Drawing convex hull (Pic)

From LiteratePrograms

The convex hull of a set of points Q is the smallest polygon that embraces every point in Q. This article explains how to draw a convex hull diagram using pic. The exact steps to convert a pic document into a graphic format is available at Hello World (Pic).

Plotting random points

Thirteen random points in a 2-D plane.

We first choose thirteen points and scatter them to a 2-dimensional plane.

 P1: ( 1,  3)
 P2: ( 2,  7)
 P3: ( 9, -2)
 P4: (-5,  7)
 P5: (-7,  2)
 P6: (-1,  3)
 P7: ( 4,  6)
 P8: (-3, -4)
 P9: ( 6,  0)
P10: (-2,  8)
P11: ( 0, -5)
P12: ( 5,  8)
P13: (-4, -1)

We draw a circle at each coordinate. Note that we need the label for each point for later use.

<<points>>=
P1: circle fill at (1, 3)
P2: circle fill at (2, 7)
P3: circle fill at (9, -2)
P4: circle fill at (-5, 7)
P5: circle fill at (-7, 2)
P6: circle fill at (-1, 3)
P7: circle fill at (4, 6)
P8: circle fill at (-3, -4)
P9: circle fill at (6, 0)
P10: circle fill at (-2, 8)
P11: circle fill at (0, -5)
P12: circle fill at (5, 8)
P13: circle fill at (-4, -1)

We place the name of each point at every coordinate. Note that special pic commands such as below, above, ljust, and rjust really come in handy.

<<names>>=
"$p_1$" at P1  below ljust
"$p_2$" at P2  below ljust
"$p_3$" at P3  below ljust
"$p_4$" at P4  below ljust
"$p_5$" at P5  below rjust
"$p_6$" at P6  below ljust
"$p_7$" at P7  below ljust
"$p_8$" at P8  below rjust
"$p_9$" at P9  below ljust
"$p_{10}$" at P10 below ljust
"$p_{11}$" at P11 below ljust
"$p_{12}$" at P12 above ljust
"$p_{13}$" at P13 below ljust

Embedding the information on points and names completes a whole pic document. We could reduce the size of pic document by adjusting scale variables. The circlerad variable defines the default radius of every circle in a document.

<<Scattered_points.pic>>=
.PS
scale = 8
circlerad = 0.2
points
names
.PE