Efficient object location determination and error analysis based on barycentric coordinates
Abstract In this paper, we propose an efficient computational method for converting local coordinates to world coordinates using specially structured coordinate data. The problem in question is the computation of world coordinates of an object throughout a motion, assuming that we only know the chan...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-07-01
|
| Series: | Visual Computing for Industry, Biomedicine, and Art |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s42492-020-00052-y |
| _version_ | 1818333776502063104 |
|---|---|
| author | Andrea Bodonyi Roland Kunkli |
| author_facet | Andrea Bodonyi Roland Kunkli |
| author_sort | Andrea Bodonyi |
| collection | DOAJ |
| description | Abstract In this paper, we propose an efficient computational method for converting local coordinates to world coordinates using specially structured coordinate data. The problem in question is the computation of world coordinates of an object throughout a motion, assuming that we only know the changing coordinates of some fixed surrounding reference points in the local coordinate system of the object. The proposed method is based on barycentric coordinates; by taking the aforementioned static positions as the vertices of a polyhedron, we can specify the coordinates of the object in each step with the help of barycentric coordinates. This approach can significantly help us to achieve more accurate results than by using other possible methods. In the paper, we describe the problem and barycentric coordinate-based solution in detail. We then compare the barycentric method with a technique based on transformation matrices, which we also tested for solving our problem. We also present various diagrams that demonstrate the efficiency of our proposed approach in terms of precision and performance. |
| first_indexed | 2024-12-13T13:57:01Z |
| format | Article |
| id | doaj.art-6c78779600734414a0829a55825f249b |
| institution | Directory Open Access Journal |
| issn | 2524-4442 |
| language | English |
| last_indexed | 2024-12-13T13:57:01Z |
| publishDate | 2020-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Visual Computing for Industry, Biomedicine, and Art |
| spelling | doaj.art-6c78779600734414a0829a55825f249b2022-12-21T23:42:52ZengSpringerOpenVisual Computing for Industry, Biomedicine, and Art2524-44422020-07-01311710.1186/s42492-020-00052-yEfficient object location determination and error analysis based on barycentric coordinatesAndrea Bodonyi0Roland Kunkli1Faculty of Informatics, University of DebrecenFaculty of Informatics, University of DebrecenAbstract In this paper, we propose an efficient computational method for converting local coordinates to world coordinates using specially structured coordinate data. The problem in question is the computation of world coordinates of an object throughout a motion, assuming that we only know the changing coordinates of some fixed surrounding reference points in the local coordinate system of the object. The proposed method is based on barycentric coordinates; by taking the aforementioned static positions as the vertices of a polyhedron, we can specify the coordinates of the object in each step with the help of barycentric coordinates. This approach can significantly help us to achieve more accurate results than by using other possible methods. In the paper, we describe the problem and barycentric coordinate-based solution in detail. We then compare the barycentric method with a technique based on transformation matrices, which we also tested for solving our problem. We also present various diagrams that demonstrate the efficiency of our proposed approach in terms of precision and performance.http://link.springer.com/article/10.1186/s42492-020-00052-yBarycentric coordinatesConversionTransformationCoordinate systemsLocation |
| spellingShingle | Andrea Bodonyi Roland Kunkli Efficient object location determination and error analysis based on barycentric coordinates Visual Computing for Industry, Biomedicine, and Art Barycentric coordinates Conversion Transformation Coordinate systems Location |
| title | Efficient object location determination and error analysis based on barycentric coordinates |
| title_full | Efficient object location determination and error analysis based on barycentric coordinates |
| title_fullStr | Efficient object location determination and error analysis based on barycentric coordinates |
| title_full_unstemmed | Efficient object location determination and error analysis based on barycentric coordinates |
| title_short | Efficient object location determination and error analysis based on barycentric coordinates |
| title_sort | efficient object location determination and error analysis based on barycentric coordinates |
| topic | Barycentric coordinates Conversion Transformation Coordinate systems Location |
| url | http://link.springer.com/article/10.1186/s42492-020-00052-y |
| work_keys_str_mv | AT andreabodonyi efficientobjectlocationdeterminationanderroranalysisbasedonbarycentriccoordinates AT rolandkunkli efficientobjectlocationdeterminationanderroranalysisbasedonbarycentriccoordinates |