Monthly Archives: February 2016

floor(x) and ceiling(x)

Simon Woodhead writes:

Floor and ceiling functions are not available in the current version of Autograph, but will be in a future version. The y = int(x) function is actually a truncation function so int(-3.2) = -3 and int(3.2) = 3. This is not the most useful function, but can be used to define ceiling and floor functions.

Open a 2D graph page and click on Function Definitions. Define:
  f(x) = ((int(x) + |int(x)|) + (int(x − 1) − |int(x − 1)|))/2
  g (x) = f(x) + 1
Then f(x) is the floor function and g(x) is the ceiling function.

floot

Modelling a bottle in 3D

bottle

First import the image, and enter lots of points along the top edge.

Select a group of points that you think could be modelled by a polynomial and use the “best Fit” option.  The default ‘sig’ fig’ is 4, but a polynomial equation needs more accuracy to plot accurately.  Use “PAGE – SETTINGS” to set the sig fig to 8. With the current best fit selected, use the PAGE menu  and the option “Copy Status Bar”, and in a 3D page use “Enter equation” and paste this in, with “Plot as 2D” ticked, and Startup Options set to the domain.

bottle2In the 3D page, select each sector, use “Find Area” with “Simpson’s Rule” selected, then “Volume” about y = 0.

bottle3