Vanishing point as the "direction point", as lines having the same directional vector, say "D", will have the same vanishing point. Mathematically, let be a point lying on the image plane, where is the focal length (of the camera associated with the image), and let be the unit vector associated with , where . If we consider a straight line in space with the unit vector and its vanishing point , the unit vector associated with is equal to , assuming both are assumed to point towards the image plane. When the image plane is parallel to two world-coordinate axes, lines parallel
Morris–Putnam point Morris–Putnam point The Morris–Putnam point (MPP or “Profit Horizon” ) is the point within a break even analysis where an algorithmic trend line indicates break even will be exceeded by n percent. Economists and Financial analysts use the Morris–Putnam point to predict the impact of commodities costs on juice and heavy metals profits. Meteorologists use "The Point" to forecast dew points and localized wind gusts. Sales people use the point to rationalize the addition of ‘fees’ to previously agreed upon prices because when modeled skillfully, the Morris–Putnam point almost always predicts future success. For example, if a citrus farm produces