Dataplot Vol 2 Vol 1

# TRANSFORM POINTS

Name:
TRANSFORM POINTS
Type:
LET Subcommand
Purpose:
Given a set of (X,Y) pairs, perform a location, scaling, and rotation transformation.
Description:
The location transformation is

X' = X - Tx
Y' = Y - Ty

with Tx and Ty denoting the X and Y translation, respectively.

The scaling transformation is

X' = X*Sx
Y' = Y*Sy

with Sx and Sy denoting the X and Y scaling, respectively.

The rotation transformation is

with denoting the angle of rotation (in radians).

Syntax:
LET <yout> <xout>= TRANSFORM POINTS <y> <x> <ty> <tx> <sy> <sx> <theta>
<SUBSET/EXPCEPT/FOR qualification>
where <y> is a variable containing the x-coordinates of the data points being transformed;
<x> is a variable containing the y-coordinates of the data points being transformed;
<ty> is a parameter containg the y-cooredinate translation;
<tx> is a parameter containg the x-cooredinate translation;
<sy> is a parameter containg the y-cooredinate scaling;
<sx> is a parameter containg the x-cooredinate scaling;
<theta> is a parameter that contains the angle of rotation; of the polygon;
<yout> is a variable containing the y-coordinates of the transformed points;
<xout> is a variable containing the x-coordinates of the transformed points;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
LET Y2 X2 = TRANSFORM POINTS Y X TY TX SY SX THETA
Default:
None
Synonyms:
None
Related Commands:
 ANGRAD = Return the counter clockwise angle, in radians, of the angle determined by three points. DPNTLINE = Compute the perpindicular distance between a point and a line defined by a point and a slope. 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. SLOPE = Compute the slope of the line determined by two points. EXTREME POINTS = Determine the extreme points of 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:
```
0.5333000E+02  0.2357000E+02
0.5037000E+02  0.1668000E+02
0.1686000E+02 -0.6469000E+02
0.5521000E+02  0.2713000E+02
0.1395000E+02 -0.6794000E+02
0.5414000E+02  0.2781000E+02
0.2704000E+02 -0.4195000E+02
0.1830000E+02 -0.6416000E+02
-0.8881000E+02 -0.2991900E+03
0.6442000E+02  0.5613000E+02
-0.1728800E+03 -0.5288300E+03
0.4743000E+02  0.1766000E+02
0.3282400E+03  0.4791700E+03
0.2137600E+03  0.1424400E+03
0.2067600E+03  0.1877700E+03
0.3593000E+02 -0.2923600E+03
0.3637600E+03  0.3094700E+03
0.2974600E+03  0.6332000E+02
0.1759800E+03 -0.1644000E+03
0.4257500E+03  0.3561300E+03
0.6733000E+02  0.9115000E+02
0.5081000E+02  0.2532000E+02
-0.2029900E+03 -0.5509600E+03
0.7737000E+02  0.6375000E+02
0.3363100E+03  0.3074700E+03
0.1296400E+03 -0.1771600E+03
0.2421000E+02 -0.5091200E+03
0.1670100E+03 -0.1446500E+03
0.2401100E+03 -0.3796800E+03
0.5067400E+03  0.4129400E+03
0.5173100E+03  0.4183700E+03
0.8339000E+02 -0.6446200E+03
0.1908800E+03  0.3463800E+03
0.1629900E+03  0.3044400E+03
-0.1138500E+03 -0.4050300E+03
0.2787200E+03  0.4979900E+03
-0.7125000E+02 -0.4863700E+03
0.2147300E+03  0.1820300E+03
-0.1757900E+03 -0.5140500E+03
-0.1993500E+03 -0.5823900E+03
0.1438700E+03  0.2333900E+03
0.2134000E+02 -0.6915000E+02
-0.4354000E+02 -0.4289700E+03
0.3219800E+03  0.4268300E+03
0.2507000E+02 -0.2689300E+03
-0.8324000E+02 -0.5685300E+03
0.8540000E+02 -0.4379000E+03
0.7870000E+02 -0.3830800E+03
-0.1064000E+02 -0.6613600E+03
0.2023700E+03 -0.3954000E+02
0.2877000E+02 -0.3549000E+02
0.1908000E+02 -0.5440000E+02
0.3766000E+02 -0.1542000E+02
0.5360000E+02  0.1845000E+02
-0.1782900E+03 -0.5311500E+03
-0.9508000E+02 -0.5267900E+03
0.1183700E+03 -0.6679000E+02
0.4384000E+02 -0.4773700E+03
0.1847200E+03 -0.5284000E+02
0.1714300E+03  0.3265600E+03
0.1928600E+03  0.3423200E+03
-0.1705300E+03 -0.4889800E+03
0.4415000E+02  0.8400000E+01
-0.1434000E+03 -0.4216400E+03
0.6579000E+02  0.2837000E+02
end of data
.
let tx = -614.1127
let ty = -368.6171
let sx = 0.0008
let sy = 0.0029
let theta = 1.1723
.
let yt2 xt2 = transform points y x ty tx sy sx theta
.
multiplot scale factor 2
multiplot corner coordinates 5 5 95 95
multiplot 2 2
.
line blank
character circle
character hw 1 0.75
character fill on
title offset 2
title case asis
.
title Original Data
plot y x
.
title Transformed Data
tic mark offset units data
tic mark offset 0.05 0.05
limits 0 1
major tic mark number 6
plot yt2 xt2
```

Date created: 02/15/2013
Last updated: 02/15/2013