Concave function second derivative is negative then it is strictly concave, but the opposite is not true, as shown by . 4. If is concave and differentiable, then it is bounded above by its first-order Taylor approximation: 5. A continuous function on is concave if and only if for any and in 6. If a function is concave, and , then is subadditive on formula_21. Proof: 1. A function is concave over a convex set if and only if the function is a convex function over the set. 2. The sum of two concave functions is itself concave and so is the
Parallel projection central or perspective projection, in which the rays pass through a fixed point called the "center" or "viewpoint", as this point is moved towards infinity. Put differently, a parallel projection corresponds to a perspective projection with an infinite focal length (the distance between the lens and the focal point in photography) or "zoom". In parallel projections, lines that are parallel in three-dimensional space remain parallel in the two-dimensional projected image. A perspective projection of an object is often considered more realistic than a parallel projection, since it more closely resembles human vision and photography. However, parallel projections are popular in