According to the 'Defining New Arrow Tip Kinds' chapter of the TikZ & PGF manual for version 3.0.1a (p. 1016), one of the parameters that must be specified every time a new arrow tip kind is defined is convex hull.
The convex hull of a shape is conceptually similar to its bounding box (but the two are not quite the same). As an illustration of the concept of a convex hull, consider the following picture of an arrow tip in design. The convex hull of the arrow tip is the triangle, whose vertices are (1,0), (-3,2), and (-3,-2).
One may wonder why the convex hull needs to be explicitly specified by the designer of the arrow tip kind, when PGF has a built-in mechanism for calculating bounding boxes. The manual addresses this question as follows (last bullet point in section 100.2 on p. 1016).
PGFautomatically keeps track of a bounding box of everything you draw. However, since arrow tips are drawn so often,
PGFcaches the code needing for drawing arrow tips internally and because of this cache it cannot determine the size of the arrow tip just based on the drawing commands used for drawing the tip. Instead, a convex hull of the arrow tip must be explicitly provided in the definition.
Why does the caching of the code needed for drawing the arrow tips preclude PGF from calculating the arrow tip's bounding-box without the user's hints?