Geometrical and Topological Issues in NMT-Based Modeling

1992 ◽  
Author(s):  
Mukul Saxena ◽  
Rajan Srivatsan ◽  
Jonathan E. Davis
Keyword(s):  
Data Structure ◽  
Geometric Modeling ◽  
Modeling Environment ◽  
Insertion Algorithm ◽  
The Face ◽  
Euler Operators ◽  
Application Specific ◽  
Model Topology

Abstract The Non-Manifold Topology (NMT) Radial Edge data structure, along with the supporting set of Euler operators, provides a versatile environment for modeling non-manifold domains. The operators provide the basic tools to construct and manipulate model topology. However, an implementation of the base functionality in a geometric modeling environment raises some geometry-related issues that need to be addressed to ensure the topological validity of the underlying model. This paper focuses on those issues and emphasizes the use of geometry in the implementation of topological operators. Enhancements to the topology manipulation operations are also discussed. Specifically, this paper describes (i) a geometry-based algorithm for face insertion within the Radial Edge data structure, (ii) a manifestation of the face-insertion algorithm to resolve topological ambiguities that arise in the design of topological glue operators, and (iii) enhancements to the topology deletion operators to meet application-specific requirements.

IMPLICIT POINT LOCATION IN ARRANGEMENTS OF LINE SEGMENTS, WITH AN APPLICATION TO MOTION PLANNING

1994 ◽  
Vol 04 (04) ◽  
pp. 369-383
Author(s):  
PANKAJ K. AGARWAL ◽  
MARC VAN KREVELD
Keyword(s):  
Data Structure ◽  
Motion Planning ◽  
Location Problem ◽  
Translational Motion ◽  
Planning Problem ◽  
Final Position ◽  
Point Location ◽  
Line Segments ◽  
Planar Region ◽  
The Face

Let [Formula: see text] be a set of n (possibly intersecting) line segments in the plane. We show that the arrangement of [Formula: see text] can be stored implicitly in a data structure of size O(n log 2n) so that the following query can be answered in time O(n1/2 log 2 n): Given two query points, determine whether they lie in the same face of the arrangement of S and, if so, return a path between them that lies within the face. This version of the implicit point location problem is motivated by the following motion planning problem: Given a polygonal robot R with m vertices and a planar region bounded by polygonal obstacles with n vertices in total, preprocess them into a data structure so that, given initial and final positions of R, one can quickly determine whether there exists a continuous collision-free translational motion of R from the initial to the final position. We show that such a query can be answered in time O((mn)1/2 log 2 mn) using O(mn log 2 mn) storage.

scholarly journals High-performance simplification of triangular surfaces using a GPU

PLoS ONE ◽  
2021 ◽  
Vol 16 (8) ◽  
pp. e0255832
Author(s):  
Mohamed H. Mousa ◽  
Mohamed K. Hussein
Keyword(s):  
Data Structure ◽  
High Performance Computing ◽  
Geometric Modeling ◽  
High Performance ◽  
Priority Queue ◽  
Mesh Simplification ◽  
Strong Impact ◽  
Topological Properties ◽  
Dynamic Memory ◽  
Performance Computing

Due to advances in high-performance computing technologies, computer graphics techniques—especially those related to mesh simplification—have been noticeably improved. These techniques, which have a strong impact on many applications, such as geometric modeling and visualization, have been well studied for more than two decades. Recent advances in GPUs have led to significant improvements in terms of speed and interactivity. In this paper, we present a mesh simplification algorithm that benefits from the parallel framework provided by recent GPUs. We customize the halfedge data structure for adaption with the dynamic memory restrictions of CUDA. The proposed algorithm is fully parallelized by employing a lock-free skip priority queue and a set of disjoint regions of the mesh. The proposed technique accelerates the simplification process while preserving the topological properties of the mesh. Some results and comparisons are provided to verify the efficiency of the proposed algorithm.

