Dataplot Vol 2 Vol 1

# EXTREME POINTS

Name:
EXTREME POINTS
Type:
LET Subcommand
Purpose:
Given a set of points, return a list of extreme points.
Description:
Given a set of (X,Y) points, return the four points

(X1,YMIN)
(XMAX,Y2)
(X3,YMAX)
(XMIN,Y4)

with XMIN, XMAX, YMIN, and YMAX denoting the minimum X value, the maximum X value, the minimum Y value, and the maximum Y value, respectively. The Xi and Yi mean the x or y coordinate corresponding to the minimum or maximum value.

Syntax:
LET <yout> <xout>= EXTREME POINTS <y> <x>
<SUBSET/EXPCEPT/FOR qualification>
where <y> is a variable containing the x-coordinates of the data points;
<x> is a variable containing the y-coordinates of the data points;
<yout> is a variable containing the y-coordinates of the extreme points;
<xout> is a variable containing the x-coordinates of the extreme points;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET Y2 X2 = EXTREME POINTS Y X
Default:
None
Synonyms:
None
Related Commands:
 POINTS IN POLYGON = Determine whether points are in the interior of a convex polygon. CONVEX HULL = Determine the convex hull of a set of points. TRANSFORM POINTS = Perform location, scale, and rotation transformation for a set of points. LINE INTERSECTIONS = Determine the intersection points for a set of lines. PARALLEL LINE = Determine the coordinates for a point that defines a parallel line determined by a point and a line defined by two points. PERPINDICULAR LINE = Determine the coordinates for a point that defines a perpindicular line determined by a point and a line defined by two points.
Applications:
Computational Geometry
Implementation Date:
2012/10
Program:
```
.  Following data from Eddy's ACM article
2.0       0.0
1.73      -1.0
1.0       1.73
0.0       2.0
0.1       0.1
-1.0      -1.73
0.2       -0.2
-1.73     1.0
-0.3      0.3
0.0       -2.0
-0.4      -0.4
-2.0      0.0
0.5       0.5
1.73      1.0
0.6       -0.6
-1.0      1.73
-0.7      0.7
-1.73     -1.0
-0.8      -0.8
1.0       -1.73
end of data
.
let y2 x2 = 2d convex hull y x
let y3 x3 = extreme points y2 x2
let xtemp = x2(1)
let ytemp = y2(1)
let x2 = combine x2 xtemp
let y2 = combine y2 ytemp
.
title case asis
title offset 2
title Extreme Points of the Convex Hull
y1label Y
x1label X
tic offset units screen
tic offset 3 3
x3label
.
character hw 1 0.75 all
character fill on all
character color black black red
character circle blank  circle
line blank solid blank
.
pre-sort off
plot y x and
plot y2 x2 and
plot y3 x3
pre-sort on
```

Date created: 01/07/2013
Last updated: 01/13/2013