crack function

I call a crack function a function built of line segments. In statistics we find her as frequency polygon,  which curve connects the maximal values of subsequent rectangles.

Some simple species:

• modulus (function) |x|, which gives the absolute value of a number: -x for x<0, x for x>=0.This curve is also called the absolute value function abs().

• needle function: the value is only unequal zero in the neighborhood of x = a.
  In the infinite case we get the delta function.
  
• The triangle curve (or zigzag curve) repeats the isosceles triangle.
  The curve can be defined as giving the distance from x to the natural number that is most close. In formula:
  
  where [x] is the entier function.
  This triangle curve can be used to construct the blancmange curve.
  
• When the voltage of a signal varies periodically between a minimum and a maximum value, the resulting curve is a block-wave or rectangular curve, thus repeating the rectangle.