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Intersection detection between three-dimensional bodies has various applications in computer graphics, video game development, robotics as well as military industries. In some respects, entities do not want to disclose sensitive information…
The \emph{thinness} of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Graphs with thinness at most two include, for example, bipartite convex graphs. Many…
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…
While well-known methods to list the intersections of either a list of segments or a complex polygon aim at achieving optimal time-complexity they often do so at the cost of memory comsumption and complex code. Real-life software…
In the realm of computer-aided design (CAD) software, the intersection of B-spline surfaces stands as a fundamental operation. Despite the extensive history of surface intersection algorithms, the challenge of handling complex intersection…
We introduce an operation that measures the self intersections of paths on a surface. As applications, we give a criterion of the realizability of a generalized Dehn twist, and derive a geometric constraint on the image of the Johnson…
Point-set embeddings and large-angle crossings are two areas of graph drawing that independently have received a lot of attention in the past few years. In this paper, we consider problems in the intersection of these two areas. Given the…
Road intersections data have been used across different geospatial applications and analysis. The road network datasets dating from pre-GIS years are only available in the form of historical printed maps. Before they can be analyzed by a…
This paper proposes an algorithm for clipping line segment against an axis-aligned rectangular window. The conventional algorithms for line segment clipping treat the clipping boundary and/or the line segment to be clipped as line. The…
We derive simplified normal forms for an area-preserving map in a neighbourhood of a degenerate resonant elliptic fixed point. Such fixed points appear in generic two-parameter families of area-preserving maps. We also derive a simplified…
Perception research provides strong evidence in favor of part based representation of shapes in human visual system. Despite considerable differences among different theories in terms of how part boundaries are found, there is substantial…
Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two…
This paper deals with the merging problem of segments of a composite B\'ezier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (P.…
We are interested in geometric approximation by parameterization of two-dimensional multiple-component shapes, in particular when the number of components is a priori unknown. Starting a standard method based on successive shape…
We study the critical points of the solution of second elliptic equations in divergence and diagonal form with a bounded and positive definite coefficient, under the assumption that the statement of the Hopf lemma holds (sign assumptions on…
A simple-triangle graph (also known as a PI graph) is the intersection graph of a family of triangles defined by a point on a horizontal line and an interval on another horizontal line. The recognition problem for simple-triangle graphs was…
We give a recipe to compute the geometric intersection number of an integral lamination with a particular type of integral lamination on an n-times punctured disk. This provides a way to find the geometric intersection number of two…
A polygon C is an intersecting polygon for a set O of objects in the plane if C intersects each object in O, where the polygon includes its interior. We study the problem of computing the minimum-perimeter intersecting polygon and the…
The ability to automatically encircle boundaries with mobile robots is crucial for tasks such as border tracking and object enclosing. Previous research has primarily focused on regular boundaries, often assuming that their geometric…
Given a surface with boundary and some points on its boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on a surface…