Solid angle to the unit sphere with center P, which can be calculated as the surface integral: where formula_5 is the unit vector corresponding to formula_6, the position vector of an infinitesimal area of surface with respect to point P, and where formula_7 represents the unit normal vector to . Even if the projection on the unit sphere to the surface S is not isomorphic, the multiple folds are correctly considered according to the surface orientation described by the sign of the scalar product formula_8. Thus one can approximate the solid angle subtended by a small facet having flat surface area ,
Solid of revolution Solid of revolution In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line (the "axis of revolution") that lies on the same plane. Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid multiplied by the figure's area (Pappus's second centroid Theorem). A representative disk is a three-dimensional volume element of a solid of revolution. The element is created by rotating a line segment (of length ) around some axis (located units