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標題: 螺旋管面之均等取樣技術
作者: 王宗銘
關鍵字: 取樣
出版社: 國立中興大學工學院;Airiti Press Inc.
摘要: 在幾何物體表面上作有效且均等的取樣是目前電腦圖學領域中成圖演算法重要研究課題。此取樣技術通常將幾何物體為各種不同的光源並使用蒙地卡羅演算法來解決全域照度的問題。目前雖已有商業用途的螺旋管面光源,但文獻上尚未發現相關的取樣技巧。因此,本文針對螺管面提出一種新的均等取樣技術,增擴增光源型態的範圍。首先,我們定義螺旋管面的數學表示式。接著,我們利用計算螺旋管面之面積時所使用之積分函數與其反函數,提出均等取樣演算法。此外,我們也發展一種名為FSSA的加速技巧,以改善反函數之計算效率。我們實作所提出的取樣技術,讓使用者以互動的方式輸入取樣數量,並即時顯示樣本分佈的視覺效果。實驗結果顯示:我們所提的取樣技術,確實能在螺旋管面產生均等的樣本。此外,產生2000個樣本,在平均誤差小於5.0×10-7的條件下,使用FSSA的加速技巧僅需約0.13秒,比未使用前快約678.9倍。此結果顯示我們所提的方法也具有相當優異的計算效能,在極小的代價下,可大幅降低取樣時間。總結研究,我們提出一個創新且有效的取樣演算法,對於在螺旋管面上做均等取樣有具體的貢獻。
Efficient and stratified sampling for various geometries has been the subject of intensive research in computer graphics community. A popular allocation is for realistic image synthesis where geometries represented as different light sources are sampled before applying Monte Carlo methods to solve the global illuminatin problem. In this paper, we present a novel stratified sampling algorithm (SSA) for the helical canal surface to extend the coverage of the light sources. As our knowledge, no stratified sampling approaches for the helical canal surface have ever been addressed in the literature. Initially, we define the mathematical expression for a helical canal surface. We then present the SSA developed from the inverse function of the Integration on helical canal surface. Furthermore, we develop an acceleration technique, Faster SSA (FSSA), to meliorate the computational efficiency, significantly reducing the time required to generate stratified samples with negligible expenses. We have implemented our algorithm on an experimental system where the implementation is effortless. In this system, the front-end user can visualize samples being generated interactively to illustrate the visual effect of SSA. Furthermore, the FSSA expedites the sample generation process considerable with the expense of little sample deviation. With FSSA, 2000 samples can be general within 0.13 second, which is almost 678.9 times faster than employing conventional SSA. The sample deviation is negligible since the average deviation for canonical number is relatively small, being less than5.0�10-7 in average for 2000 samples. In conclusion, the proposed stratified sampling algorithm is novel, efficient and feasible for a helical canal surface.
ISSN: 1017-4397
Appears in Collections:第13卷 第3期



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