Intrinsic Mesh Simplification

This paper presents a novel simplification method for removing vertices from an intrinsic triangulation corresponding to extrinsic vertices lying on near-developable (i.e., with limited Gaussian curvature) and general surfaces. We greedily process all intrinsic vertices with an absolute Gaussian curvature below a user selected threshold. For each vertex, we repeatedly perform local intrinsic edge flips until the vertex reaches the desired valence (three for internal vertices or two for boundary vertices) such that removal of the vertex and incident edges can be locally performed in the intrinsic triangulation. Each removed vertex's intrinsic location is tracked via (intrinsic) barycentric coordinates that are updated to reflect changes in the intrinsic triangulation. We demonstrate the robustness and effectiveness of our method on the Thingi10k dataset and analyze the effect of the curvature threshold on the solutions of PDEs

Field D* pathfinding in weighted simplicial complexes

Includes abstract.Includes bibliographical references.The development of algorithms to efficiently determine an optimal path through a complex environment is a continuing area of research within Computer Science. When such environments can be represented as a graph, established graph search algorithms, such as Dijkstra’s shortest path and A*, can be used. However, many environments are constructed from a set of regions that do not conform to a discrete graph. The Weighted Region Problem was proposed to address the problem of finding the shortest path through a set of such regions, weighted with values representing the cost of traversing the region. Robust solutions to this problem are computationally expensive since finding shortest paths across a region requires expensive minimisation. Sampling approaches construct graphs by introducing extra points on region edges and connecting them with edges criss-crossing the region. Dijkstra or A* are then applied to compute shortest paths. The connectivity of these graphs is high and such techniques are thus not particularly well suited to environments where the weights and representation frequently change. The Field D* algorithm, by contrast, computes the shortest path across a grid of weighted square cells and has replanning capabilites that cater for environmental changes. However, representing an environment as a weighted grid (an image) is not space-efficient since high resolution is required to produce accurate paths through areas containing features sensitive to noise. In this work, we extend Field D* to weighted simplicial complexes – specifically – triangulations in 2D and tetrahedral meshes in 3D

Space and Time Constrained Task Scheduling for Crowd Simulation

Crowd simulation, through the generation of realistic pedestrian ows and densities, has a great potential as a validation tool for urban planning or design of public buildings. In macroscopic simulations approaches, agents are modelled such as their behaviour mimics human's one in similar situations. As a consequence, realistic macroscopic phenomena are expected to emerge from the sum of all agents decisions. When performing an intended activity, people decisions and behaviour mainly consist in scheduling tasks that compose this activity, planning paths between locations where these tasks should be performed, navigating along the planned paths and performing the scheduled tasks. In this paper, we focus on the task scheduling process. This task scheduling process aims at selecting where, when and in which order several tasks, representing the intended activity, should be performed. The proposed model handles spatial and temporal constraints relating to the environment and to the agent itself. Personal preferences, characterizing the agent, are also taken into account. Produced task schedules are optimized on the long term and exhibit adequate choices of locations and times with respect to the agent intended activity and its environment. We conducted an experiment that shows that our algorithm produces task schedules which are representative of human's ones. Once computed, these task schedules are relaxed and used to drive a microscopic crowd simulation in which observable ows of pedestrians emerge from the scheduled individual activities. Such simulations are easy to produce and do not require the use of a complex decisional model.La simulation de foule, à travers la génération de flux et de densités de piétons réalistes, possède un grand potentiel en tant qu'outil de validation d'aménagements urbains. Les approches microscopiques visent à modéliser des agents virtuels dont le comportement imite celui d'humains se trouvant dans des situations similaires. En conséquence, l'apparition de phénomènes macroscopiques doit résulter de la somme des décisions des agents. Les décisions et comportements des personnes effectuant une activité consistent principalement à ordonnancer les tâches qui constituent cette dernière, planifier des chemins entre les lieux où les tâches doivent être effectuées, naviguer le long de ces chemins et effectuer ces tâches. Dans cet article, nous nous focalisons sur le processus d'ordonnancement de tâches. Ce processus vise à sélectionner où, quand et dans quel ordre des tâches, représentant une activité désirée, doivent être effectuées. Le modèle proposé gère les contraintes temporelles et spatiales associées à l'environnement et à l'agent lui-même ainsi que les préférences personnelles qui caractérisent l'agent. Les ordonnancements de tâches calculés sont optimisés sur la durée et démontrent des choix de lieux et d'horaires en adéquation avec l'activité de l'agent et son environnement. Nous avons effectué une expérience qui a démontré que notre algorithme produit des ordonnancements de tâches représentatifs de ceux effectuées par des humains. Après une phase de relaxation des contraintes temporelles associées à l'ordonnancement, ce dernier est utilisé pour diriger un modèle microscopique de simulation de foule. Des flots et densités de piétons réalistes émergent des activités individuelles. Ces simulations sont aisées à produire et ne nécessitent pas d'utiliser de modèle décisionnel complexe, permettant ainsi de peupler rapidement et de manière réaliste des environnements complexes