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...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
IEEE
2021-01-01
|
Series: | IEEE Access |
Subjects: | |
Online Access: | https://ieeexplore.ieee.org/document/9409150/ |
_version_ | 1828112057860358144 |
---|---|
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. |
first_indexed | 2024-04-11T11:44:39Z |
format | Article |
id | doaj.art-97b9f42b58bd402ea3fd2b78a1e62a09 |
institution | Directory Open Access Journal |
issn | 2169-3536 |
language | English |
last_indexed | 2024-04-11T11:44:39Z |
publishDate | 2021-01-01 |
publisher | IEEE |
record_format | Article |
series | IEEE Access |
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/ |
work_keys_str_mv | AT haiyanyu anewapproachtoanalyzinginteractionsoftwoobjectsinspacebasedonaspeciallytailoredlocalcoordinatesystem AT yuanjunhe anewapproachtoanalyzinginteractionsoftwoobjectsinspacebasedonaspeciallytailoredlocalcoordinatesystem AT wenjunzhang anewapproachtoanalyzinginteractionsoftwoobjectsinspacebasedonaspeciallytailoredlocalcoordinatesystem AT haiyanyu newapproachtoanalyzinginteractionsoftwoobjectsinspacebasedonaspeciallytailoredlocalcoordinatesystem AT yuanjunhe newapproachtoanalyzinginteractionsoftwoobjectsinspacebasedonaspeciallytailoredlocalcoordinatesystem AT wenjunzhang newapproachtoanalyzinginteractionsoftwoobjectsinspacebasedonaspeciallytailoredlocalcoordinatesystem |