Least-Squares Estimation of Tangent Space for a Triangular Mesh
This paper presents a novel method for computing an orthonormal tangent space at every vertex of a triangular mesh provided with texture coordinates, which is essential in normal mapping. Our method employs least-squares estimation of rotation between two sets of corresponding points: one set from t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/14/7/2834 |
| _version_ | 1797212914068750336 |
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| author | Min Gyu Choi |
| author_facet | Min Gyu Choi |
| author_sort | Min Gyu Choi |
| collection | DOAJ |
| description | This paper presents a novel method for computing an orthonormal tangent space at every vertex of a triangular mesh provided with texture coordinates, which is essential in normal mapping. Our method employs least-squares estimation of rotation between two sets of corresponding points: one set from the positions of the 1-ring neighbors of a vertex in texture space and the other set from their corresponding positions in world space. This optimal rotation represents a local space transformation that defines the tangent space at the vertex. Consequently, our method ensures that the resulting tangent space is inherently orthonormal, eliminating the need for intricate operations such as averaging and orthonormalization, which are required in the previous methods. In addition, we introduce texture space alignment of triangles to address vertices on seams, which are inevitable in texture mapping to a closed surface mesh. Experimental results demonstrate the effectiveness of the proposed methods in various experiments. |
| first_indexed | 2024-04-24T10:49:57Z |
| format | Article |
| id | doaj.art-6a7697aa39e24b83849ad7c0d2f77a97 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-04-24T10:49:57Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-6a7697aa39e24b83849ad7c0d2f77a972024-04-12T13:14:57ZengMDPI AGApplied Sciences2076-34172024-03-01147283410.3390/app14072834Least-Squares Estimation of Tangent Space for a Triangular MeshMin Gyu Choi0Department of Computer Science, Kwangwoon University, Seoul 01897, Republic of KoreaThis paper presents a novel method for computing an orthonormal tangent space at every vertex of a triangular mesh provided with texture coordinates, which is essential in normal mapping. Our method employs least-squares estimation of rotation between two sets of corresponding points: one set from the positions of the 1-ring neighbors of a vertex in texture space and the other set from their corresponding positions in world space. This optimal rotation represents a local space transformation that defines the tangent space at the vertex. Consequently, our method ensures that the resulting tangent space is inherently orthonormal, eliminating the need for intricate operations such as averaging and orthonormalization, which are required in the previous methods. In addition, we introduce texture space alignment of triangles to address vertices on seams, which are inevitable in texture mapping to a closed surface mesh. Experimental results demonstrate the effectiveness of the proposed methods in various experiments.https://www.mdpi.com/2076-3417/14/7/2834normal mappingtangent spaceleast-squares estimationoptimal rotation |
| spellingShingle | Min Gyu Choi Least-Squares Estimation of Tangent Space for a Triangular Mesh Applied Sciences normal mapping tangent space least-squares estimation optimal rotation |
| title | Least-Squares Estimation of Tangent Space for a Triangular Mesh |
| title_full | Least-Squares Estimation of Tangent Space for a Triangular Mesh |
| title_fullStr | Least-Squares Estimation of Tangent Space for a Triangular Mesh |
| title_full_unstemmed | Least-Squares Estimation of Tangent Space for a Triangular Mesh |
| title_short | Least-Squares Estimation of Tangent Space for a Triangular Mesh |
| title_sort | least squares estimation of tangent space for a triangular mesh |
| topic | normal mapping tangent space least-squares estimation optimal rotation |
| url | https://www.mdpi.com/2076-3417/14/7/2834 |
| work_keys_str_mv | AT mingyuchoi leastsquaresestimationoftangentspaceforatriangularmesh |