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題 名 | 以牛頓區間法求解參數曲面間的交集=Using Interval Newton Method to Solve the Intersection of Parametric Surfaces |
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作 者 | 尤春風; 郭錦誠; | 書刊名 | 國立臺灣大學工程學刊 |
卷 期 | 72 1998.02[民87.02] |
頁 次 | 頁113-130 |
分類號 | 440.11 |
關鍵詞 | 非線性方程組; 區間牛頓法; 參數曲面; 交集; Nonlinear equations; Interval newton method; Parametric surface; Intersection; |
語 文 | 中文(Chinese) |
中文摘要 | 求解兩曲面間交集的問題,一直是計算幾何學研究的重點之一。本文將兩參數曲面間關鍵點的關係轉換為非線性方程組,再藉由非線性方程組的求解法則-區間牛頓法來求解。由於本法則可求出兩曲面間的關鍵點,對於曲面間發生小迴圈、交線分歧和點相切等數值奇異的交集形態可加以掌握。本文利用起始點劃分追蹤區域的方法可避免追蹤交線時發生超過曲面邊界,或追蹤封閉交線時無法終止的現象。文中並列舉數個測試實例,以驗證本法則求解曲面間交線的可行性。 |
英文摘要 | The problem of solving the intersections of surfaces is the core of computational geometry. In this paper, the relationship of critical points will be transformed into a set of nonlinear equations. One robust method, Interval Newton Method, is utilized to solve all solutions. Therefore, all the critical points can be solved, and the singular types of intersections such as small loops, branched curves and tangential points can be found. The parametric domain is divided into some zones in order to avoid tracing over the surface boundary and tracing a closed loop endlessly. Finally, some illustrations are shown to verify the feasibilities of the proposed algorithms. |
本系統中英文摘要資訊取自各篇刊載內容。