過去十年，繪圖晶片有長足的進步，特別是繪圖處理器(GPU)在能力上
的提升；其中最為重要的兩個改變是1) 在即時繪圖中使用可程式化單元
(programmable shaders)，2) 將繪圖晶片應用於一般非繪圖運算(GPGPUs)以
及進階繪圖中。這些進步使得過去只能出現在預先繪製好的動畫中的細緻幾
何模型、栩栩如生的模型表面，如今都已經可以即時(real-time)的被繪畫出
來。
現代的遊戲通常使用大量的小三角片來提高最終影像的畫質，傳統繪圖
晶片的演算法對於處理巨量的小型三角片比起Inverse Displacement Mapping
這一類的繪圖方法是比較沒有效率的，特別是傳統演算法中的Rasterization
這個步驟；因為傳統的演算法是針對大型三角片模型而設計的。然而現有的
Inverse Displacement Mapping 方法都只適用於一般平坦表面，對於一般模型
資料常出現的任意曲面卻無法適用。為了突破這個限制，我發展了一個任意
曲面適用的演算法 (詳述於第二章中)。透過這個方法，模型的輪廓、表面的
細節都能在即時(Real-time)的前提下完成。
在電腦圖學中，『即時(Real-time) 全域照明』是一個很大的挑戰，一般
一張圖就算運用最新的硬體加速也來是需要數分鐘甚至數天才能完成。因
此，要達到即時全域照明除了需要更好的硬體外也需要更聰明的演算法才有
可能。在第三章中，一個兼顧時空的演算法被提出來計算低頻的間接照明效
果。這個方法透過分散大量計算到整個序列的影像中來減少計算時間，最終
可以大量的減少每一張圖所需要的計算時間；因此透過這個演算法，全域照
明中的間接照明效果便可以每秒鐘24 張以上的速度被繪製，達到即時繪圖
的實現要求。

In the past decade, graphics hardware has improved dramatically, especially
on the capabilities of graphics processing units (GPUs). The most prominent
improvements are realization of programmable shaders for real-time rendering
and general purpose computation with graphics processing units (GPGPUs) for
advance rendering. The exquisite geometry details and vivid surface shading are
therefore produced in real time.
Modern games usually present the geometry details with a huge number of
small-area primitives to improve the quality of final videos. To render such
scenes, inverse displacement mapping methods, one kind of ray-tracing-based
method, are a better choice than the rasterization approaches (used in traditional
real-time 3D graphics) which is designed for large-area primitives. However,
existed inverse displacement mapping methods are limited to planar surface. To
eliminate the constraint, I propose an arbitrary-surface-supported inverse
displacement mapping method in 2. With the proposed algorithm, the silhouette
and geometry detail are rendered correctly in real time.
In computer graphics, “Real-time” global illumination is a big challenge. It
still takes minutes to days to synthesize a single image, even though the newest
graphics hardware (GPGPUs) speeds up the process by 2~100 times. Thus, not
only computing power but also better algorithms are required to achieve real time.
In 3, a spatio-temporal approach for the low-frequency indirect lighting is
proposed. This method amortizes the cost over a sequence of image frames. As
the result, the computing power requirement is dramatically reduced, and the
indirect lighting effect is rendered in real-time.

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