Polar Coordinates

BlitzMax Forums/BlitzMax Programming/Polar Coordinates

Krischan (Posted 2012) [#1]

I have a problem simulating the Photoshop Polar Coordinates functions "Rectangular to Polar" and "Polar to Rectangular". It doesn't look correct and I don't know why. Can anybody help? You need two images, the "ps.png" is a screenshot from Photoshop how it should look like after. EDIT: fixed it somehow but still buggy, changed the images to show the problem in a better way uv.png ps.png My current output SuperStrict Framework BRL.GLMax2D Import BRL.GLMax2D Import BRL.PNGloader Import BRL.Pixmap Graphics 768,512 Cls Local image:TPixmap=LoadPixmap("uv.png") Local polar:TPixmap=CreatePixmap(256,256,PF_RGBA8888) Local back:TPixmap=CreatePixmap(256,256,PF_RGBA8888) Local x:Float,y:Float,r:Float,q:Float Local xx:Float,yy:Float Local rgb:Int For x=0 To 255 Step 0.25 For y=0 To 255 Step 0.25 rgb=ReadPixel(image,255-x,y) r=y q=Normalize(x,0,255,0,360)-90 xx=r*Cos(q)/2.0 yy=r*Sin(q)/2.0 WritePixel(polar,128+xx,128+yy,rgb) Next Next For x=0 To 255 For y=0 To 255 r=y q=Normalize(x,0,255,0,360) xx=r*Cos(q)/2.0 yy=r*Sin(q)/2.0 rgb=ReadPixel(polar,128+xx,128+yy) WritePixel(back,x,y,rgb) Next Next Local ps:TPixmap=LoadPixmap("ps.png") While Not KeyDown(KEY_ESCAPE) Cls DrawPixmap(image,0,0) DrawPixmap(polar,256,0) DrawPixmap(back,512,0) DrawPixmap(ps,0,256) Flip False Wend End Function Normalize:Float(value:Float=128.0,value_min:Float=0.0,value_max:Float=255.0,norm_min:Float=0.0,norm_max:Float=1.0) Return ((value-value_min)/(value_max-value_min))*(norm_max-norm_min)+norm_min End Function Last edited 2012

Warpy (Posted 2012) [#2]

Here you go. I've explained it a tiny bit, but there's a lot of trigonometry and so on. It really needs some diagrams to fully explain, but I don't have the time. SuperStrict Framework BRL.GLMax2D Import BRL.GLMax2D Import BRL.PNGloader Import BRL.Pixmap Graphics 768,512 Cls Local image:TPixmap=LoadPixmap("uv.png") Local polar:TPixmap=CreatePixmap(256,256,PF_RGBA8888) Local back:TPixmap=CreatePixmap(256,256,PF_RGBA8888) Local x:Float,y:Float,r:Float,q:Float,maxr:Float Local xx:Float,yy:Float Local rgb:Int 'instead of drawing a pixel on the polar image for each pixel in the source, 'for each pixel on the polar image, find its corresponding pixel in the source 'this ensures that all of the polar image is coloured in For x=0 To 255 For y=0 To 255 If x=128 And y=128 'deal with the centre of the image q = 0 r = 0 Else xx = 128-x yy = y-128 q = ATan2(yy,xx)+90 'get the angle of this point r = Sqr(xx*xx+yy*yy) 'get the distance from the centre 'the radius is stretched to the edge of the square. Find how far that is, and scale accordingly If Abs(xx)>Abs(yy) maxr = Abs(r * 128.0/xx) Else maxr = Abs(r*128.0/yy) EndIf r :* 255.0/maxr 'make it so the radius for this angle goes from 0-255 instead of 0-maxr If q<0 Then q:+360 'make sure the angle is positive q :* 255.0/360 'then scale 0-360 down to 0-255 EndIf rgb=ReadPixel(image,q,r) 'read from the calculated co-ordinates in the source image WritePixel(polar,x,y,rgb) Next Next 'same idea, but we're doing the opposite transformation For x=0 To 255 For y=0 To 255 q = 270-x*360.0/255 'get the angle for this point xx = Cos(q) '(xx,yy) is a vector pointing in the right direction, but we need to scale it yy = Sin(q) If Abs(xx)>Abs(yy) maxr = Abs(127/xx) Else maxr = Abs(127/yy) EndIf r = y*maxr/255 'get the radius xx:*r 'scale the vector by the radius yy:*r rgb=ReadPixel(polar,xx+128,yy+128) 'read the corresponding pixel from the polar image WritePixel(back,x,y,rgb) Next Next Local ps:TPixmap=LoadPixmap("ps.png") While Not KeyDown(KEY_ESCAPE) Cls DrawPixmap(image,0,0) DrawPixmap(polar,256,0) DrawPixmap(back,512,0) DrawPixmap(ps,0,256) Flip False Wend End

