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This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
In practical applications, effectively segmenting cracks in large-scale computed tomography (CT) images holds significant importance for understanding the structural integrity of materials. Classical image-processing techniques and modern…
This contribution presents a brief survey of clipping and intersection algorithms in E2 and E3 with a nearly complete list of relevant references. Some algorithms use the projective extension of the Euclidean space and vector-vector…
We develop data structures for intersection queries in four dimensions that involve segments, triangles and tetrahedra. Specifically, we study three main problems: (i) Preprocess a set of $n$ tetrahedra in $\reals^4$ into a data structure…
These notes accompany the open-source code published in GitHub which implements a GPU-based line-segment, surface-triangle intersection algorithm in CUDA. It mentions some relevant works and discusses issues specific to this implementation.…
Ruled surface is widely used in engineering design such as parting surface design of injection mold and checking surface design of checking fixture, which are usually generated by offsetting 3D curves. However, in 3D curve offset, there…
We revisit the algorithmic problem of finding a triangle in a graph (\textsc{Triangle Detection}), and examine its relation to other problems such as \textsc{3Sum}, \textsc{Independent Set}, and \textsc{Graph Coloring}. We obtain several…
Recent advances in the area of plane segmentation from single RGB images show strong accuracy improvements and now allow a reliable segmentation of indoor scenes into planes. Nonetheless, fine-grained details of these segmentation masks are…
We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When cutting away a region from a solid piece of material -- such as steel, wood, ceramics, or plastic -- using a rough tool in a…
We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of…
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…
We introduce a fast, high-precision algorithm for calculating intersections between great circle arcs and lines of constant latitude on the unit sphere. We first propose a simplified intersection point formula with improved speed and…
In this work, we present a workspace-based planning framework, which though using redundant workspace key-points to represent robot states, can take advantage of the interpretable geometric information to derive good quality collision-free…
Segmentation of overlapping convex objects has various applications, for example, in nanoparticles and cell imaging. Often the segmentation method has to rely purely on edges between the background and foreground making the analyzed images…
Concrete is the standard construction material for buildings, bridges, and roads. As safety plays a central role in the design, monitoring, and maintenance of such constructions, it is important to understand the cracking behavior of…
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…
A complete treatment of the intersections of two geodesics on the surface of an ellipsoid of revolution is given. With a suitable metric for the distances between intersections, bounds are placed on their spacing. This leads to fast and…
The incircle of a triangle touches the sides of the triangle in three points. It is well known that the lines from these points to the opposite vertices meet at a point known as the Gergonne point of the triangle. We use a computer to…
We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a line segment, a…
Recently, reconstructing scenes from a single panoramic image using advanced 3D Gaussian Splatting (3DGS) techniques has attracted growing interest. Panoramic images offer a 360$\times$ 180 field of view (FoV), capturing the entire scene in…