Laplacian matrix. Hence central to our approach is a metric first algorithm that interactively reconstructs a shape for matching the prescribed curvatures. Given Gaussian

Designing the layouts and simulating the assembly of cables are based on flexible cable modeling technology. In this paper, we review the methods used to model deformable cable-like objects. At present, the physical models of one-dimensional cable-like flexible objects are mostly elastic. There are different types of models, which we can classify as mass–spring, multi-body, elastic rod, dynamic spline