EXTREME POINTS

EXTREME POINTS

LET Subcommand

Given a set of points, return a list of extreme points.

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 X_i and Y_i mean the x or y coordinate corresponding to the minimum or maximum value.

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.

LET Y2 X2 = EXTREME POINTS Y X

None

None

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.

Computational Geometry

2012/10

 
.  Following data from Eddy's ACM article
read x y
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