| Summary: | 碩士 === 國立中央大學 === 土木工程學系 === 103 === The paper aims to contact of polyhedral particles, On the basis of the theory of contact detection offered by Hsiu-chen Hsu (Vertex-to-Face contact detection and Edge-to-Edge contact detection), carrying on the investigation of Tetrahedron-to-Tetrahedron contact. This study classify Tetrahedron-to-Tetrahedron contact situations，there are six assembles of Tetrahedron-to-Tetrahedron contact situations :Vertex-to-Vertex、Vertex-to-Edge、Vertex-to-Face、Edge-to-Edge、Edge-to-Face、Face-to-Face. Traditional contact of polyhedral particles, contact judgement unit is one random shape particle means the polyhedron- to -polyhedron contact is more difficult and complex than the Tetrahedron-to-Tetrahedron contact. This sturdy intends to reduce the complex level of contact, random shaping polyhedron-to -polyhedron contact transform uniform shaping Tetrahedron- to-Tetrahedron contact (one polyhedron has two or more Tetrahedrons), polyhedron- to -polyhedron contact Transforms to Tetrahedron-to-Tetrahedron contact must be the tendency, because deforming and discrete problem needs to analysis the elements cutting from polyhedron, then could discuss internal Phenomenon of polyhedron-to -polyhedron contact.
The two same polyhedron-to -polyhedron contact assembles, the result with polyhedron cutting to some tetrahedrons and the result with polyhedron no cutting to some tetrahedrons are different, if using traditional contact judgement method(Hsiu-chen Hsu whose method)，the result with polyhedron cutting to some tetrahedrons change to weird, appearing unreasonable translation and rotation. By the study, finding out if Tetrahedron-to-Tetrahedron contact using traditional contact judgement method has the problem with repeat counting contact nodal points causing motion error.
The study provides new thought Rotating-window-plane method about contact detection, the thought is trying to seeking the obviously separating view of two non-contact polyhedrons or less closing view between two non-contact polyhedrons.Rotating observing window with Ball-coordinate then projenting polyhedrons to observing window to judge wheter contact or non-contact.The Cutting-plane method has highly accuracy and easy understanding, which is more accurate than traditional envelope method.The study also improve traditional envelope method to new envelope method, to less missing catching contact.
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