Polar Image

#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"
	endif
	
	// WMRadiusAndAngleInRadianstoXY needs radians
	if( degreesOrRadians == 1 )	// degrees
		$angleWave *= pi/180	// convert to radians
	endif

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

	// 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
End

// 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
		else
			angle= zeroAngleRadians + angle
		endif
		xx= rw[i] * cos(angle)
		yy= rw[i] * sin(angle)
		rw[i]= xx
		aw[i]= yy
	endfor
end

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
End