多面幾何模型逆投影分析之研究

Back Projection Analysis of Polyhedral Geometric Models

陳建安(Jian-an Chen)

指導教授 ： 莊漢東

國立中央大學/工學院/機械工程學系/碩士(2008年)

摘要

以輸入關鍵字（Keyword）為介面之資料庫或網路搜尋為目前普遍應用之方法，由於文、數字在電腦系統內有其標準的編碼格式，因此文、數字之比對容易，搜尋速度快，但是，以關鍵字為主的搜尋引擎卻無法有效的描述幾何物體。近年來，隨著電腦輔助設計與製造（CAD/CAM）及數位模型資料量的快速成長，幾何模型資料量日漸龐大，藉由群組技術的編碼、分類與查詢已無法滿足需求，不論在工程應用或多媒體資料管理上，有效與可靠的模型比對與搜尋技術有待進一步地發展。
本研究目的是探討如何以模型外形及投影輪廓之特徵資料，運用啟發性幾何推理（Heuristic Geometric Reasoning）思考邏輯法則，建立可行之3D模型與查詢輪廓之對應關係，同時發展疊代計算投影視角（Viewing Angle）之分析，以解決此問題。
啟發性幾何思考邏輯法則主要考慮模型頂點與邊之凹凸屬性，做為決定投影輪廓特徵之主要因素，本研究中，第一階段是分析使用者輸入輪廓，利用點、線之間的連接特性進行二維幾何分析。第二階段則進行幾何模型STL檔案讀取以及各項化簡與分析之過程。第三階段對模型進行初步對齊，利用第一階段所得之幾何特徵於三維模型中得到初始投影。第四階段先針對二維圖形與三維模型之間的比例關係，以及二維圖形缺乏深度資訊的問題擬定修正策略，再以ICP演算法疊代計算進行精度比對。

關鍵字

搜尋引擎 ； 輪廓特徵 ； 啟發性幾何推理 ； 比對

並列摘要

Nowadays, the common way of data searching and internet searching is to enter the keywords. Since the words and numbers are memorized by standard form, it is easy to match and search quickly. However, it is not effective to find a geometric object by entering the keywords in the existing search engines. With the development of Computer Aided Design/Manufacture and graphic engine in recent years, the data of geometric models has been growing rapidly, resulting in unsatisfying speed of coding and classing by Group Technology when searching. The available technique of models matching and searching is necessary to be developed in engineering and multimedia managing.
The purpose of the research is to discuss how to use the Heuristic Geometric Reasoning method by analyzing the characteristics of models and projective contour. Establish feasible corresponding relation between 3D model and entering shape, and develop iterative calculation of Viewing Angle to solve the searching problem.
The main idea of Heuristic Geometric Reasoning method is to determine the projective contour-characteristics by considering the concave and convex of the points and edges. In this research, four stages are implemented to reach the goal. First of all, analysis of connective quality between points and edges of the entering contour is completed, following by the STL file of geometric models being read and analyzed. Third, initial projection is obtained form geometric characteristics. Finally, to adjust proportion between 2D figure and 3D model, presume the z-coordinate, and calculate precision-coordination by ICP algorithm, are included in the forth stage.

並列關鍵字

Heuristic Geometric Reasoning ； matching ； contour-characteristic ； searching engine

參考文獻

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