Geometric analysis of simple surfaces
Simple surfaces such as planes, spheres, cylinders and cones are important in mathematics and in certain aspects of engineering. Therefore, the understanding and accurate representation of these intersections is important. There is already a lot of work being done on this subject but most are either...
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| Format: | Final Year Project (FYP) |
| Language: | English |
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2013
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| Online Access: | http://hdl.handle.net/10356/54126 |
| _version_ | 1826120858678067200 |
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| author | Heng, Jinliang. |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Heng, Jinliang. |
| author_sort | Heng, Jinliang. |
| collection | NTU |
| description | Simple surfaces such as planes, spheres, cylinders and cones are important in mathematics and in certain aspects of engineering. Therefore, the understanding and accurate representation of these intersections is important. There is already a lot of work being done on this subject but most are either incomplete or too difficult to refer to. Also, there has not been consistency in method and notations when referring to different sources. This motivates the embarkment of the project to generate a volume of information in regards to intersections between two quadric entities in Euclidean space and will focus its method and mathematics from hand-written notes by Dr. Neil Rigby. MATLAB programming will be used to validate and generate graphics for the different intersection cases. The product of this project will provide mathematical equations and explanations that are essential for a reader looking to actually solve these intersection problems. Future extension to the project can include other geometric entities such as circles, parabolas and hyperbolas intersections. Tori, paraboloids, hyperboloids and other non-degenerate surfaces can also be considered. Even further, intersection between an intersection curve (of two quadrics) with another quadric for the modelling of intersection between three entities is possible. |
| first_indexed | 2024-10-01T05:23:20Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/54126 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:23:20Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/541262023-03-04T18:18:56Z Geometric analysis of simple surfaces Heng, Jinliang. School of Mechanical and Aerospace Engineering DRNTU::Engineering Simple surfaces such as planes, spheres, cylinders and cones are important in mathematics and in certain aspects of engineering. Therefore, the understanding and accurate representation of these intersections is important. There is already a lot of work being done on this subject but most are either incomplete or too difficult to refer to. Also, there has not been consistency in method and notations when referring to different sources. This motivates the embarkment of the project to generate a volume of information in regards to intersections between two quadric entities in Euclidean space and will focus its method and mathematics from hand-written notes by Dr. Neil Rigby. MATLAB programming will be used to validate and generate graphics for the different intersection cases. The product of this project will provide mathematical equations and explanations that are essential for a reader looking to actually solve these intersection problems. Future extension to the project can include other geometric entities such as circles, parabolas and hyperbolas intersections. Tori, paraboloids, hyperboloids and other non-degenerate surfaces can also be considered. Even further, intersection between an intersection curve (of two quadrics) with another quadric for the modelling of intersection between three entities is possible. Bachelor of Engineering (Mechanical Engineering) 2013-06-13T08:59:20Z 2013-06-13T08:59:20Z 2013 2013 Final Year Project (FYP) http://hdl.handle.net/10356/54126 en Nanyang Technological University 206 p. application/pdf |
| spellingShingle | DRNTU::Engineering Heng, Jinliang. Geometric analysis of simple surfaces |
| title | Geometric analysis of simple surfaces |
| title_full | Geometric analysis of simple surfaces |
| title_fullStr | Geometric analysis of simple surfaces |
| title_full_unstemmed | Geometric analysis of simple surfaces |
| title_short | Geometric analysis of simple surfaces |
| title_sort | geometric analysis of simple surfaces |
| topic | DRNTU::Engineering |
| url | http://hdl.handle.net/10356/54126 |
| work_keys_str_mv | AT hengjinliang geometricanalysisofsimplesurfaces |