Polar Image

The DisplayPolarImage macro accepts a 2-D matrix of radius and angle and creates an image plot from the data.

The method involves interpolating to a grid, using NaN to render the portion outside of the polar circle transparent.

This version adds two parameters to set the angle=0 location and whether angles increase clockwise or counter-clockwise.

#pragma rtGlobals=1     // Use modern global access method.
#include <MatrixToXYZ>, menus=0
#include <XYZToMatrix>, menus=0
#include <XYZToTripletToXYZ>, menus=0

Macro DisplayPolarImage(mat,degreesOrRadians,xIsAngle, angle0WhereStr, angleDirectionStr)
    String mat
    Prompt mat,"radius/angle matrix",popup,WaveList("*",";","DIMS:2")
    Variable degreesOrRadians=2 // initially radians
    Prompt degreesOrRadians,"angle units",popup,"degrees;radians;"  // 1,2
    Variable xIsAngle=1 // X Scaling
    Prompt xIsAngle,"Angle from",popup,"X scaling;Y scaling;"   // 1,2
    String angle0WhereStr= "right"  // 0 degrees
    Prompt angle0WhereStr, "Angle 0 at:", popup, "top;left;right;bottom;"
    String angleDirectionStr="counter-clockwise"
    Prompt angleDirectionStr, "Angles Increase:", popup, "clockwise;counter-clockwise;"
    Silent 1; PauseUpdate
    MatrixToXYZ(mat,mat,2,2)    // creates mat+"X", mat+"Y", mat+"Z" waves
    String zWave= mat+"Z"
    String angleWave, radiusWave

    if( xIsAngle == 1 ) // X dimension is angle
        angleWave= mat+"X"
        radiusWave= mat+"Y"
    else    // Y dimension is angle
        angleWave= mat+"Y"
        radiusWave= mat+"X"
    // WMRadiusAndAngleInRadianstoXY needs radians
    if( degreesOrRadians == 1 ) // degrees
        $angleWave *= pi/180    // convert to radians

    // Apply polar to rectangular conversion into an XYZ matrix
    Variable zeroAngleWhere=0
    if( CmpStr(angle0WhereStr,"top") == 0 )
        zeroAngleWhere= 90
    if ( CmpStr(angle0WhereStr,"left") == 0 )
        zeroAngleWhere= 180
    if ( CmpStr(angle0WhereStr,"bottom") == 0 )
        zeroAngleWhere= -90
    Variable angleDirection = 1 // clockwise
    if( CmpStr(angleDirectionStr, "counter-clockwise") == 0 )
        angleDirection= -1

    // Change of Variables
    String xWave= radiusWave
    String yWave= angleWave
    // Create and display a (rectangular) image from the resulting XY (circular) domain
    String matName= UniqueName(mat+"Image",1,0)
    XYZtoMatrix(xWave,matName,yWave,,zWave,,2,) // specify your own density and whether to display

// convert two waves in-place from radius, angle (in radians!) to x,y
Function WMRadiusAndAngleInRadianstoXY(rw,aw, zeroAngleWhereDegrees, positiveForClockwise)
    Wave rw,aw  // radius, angle in radians
    Variable zeroAngleWhereDegrees  // 0 is right, -90 is bottom, 90 is top, +/180 is left
    Variable positiveForClockwise
    Variable zeroAngleRadians= zeroAngleWhereDegrees * pi/180
    Variable isClockwise= positiveForClockwise > 0
    Variable i, n= numpnts(rw)
    Variable xx, yy
    for(i=0; i<n; i+=1 )
        Variable angle= aw[i]
        if( isClockwise )
            angle= zeroAngleRadians - angle
            angle= zeroAngleRadians + angle
        xx= rw[i] * cos(angle)
        yy= rw[i] * sin(angle)
        rw[i]= xx
        aw[i]= yy

Macro MakeDemoRadialMatrix()

    Variable nx=25
    Variable ny=50
    Make/O/N=(nx,ny) matrix
    SetScale x -180, 180, "deg", matrix     // x dimension is angle, +/- pi
    SetScale y 3,50,"m", matrix         // y dimension is radius, 3 to 50
    matrix=  y * sin(x/180*pi) * sin(x/180*pi)
    Newimage matrix
    ModifyGraph nticks(top)=5




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