臺灣博碩士論文加值系統

在本篇論文中，我們將提出「2.5 維彈跳射線追蹤法」來模擬在一個
大且空房間之聲波傳播。與三維彈跳射線法不同的是，首先，藉由先忽略
掉其中的一個維度，我們先將一個三維的問題簡化成二維；然後，我們從
一個波源射出二維的射線一直到此射線柱打到牆壁。為了方便，我們假設
牆壁是堅硬的（rigid） ；藉由反射定律，我們可以追蹤此射線柱之反射
射線柱的新方向，一直到它又打到另一面牆。在每次的彈跳，我們都必須
檢查接收點是否有落在射線柱裡面。若是有，那一條二維射線就可決定，
此在此同時，我們在將第三維考慮進去；最後，我們將可藉由所對應的影
像（image） 以及此三維的路徑，算出所對應的場強。將此過程不斷重複
直到所有的射線柱都已追蹤完畢，將之總和起來，便可得到每個波源所產
生的貢獻。與原始三維的方法比較起來，二點五維的方法效率較高且較省
時，藉由此法，我們可以計算在不同建築物的聲波場強分佈，且可以得到
令人滿意的結果。

In this thesis,we will propose a method,the 2.5D SBR-image method,
to simulate sound wave propagation in a large empty room.First,we
simplify a 3D problem into a 2D one by initially neglecting the
third dimension.Then,we shoot 2D ray tubes from a sound source until
it hits a wall which we assume to be a rigid wall in most cases for
simplicity.In accordance with the law of reflection,we can trace the
ray tube in its new direction towards the next wall.In every bounce,
we have to examine if the receiver falls within the ray tube.Once it
does,an exact 2D ray path is determined and we consider the effect of
the third dimension at the same time.Finally,we calculate the field
due to the correspondent image along the real 3D ray path.This procedure
repeated until all of the ray tubes have been traced.By superposition,
we are able to calculate the contribution of every equivalent sound
source individually.Compared with the original 3D SBR-image method,
2.5D SBR-image method is more efficient and time-saving.By this method,
we computed the distribution of sound pressure in different kinds of
buildings.The results are rather satisfactory.