A comparison of the cognitive actions of designers in geometry-based and parametric design environments

2020 ◽  
Vol 45 (1/2) ◽  
pp. 87-101 ◽  
Author(s):  
Çetin Tünger ◽  
Şule Taşlı Pektaş
Keyword(s):  
Geometric Modeling ◽  
Parametric Design ◽  
Design Tool ◽  
Content Type ◽  
Cognitive Behaviors ◽  
Design Environments ◽  
Modeling Environment ◽  
Design Alternatives ◽  
Cognitive Actions ◽  
Alternative Designs

Purpose This paper aims to compare designers’ cognitive behaviors in geometry-based modeling environments (GMEs) and parametric design environments (PDEs). Design/methodology/approach This study used Rhinoceros as the geometric and Grasshopper as the parametric design tool in an experimental setting. Designers’ cognitive behaviors were investigated by using the retrospective protocol analysis method with a content-oriented approach. Findings The results indicated that the participants performed more cognitive actions per minute in the PDE because of the extra algorithmic space that such environments include. On the other hand, the students viewed their designs more and focused more on product–user relation in the geometric modeling environment. While the students followed a top-down process and produced less number of topologically different design alternatives with the parametric design tool, they had more goal setting activities and higher number of alternative designs in the geometric modeling environment. Originality/value This study indicates that cognitive behaviors of designers in GMEs and PDEs differ significantly and these differences entail further attention from researchers and educators.

Physical Modeling of Mechanical Objects of Constrained Movement

1997 ◽  
Author(s):  
Imre Horváth ◽  
György Kuczogi
Keyword(s):  
Physical Modeling ◽  
Geometric Modeling ◽  
Moving Objects ◽  
Computational Method ◽  
Arbitrary Sequence ◽  
Mechanical Equipment ◽  
Integrated Simulation ◽  
Modeling Environment ◽  
Multiple Collisions ◽  
Mechanical Objects

Abstract Presented is a computational method for physical modeling of mechanical objects of constrained movement. In a physical modeling environment, an object’s behavior is modeled as it is implied by its geometry and substance, and the appearing physical (mechanical, thermal, and other) phenomena. The developed software is able to describe various forms of movement of a rigid object, configure obstacles in the space, check for collisions of the moving object with the obstacles, and compute post-collision trajectories of the object. The motivation for the background research is an industrial problem, namely, spatial positioning of moving objects without using extra energy. The novelty of this work is in (a) the interactive definition of constituents of the modeling environment, (b) the integrated simulation of an arbitrary sequence of spatial movements and multiple collisions, and (c) the applicability to preliminary design of mechanical equipment. The process of physical modeling has been implemented in six phases: (a) geometric modeling and determination of the substantial attributes of the object, (b) computing of the pre-defined movements, (c) specification and positioning obstacles in the space, (d) checking for single and multiple collisions, (e) computing of post-collision movements, and (f) controlling of multiple and repeated events. Among others, the developed software is able to compute compound movements in the space and any sequence of eccentric collisions with four types of obstacles.

Face-based data structure and its application to robust geometric modeling

1995 ◽  
Author(s):  
Masatake Higashi ◽  
Fuyuki Torihara ◽  
Nobuhiro Takeuchi ◽  
Toshio Sata ◽  
Tsuyoshi Saitoh ◽  
...  
Keyword(s):  
Data Structure ◽  
Geometric Modeling

scholarly journals Towards the suppression of blend chains using Euler operators and open geometric modeling kernel

2019 ◽  
Author(s):  
Сергей Сляднев ◽  
Sergey Slyadnev ◽  
Вадим Турлапов ◽  
Vadim Turlapov
Keyword(s):  
Geometric Modeling ◽  
Boundary Representation ◽  
Batch Mode ◽  
Topology Analysis ◽  
Adjacency Graph ◽  
Essential Properties ◽  
A Chain ◽  
Euler Operators ◽  
Two Stages ◽  
Local Topology

This paper presents a CAD model simplification procedure which consists of recognition and suppression of certain types of blend chains. The proposed method involves Euler operators KEV, KEF, and KFMV, which are developed on top of open-sourced geometric modeling kernel. The simplification process employs two stages: recognition and suppression. The suppression stage ensures the geometric and topological validity of the simplification result. The present approach is targeted for use in a batch mode, which poses strict requirements to the robustness of the suppression algorithm. The essential properties of the presented approach are its sustainability, the predictability of the result and the extensible architecture, which allows for adding new topological cases without affecting the algorithm’s core. At the recognition stage, the algorithm constructs an attributed adjacency graph, which is then enriched with such information as edges’ types, their properties, and the assumed kinds of blend faces. At the suppression stage, the algorithm iterates the adjacency graph and composes the blend candidate faces into the chains. For each face in a chain, a local topology analysis is performed to determine the corresponding sequence of Euler operators which are supposed to eliminate that face. The algorithm allows for extensions through adding descriptors of the new topology situations into the processing. After the Euler operators are done, the affected edges are reconstructed to obtain a watertight boundary representation of the model.

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