TRANSFORM POINTS

TRANSFORM POINTS

LET Subcommand

Given a set of (X,Y) pairs, perform a location, scaling, and rotation transformation.

The location transformation is
X' = X - T_x
Y' = Y - T_y


with T_x and T_y denoting the X and Y translation, respectively.

The scaling transformation is

X' = X*S_x
Y' = Y*S_y


with S_x and S_y denoting the X and Y scaling, respectively.

The rotation transformation is




with denoting the angle of rotation (in radians).

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.

LET Y2 X2 = TRANSFORM POINTS Y X TY TX SY SX THETA

None

None

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.

Computational Geometry

2012/10

 
read x y
  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