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Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…
Shape retrieval and alignment are a promising avenue towards turning 3D scans into lightweight CAD representations that can be used for content creation such as mobile or AR/VR gaming scenarios. Unfortunately, CAD model retrieval is limited…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
Multi-directional 3D printing has the capability of decreasing or eliminating the need for support structures. Recent work proposed a beam-guided search algorithm to find an optimized sequence of plane-clipping, which gives volume…
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…
With the rapid advancement of 3D sensing technologies, obtaining 3D shape information of objects has become increasingly convenient. Lidar technology, with its capability to accurately capture the 3D information of objects at long…
This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high…
We introduce a method to analyze and modify a shape to make it manufacturable for a given additive manufacturing (AM) process. Different AM technologies, process parameters or materials introduce geometric constraints on what is…
Three-dimensional nanoarchitectures are widely used across various areas of physics, including spintronics, photonics, and superconductivity. In this regard, thin curved 3D membranes are especially interesting for applications in nano- and…
Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric…
We develop a heuristic for the density of integer points on affine cubic surfaces. Our heuristic applies to smooth surfaces defined by cubic polynomials that are log K3, but it can also be adjusted to handle singular cubic surfaces. We…
A novel approach for creating tool paths for continuous carbon fiber-reinforced thermoplastic 3D printing is introduced. The aim is to enable load-bearing connections while avoiding non-manufacturable crossings of paths by generating layer…
Geometric calibration of cameras and projectors is an essential step that must be performed before any imaging system can be used. There are many well-known geometric calibration methods for calibrating systems comprised of multiple…
In these days, 3D-printer is on the rise in various fields including radiation therapy. This preliminary study aimed to estimate the dose characteristics of the 3D-printer materials which could be used as the compensator or immobilizer in…
This paper validates 3D simulation results of electron beam melting (EBM) processes comparing experimental and numerical data. The physical setup is presented which is discretized by a three dimensional (3D) thermal lattice Boltzmann method…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
Image editing and compositing have become ubiquitous in entertainment, from digital art to AR and VR experiences. To produce beautiful composites, the camera needs to be geometrically calibrated, which can be tedious and requires a physical…
Humans perceive and construct the surrounding world as an arrangement of simple parametric models. In particular, man-made environments commonly consist of volumetric primitives such as cuboids or cylinders. Inferring these primitives is an…
In this paper we consider Hugelschaffer cubic curves which are generated using appropriate geometric constructions. The main result of this work is the mode of explicitly calculating the area of the egg-shaped part of the cubic curve using…
Additive manufacturing is a process that has facilitated the cost effective production of complicated designs. Objects fabricated via additive manufacturing technologies often suffer from dimensional accuracy issues and other part specific…