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The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…
In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…
Given two curves in $\PP^3$, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the…
Direct B-Rep generation is increasingly important in CAD workflows, eliminating costly modeling sequence data and supporting complex features. A key challenge is modeling joint distribution of the misaligned geometry and topology. Existing…
B-splines are widely used in the fields of reverse engineering and computer-aided design, due to their superior properties. Traditional B-spline surface interpolation algorithms usually assume regularity of the data distribution. In this…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
Robotic surgical subtask automation has the potential to reduce the per-patient workload of human surgeons. There are a variety of surgical subtasks that require geometric information of subsurface anatomy, such as the location of tumors,…
Most autonomous cars rely on the availability of high-definition (HD) maps. Current research aims to address this constraint by directly predicting HD map elements from onboard sensors and reasoning about the relationships between the…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
Mapping is an important part of many robotic applications. In order to measure the performance of the mapping process we have to measure the quality of its result: the map. The map is essential for robotic algorithms like localization and…
This paper is devoted to presenting a new approach to determine the intersection of two quadrics based on the detailed analysis of its projection in the plane (the so called cutcurve) allowing to perform the corresponding lifting correctly.…
Maps are arguably one of the most fundamental concepts used to define and operate on manifold surfaces in differentiable geometry. Accordingly, in geometry processing, maps are ubiquitous and are used in many core applications, such as…
Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have different degrees. We describe a simple algorithmic construction of a set of basis functions for the space of multi-degree splines, with similar…
The problem of computing saddle points is important in certain problems in numerical partial differential equations and computational chemistry, and is often solved numerically by a minimization problem over a set of mountain passes. We…
Continuous formulations of trajectory planning problems have two main benefits. First, constraints are guaranteed to be satisfied at all times. Secondly, dynamic obstacles can be naturally considered with time. This paper introduces a novel…
The problem of finding a path between two points while avoiding obstacles is critical in robotic path planning. We focus on the feasibility problem: determining whether such a path exists. We model the robot as a query-specific rectangular…
Mapper algorithm can be used to build graph-based representations of high-dimensional data capturing structurally interesting features such as loops, flares or clusters. The graph can be further annotated with additional colouring of…
Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…
A numerical algorithm to compute the topological entropy of multimodal maps is proposed. This algorithm results from a closed formula containing the so-called min-max symbols, which are closely related to the kneading symbols. Furthermore,…
The geometric intersection number of a curve on a surface is the minimal number of self-intersections of any homotopic curve, i.e. of any curve obtained by continuous deformation. Given a curve $c$ represented by a closed walk of length at…