The irradiance Jacobian for partially occluded polyhedral sources
The irradiance Jacobian for partially occluded polyhedral sources
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DOI：
10.1145/192161.192250
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发表时间：
1994-07
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影响因子：
--
通讯作者：
James Arvo
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文献类型：
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作者：
James Arvo
均匀亮度的多面体光源在表面上一点的辐照度由众所周知的解析公式给出。在本文中，我们推导了辐照度雅可比行列式的相应解析表达式，即辐照度矢量表示的导数。尽管结果对于未遮挡源来说是基本的，但在半影内，辐照度雅可比行列式必须包含比辐照度或矢量辐照度更多的有关阻挡物的信息。这里提出的表达式适用于任意数量的多面体阻挡器，并且只需要标准多边形裁剪的较小扩展即可进行评估。为了说明其用途，简要描述了三个相关应用：等勒克斯轮廓的直接计算、查找局部辐照度极值和等网格划分。等照度等值线是整个表面上恒定辐照度的曲线，可以使用基于辐照度雅可比行列式的预测校正器方法来跟踪。类似地，可以使用下降法找到局部极值。最后，等网格划分是一种新的表面网格生成方法，它结合了等距轮廓系列。
The irradiance at a point on a surface due to a polyhedral source of uniform brightness is given by a well-known analytic formula. In this paper we derive the corresponding analytic expression for the irradiance Jacobian, the derivative of the vector representation of irradiance. Although the result is elementary for unoccluded sources, within penumbrae the irradiance Jacobian must incorporate more information about blockers than either the irradiance or vector irradiance. The expression presented here holds for any number of polyhedral blockers and requires only a minor extension of standard polygon clipping to evaluate. To illustrate its use, three related applications are briefing described: direct computation of isolux contours, finding local irradiance extrema, and iso-meshing. Isolux contours are curves of constant irradiance across a surface that can be followed using a predictor-corrector method based on the irradiance Jacobian. Similarly, local extrema can be found using a descent method. Finally, iso-meshing is a new approach to surface mesh generation that incorporates families of isolux contours.