A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially- Tailored Local Coordinate System

Conventionally, geometric computing problems are treated as algebraic computing problems by representing a geometric object in a global reference coordinate system. This approach has two problems. The first problem is that the intuitive view of the interaction of objects is lost, and the second prob...

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Main Authors: Haiyan Yu, Yuanjun He, Wenjun Zhang
Format: Article
Language:English
Published: IEEE 2021-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/9409150/
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author Haiyan Yu
Yuanjun He
Wenjun Zhang
author_facet Haiyan Yu
Yuanjun He
Wenjun Zhang
author_sort Haiyan Yu
collection DOAJ
description Conventionally, geometric computing problems are treated as algebraic computing problems by representing a geometric object in a global reference coordinate system. This approach has two problems. The first problem is that the intuitive view of the interaction of objects is lost, and the second problem is that algebraic computing is prone to errors for degenerated cases related to the interaction of (e.g., notable case of “divided by zero”). In this paper, we propose a new approach to geometric computing especially to analyze the interaction of two objects (e.g., two triangles). The main idea behind this new approach is a specially-tailored local coordinate system for two interacting objects is defined, which makes the projection of the objects on this local coordinate system represent the true geometry of the objects. This idea significantly departs from the conventional approach which is primarily based on the concept of the global coordinate system. Three examples are provided to illustrate the effectiveness of the proposed approach. Among them, one example is related to the robustness of methods for analyzing the relations of two interacting objects, which is still an open issue in the field of geometric computing and suggests that the proposed approach could have some benefit to robustness in analysis.
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spelling doaj.art-97b9f42b58bd402ea3fd2b78a1e62a092022-12-22T04:25:40ZengIEEEIEEE Access2169-35362021-01-019602586026410.1109/ACCESS.2021.30745099409150A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially- Tailored Local Coordinate SystemHaiyan Yu0https://orcid.org/0000-0001-9707-5225Yuanjun He1Wenjun Zhang2https://orcid.org/0000-0001-7973-8769College of Mechanical Engineering, Donghua University, Shanghai, ChinaDepartment of Computer Science, Shanghai Jiaotong University, Shanghai, ChinaDepartment of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK, CanadaConventionally, geometric computing problems are treated as algebraic computing problems by representing a geometric object in a global reference coordinate system. This approach has two problems. The first problem is that the intuitive view of the interaction of objects is lost, and the second problem is that algebraic computing is prone to errors for degenerated cases related to the interaction of (e.g., notable case of “divided by zero”). In this paper, we propose a new approach to geometric computing especially to analyze the interaction of two objects (e.g., two triangles). The main idea behind this new approach is a specially-tailored local coordinate system for two interacting objects is defined, which makes the projection of the objects on this local coordinate system represent the true geometry of the objects. This idea significantly departs from the conventional approach which is primarily based on the concept of the global coordinate system. Three examples are provided to illustrate the effectiveness of the proposed approach. Among them, one example is related to the robustness of methods for analyzing the relations of two interacting objects, which is still an open issue in the field of geometric computing and suggests that the proposed approach could have some benefit to robustness in analysis.https://ieeexplore.ieee.org/document/9409150/Geometric computinggeometric methoddimension reductionprojectiongeometric transformation
spellingShingle Haiyan Yu
Yuanjun He
Wenjun Zhang
A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially- Tailored Local Coordinate System
IEEE Access
Geometric computing
geometric method
dimension reduction
projection
geometric transformation
title A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially- Tailored Local Coordinate System
title_full A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially- Tailored Local Coordinate System
title_fullStr A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially- Tailored Local Coordinate System
title_full_unstemmed A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially- Tailored Local Coordinate System
title_short A New Approach to Analyzing Interactions of Two Objects in Space Based on a Specially- Tailored Local Coordinate System
title_sort new approach to analyzing interactions of two objects in space based on a specially tailored local coordinate system
topic Geometric computing
geometric method
dimension reduction
projection
geometric transformation
url https://ieeexplore.ieee.org/document/9409150/
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