在全球氣候日益暖化的情況之下，森林大火對人類生命財產的威脅已經在世界各地成為一個嚴重的問題。一個可靠的野火模擬系統將可以有效的預測火勢蔓延並且能夠用來協助消防單位控制火區並且減少環境的破壞。電腦上模擬並且視覺化野火蔓延有兩種主要的研究類型：以柵格(raster)為基礎的展現方法和以矢量(vector)為基礎的展現方法。兩種方法各有他們的優點和缺失。以矢量為基礎的展現方法有一個最大的挑戰是不同擴張面交錯融合(crossover)的問題。在 1998 年 Osher 和 Sethian [1] 發表水平集法(level set method)的概念之前，所有對擴張面交錯融合問題的解決方法都需要煩瑣且耗時的計算。水平集方法是眾所周知的，能夠輕易的處理各種拓撲結構變化的問題，例如合併或撕裂接口。因此以矢量為基礎的展現方法來模擬火勢蔓延的模擬系統就可以利用水平集方法來解決野火蔓延交錯時的問題。第一位利用水平集法的概念來建立野火蔓延模擬系統的研究學者是 V. Mallet, D. Keyes, and F. Fendell [2]。他們利用惠更斯(Huygens)原理和橢圓形擴散假設來計算野火蔓延的距離和方向、然後結合水平集法的概念來擴大野火的蔓延。2009 年他們發表的論文中顯示出在控制風勢的情況下表現的完美橢圓火形。但是野火的蔓延還需要考慮地形地貌等的複雜環境。在這篇研究中、我們希望利用羅瑟梅爾火勢擴散的數學模型運用在水平集方法中來建立一個更適合自然環境的野火模擬系統。羅瑟梅爾火勢擴散的數學模型是美國用在建立野火模擬系統最廣泛的一個數學公式。我們的目標是將羅瑟梅爾模型分割成燃料、風勢和地形三個部分。將這三個部分分別利用水平集法來計算野火蔓延的距離，再將其結合算出最終的距離和方向。因為羅瑟梅爾模型是一維空間的擴散公式，我們還必需利用惠更斯原理和橢圓形擴散假設來計算野火蔓延的方向使之可以用來計算二維空間的擴展。

Fire hazard and its destruction become a big issue around the world especially in the context of global warming. A reliable fire simulation model will be a useful tool for fire safety managers to control the destruction area. There are two major simulation methods which are raster-based method and vector-based method to simulate the fire spread in computer. Both methods have their own advantage and challenging. One of the most challenging for vector -based method is crossover problem. Regardless of which method is chosen, it is definitely a tedious, time and resource consuming process to calculate crossover until level set methods is introduced by Osher and Sethian [1] at 1988. Level set methods are well known for its ability to easily handle topological changes such as merging or breaking interfaces. Therefore the level set method can be applied to resolve the crossover issue in fire spread model using vector-based method. Level set methods need a suitable fire model to expand the surface. The first and most recent model to apply level set methods to expand fire spread is introduced by V. Mallet, D. Keyes, and F. Fendell [2]. The maturity of the model which focuses most on wind factor still requires improvement to fit the real world fire spread. Rothermel's fire model is the most commonly used fire model to simulate fire spread in America. The goal of this research is to enhance the existing Rothermel's fire model and apply level set methods to this modified model to forecast the behavior of ground fire spread in the much more complex real world simulation.