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The aim of this paper is to present a new method of approximation of planar data set using only arcs or segments. The first problem we are trying to solve is the following: the CNC machines can work only with simple curves (arcs or…
3D shape generation is a challenging problem due to the high-dimensional output space and complex part configurations of real-world objects. As a result, existing algorithms experience difficulties in accurate generative modeling of 3D…
The significant optical and size benefits of using a curved focal surface for imaging systems have been well studied yet never brought to market for lack of a high-quality, mass-producible, curved image sensor. In this work we demonstrate…
Convolutional neural networks are capable of learning powerful representational spaces, which are necessary for tackling complex learning tasks. However, due to the model capacity required to capture such representations, they are often…
Recent studies show increasing demands and interests in automatically generating layouts, while there is still much room for improving the plausibility and robustness. In this paper, we present a data-driven layout framework without model…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
We show that all non-developable ruled surfaces endowed with Ricci metrics in the three-dimensional Euclidean space may be constructed using curves of constant torsion and its binormal. This allows us to give characterizations of the…
Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict…
We propose a new generative model for layout generation. We generate layouts in three steps. First, we generate the layout elements as nodes in a layout graph. Second, we compute constraints between layout elements as edges in the layout…
Inspired by the seminal result that a graph and an associated rotation system uniquely determine the topology of a closed manifold, we propose a combinatorial method for reconstruction of surfaces from points. Our method constructs a…
Converting quad meshes to smooth manifolds, guided subdivision offers a way to combine the good highlight line distributions of recent G-spline constructions with the refinability of subdivision surfaces. Specifically, we present a C2…
Microrobotics is an attractive area of research as small-scale robots have the potential to improve the precision and dexterity offered by minimally invasive surgeries. One example of such a tool is a pair of micro-surgical scissors that…
Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases, we also address developable surfaces and ruled surfaces. The…
Traditional computer graphics rendering pipeline is designed for procedurally generating 2D quality images from 3D shapes with high performance. The non-differentiability due to discrete operations such as visibility computation makes it…
With the emergence of data-driven approaches in science, there is growing interest in their application to manufacturing, particularly in surface precision engineering. However, generating large datasets required for model training is often…
We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem…
Object shaping by grinding is a crucial industrial process in which a rotating grinding belt removes material. Object-shape transition models are essential to achieving automation by robots; however, learning such a complex model that…
We consider the task of generating realistic 3D shapes, which is useful for a variety of applications such as automatic scene generation and physical simulation. Compared to other 3D representations like voxels and point clouds, meshes are…
Our work aims to estimate the camera motion mounted on the head of a mobile robot or a moving object from RGB-D images in a static scene. The problem of motion estimation is transformed into a nonlinear least squares function. Methods for…
Popular industrial robotic problems such as spray painting and welding require (i) conditioning on free-shape 3D objects and (ii) planning of multiple trajectories to solve the task. Yet, existing solutions make strong assumptions on the…