Krischan (Posted 2012) [#3]

Thanks, that is even more complex than I thought. Your version outputs a slightly different image than PS, still with a noticable vertical line in the middle on the upper right image (the polar to rectangular), but what could be the reason for that? Last edited 2012

Warpy (Posted 2012) [#4]

I reckon it's just differences in rounding errors or sampling from the source pixmap. The section at the top of the polar->rect image corresponds to the middle of the circle, so small errors can mean a big change in angle.

Krischan (Posted 2012) [#5]

If i take a different picture like an UV matrix it looks completely different, interesting. Just change the image names to uv2/ps2: uv2.png ps2.png Screenshot Your algorithm creates a quadratic "tunnel" effect while photoshop creates a round "tunnel" effect. Funny.

Noobody (Posted 2012) [#6]

Like this? SuperStrict Framework BRL.GLMax2D Import BRL.GLMax2D Import BRL.PNGloader Import BRL.Pixmap Graphics 768,512 Local Image:TPixmap = LoadPixmap("uv.png") Local PS :TPixmap = LoadPixmap("ps.png") Local Polar:TPixmap = CreatePixmap(256, 256, PF_RGBA8888) Local Back :TPixmap = CreatePixmap(256, 256, PF_RGBA8888) For Local X:Int = 0 Until 256 For Local Y:Int = 0 Until 256 Local A:Int = X - 128 Local B:Int = Y - 128 Local Angle:Float = ATan2(B, -A) Local Dist :Float = Min(Sqr(A*A + B*B)*2.0, 255.0) Angle = (Angle + 450.0) Mod 360.0 Local Q:Int = Int(Angle*255.0/360.0) Local R:Int = Int(Dist) If Not (A Or B) Then Q = 0 R = 0 EndIf Local RGB:Int = ReadPixel(Image, Q, R) WritePixel(Polar, X, Y, RGB) Next Next For Local X:Int = 0 Until 256 For Local Y:Int = 0 Until 256 Local Angle:Float = 270.0 - X*360.0/255.0 Local Dist:Float = Y*0.5 Local PolarX:Int = Int(Cos(Angle)*Dist) + 127 Local PolarY:Int = Int(Sin(Angle)*Dist) + 127 Local RGB:Int = ReadPixel(Polar, PolarX, PolarY) WritePixel(Back, X, Y, RGB) Next Next While Not KeyDown(KEY_ESCAPE) Cls DrawPixmap(Image, 0, 0) DrawPixmap(Polar, 256, 0) DrawPixmap(Back, 512, 0) DrawPixmap(PS, 0, 256) Flip Wend End

Krischan (Posted 2012) [#7]

Yes, that's it. Thanks!!!

xlsior (Posted 2012) [#8]

Now... What does one actually -use- polar coordinate transforms for?

Krischan (Posted 2012) [#9]

A lot of things. In my special case I try to create a random planet texture on the fly and the polar coordinates routine is used to help delete the pinching effect at the poles if you wrap it around a sphere. If you have Photoshop (or GIMP) you can try the following: - load a 2:1 resolution texture (ex. 512x256) - copy the upper half part (512x128) to a new image - stretch the image to 512x512 - apply Polar Coordinates "Rectangular to Polar" - delete the pinch effect in the image center (Blur or Stamp Tool) manually - apply Polar Coordinates "Polar to Rectangular" - resize the image back to 512x128 - copy the part over the original position back - turn the complete image 180° - start again with the upper half part (which is the lower half part) If done properly you'll get from the top texture the bottom texture which wraps seamless around a sphere while maintaing most of the detail in the equatorial area and has no pole pinch effect anymore. Other useful effects include exploding effects combined with wind filter if you rotate the texture 90° CW or CCW first: Last edited 2012

xlsior (Posted 2012) [#10]

Thanks for the nice example -- I never got into any of the 3D stuff, so didn't think about these kinds of problems/solutions.

* (Posted 2012) [#11]

@Krischan:Ya could make a brilliant Captain Blood game with that system :D