摘要
我們提出一個即時柔和陰影演算法，目標是能夠同時支援較柔順與不柔順的影子(就像是預先計算放射傳遞裡頭的全頻率影子)、動態場景、區域複雜形狀光源。
我們的方法包括前置處理以及描繪畫面，這是由動態場景下的預先計算陰影場域 [10] 這篇論文所激勵，且基於區域可見性理論。主要的想法是將五維度的陰影場域換成射線空間足跡地圖，這是發展自射線空間分解針對區域可見性 [13]，原先用來解決區域可見性的問題。
針對每一個遮蔽物與區域性光源，我們會個別建立一個射線空間足跡地圖於前置處理時。針對克服可見性問題與陰影問題的不同，主要的關鍵困難在於：1)如何改變射線空間分解針對區域可見性成一個新的演算法為了提升描繪畫面的效能 2) 提供一個新的融合迴圈演算法去前置處理每一個場景物體以保持常數數量的射線空間足跡地圖，這保證了即時效能、低記憶體成本、以及在區域複雜形狀光源下的柔和陰影品質。

Abstract
This thesis presents a real-time soft shadow algorithm for supporting the rendering of soft and hard shadow (similar to all-frequency shadow in Pre-computed Radiance Transfer (PRT)) in dynamic scenes. The thesis, at the same time, supports local area lights of arbitrary shape.
The method includes preprocess and rendering part, which is motivated by the work Shadow Fields by Zhou et al. [10], and is also based on from-region visibility works. The main idea is to replace the 5D shadow fields with ray space footprint maps (derived by Leyvand et al. [13]), which originally solved from-region visibility problems. For each occluder and local light source, a ray-space footprint map can be built separately in the pre-process. In runtime, we only need to lookup these pre-computed maps to calculate shadow value for each visible fragment.
For overcoming the difference between visibility and shadow problems, the key difficulties are: 1) changing Ray Space Factorization [13] to a novel algorithm with preprocess version for enhancing the performance of rendering 2) providing a novel fusion loop algorithm to preprocess each scene entity for keeping constant number of ray space footprint maps, which guarantees the real-time performance, low memory cost, and quality for soft shadow with local area lights of arbitrary shape.

Keywords Pre-computed radiance transfer, From-region visibility, Ray space, Occluder, Fusion.

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