论文标题
在任意多边形截面上投影的实体角度的分析公式
Analytical Formulae for Projected Solid Angle on Arbitrary Polygonal Cross Sections
论文作者
论文摘要
从多边形横截面计算实体角度的封闭形式的解是众所周知的，但是通常无法使用用于计算投影实体角度的类似公式。使用高斯 - 基因网定理得出了用于计算任意形状多边形的投影实体角度的公式。这是通过将投影的实体角积分转换为球形贴片上积分不可分割的，然后通过高斯 - 邦网将其简化为简单的求和，从而可以精确地计算出投影的实体角度。公式的应用允许在离散间隔内精确计算投影的实体角度，这些间隔可用于将辐射通量计算为表面或查看自由空间的因素。
Closed form solutions for the computation of the solid angle from polygonal cross-sections are well known, however similar formulae for computation of projected solid angle are not generally available. Formulae for computing the projected solid angle from arbitrarily shaped polygons are derived using the Gauss-Bonnet theorem. This is accomplished by transforming the projected solid angle integral to an integral over a spherical patch, which is then reduced by Gauss-Bonnet to a simple summation over its edges, allowing the projected solid angle to be computed exactly. Application of the formulae allows exact calculation of projected solid angle over discrete intervals which may be used for computing radiative flux to surfaces or view factors to free space.
