路思義教堂之3D曲面模型建立與模擬

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题名:	路思義教堂之3D曲面模型建立與模擬
其它题名:	3D Surface Modeling and Simulation ofLuce Chapel
作者:	王世銘 WANG,SHIH-MING
贡献者:	黃皇男 Huang,Huang-Nan 應用數學系
关键词:	路思義教堂;二次曲線;圓錐曲線;Conoid 曲面;CAD/CAM;3D模型 Luce Chapel;quadractic equation;conic curve;Conoid surface;CAD/CAM;3D model
日期:	2016
上传时间:	2017-07-17T06:02:47Z (UTC)
摘要:	本研究的目的在於嘗試計算本校著名地標路思義教堂的數學模型，作?精確3D 模型的建立依據。路思義教堂由係由四片（單側兩片）曲面所組成，每片曲面為由前後兩組曲線所構成，即教堂的外型取決於四組曲線而定。研究首先以不同的二次（圓錐）曲線匹配教堂 CAD 檔案數據的四組曲線，並估算每組的對應誤差。再以此成果為基礎，進一步將曲線方程回溯到架構四片曲面所對應的圓錐曲面，並利用教堂 CAD 檔案提供的正向厚度，以建立含厚度在內的真正曲面以及架構出教堂曲面的數位結構。最後將教堂曲面的數位結構轉為 3D CAD/CAM檔案，進而使用 3D 列印機製作路思義教堂準確的 3D 實體模型。 The purpose of this study tires to find the mathematical model of Luce Chapel in Tunghai University for establishing its accurate 3D model. The Luce Chapel consists four surfaces in symmetry about the longitudinal plane and there are four curves in representing two surfaces in each side. Firstly, quadratic equation (conic curves) are generated to interpolate these four different curves based on the numerical data provided by the corresponding CAD file and the associated errors during interpolation are also estimated. Based on the knowledge of these four equations, we generate the data for two separate surfaces with the indicated normal thickness from the CAD file. Furthermore the corresponding Conoid surfaces are regressively obtained to represent the front and rear surface of the chapel and its 3D model representation is then generated. In the last, the 3D model is output as CAD/CAM file and then is printed by the 3D printer as a real accurate 3D model of the Luce Chapel.
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