摘 要
物件近似為一種普遍使用於電腦繪圖、計算幾何學計算物件間相交(Object Intersection)與機器人自動避碰(Collision Avoidance)軌跡規劃分析的方法。藉由適當之物件近似可將複雜之物體以簡單體積來近似，如此便可利用簡單的方法初步分析兩物體相交或發生碰撞之可能性。若兩近似體不存在任何交集，則代表實際物體也不可能發生相交或碰撞之情形。反之，若兩近似體存在著交集，則兩物體有可能存在相交或碰撞之情形，此時才需要再進一步執行複雜之計算。
所以為能更快速且方便的提供碰撞偵測比對，本計畫將結合保守近似之包覆矩形具有長寬高之彈性變化與積極近似包覆圓球的概念，探討不等軸之包覆橢圓球(Bounding Elliposid)近似方法，相較於目前用於偵測橢圓球的方法，本研究加上了密度評估的策略，能讓嵌合計算出的橢圓球更接近物體外形，進而在碰撞偵測上能更準確。

Abstract
Bounding volume are widely employed in many areas of computer graphics.Usually,we use crude approximations of the scene geometry to speed up some time-consuming computations, such as object intersection or collision avoidance, etc.Test was performed to check if overlapping of the bounding boxes occurs.If it occurs,we need further computations.
In order to fast and effectively computes the object intersection or collision avoidance,this investigaton combined bounding box with bounding spherea as the method of bounding ellipsoid.In this investigation,we combine least squares ellipsoid specific fitting with weights estimation such that the collision detection will be more accurate.

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