RE: [Flashcoders] OT: Need math help
I wonder if someone would be willing to help me off-list with a math problem or can refer me to a more appropriate person/list to ask this question: I have a photograph of a rectangle where the camera was slightly off-center and not parallel to the plane of the rectangle, so in the resulting photo, the rectangle is slightly distorted. I want to distort the image by repositioning the corner points of the photograph so that the interior rectangle is precisely positioned and sized. 1) I know the size of the photo, 2) I know the coordinates of the rectangle's corners in the photo 3) I know the coordinates where I want the rectangle's corners to be after the transformation. I need to know the new coordinates of the photo's corners to achieve #3. Just an addendum to my previous email: I didn't think it through properly. My note about the affine transformations said it all: I forgot perspective. I don't have time right now to think about the full answer, which may involve a 4x4 matrix (in order to take into account the third dimension). But there's probably an easier solution. Danny ___ Flashcoders@chattyfig.figleaf.com To change your subscription options or search the archive: http://chattyfig.figleaf.com/mailman/listinfo/flashcoders Brought to you by Fig Leaf Software Premier Authorized Adobe Consulting and Training http://www.figleaf.com http://training.figleaf.com
RE: [Flashcoders] OT: Need math help
I wonder if someone would be willing to help me off-list with a math problem or can refer me to a more appropriate person/list to ask this question: I have a photograph of a rectangle where the camera was slightly off-center and not parallel to the plane of the rectangle, so in the resulting photo, the rectangle is slightly distorted. I want to distort the image by repositioning the corner points of the photograph so that the interior rectangle is precisely positioned and sized. 1) I know the size of the photo, 2) I know the coordinates of the rectangle's corners in the photo 3) I know the coordinates where I want the rectangle's corners to be after the transformation. I need to know the new coordinates of the photo's corners to achieve #3. I don't know if you got the offlist answer you asked for, but it's probably a question worth answering on-list too. Basically what you need to do is to invert a transformation matrix. So you need to start by constructing the matrix M used to transform the original rectangle R = (0,-H,W,0) to the distorted rectangle: that is (using homogeneous coordinates (the kind used in Flash's own Matrix object)), M maps (0,0,1) to (x1,y1,1), (0,-H,1) to (x2,y2,1), (W,-H,1) to (x3,y3,1) and (W,0,1) to (x4,y4,1). This matrix *ought* to be given by: ( (x1-x2)/H (x4-x1)/W x1) ( (y1-y2)/H (y4-y1)/W y1) ( 0 0 1 ) I say 'ought' because if your camera has a non-parallel distortion, this matrix may fail to correctly transform the fourth point to (x3,y3,1). If that's true, there's no matrix that will work (all matrix transformations are affine, meaning they transform parallel lines into parallel lines). Once you have this matrix M, you can invert it to get M'(If you can't do that, I can explain how) and apply M' to the corners of your image to get your un-transformed rectangle. Best Danny ___ Flashcoders@chattyfig.figleaf.com To change your subscription options or search the archive: http://chattyfig.figleaf.com/mailman/listinfo/flashcoders Brought to you by Fig Leaf Software Premier Authorized Adobe Consulting and Training http://www.figleaf.com http://training.figleaf.com
Re: [Flashcoders] OT: Need math help
I'm not going to pretend to know what you guys are talking about, but you may be able to garner some useful info from this Distort Image class... http://sandy.media-box.net/blog/distortimage-20-the-fastest-way-to-freely-distort-image-with-flash-in-actionscript.html dunc On 7/13/06, Danny Kodicek [EMAIL PROTECTED] wrote: I wonder if someone would be willing to help me off-list with a math problem or can refer me to a more appropriate person/list to ask this question: I have a photograph of a rectangle where the camera was slightly off-center and not parallel to the plane of the rectangle, so in the resulting photo, the rectangle is slightly distorted. I want to distort the image by repositioning the corner points of the photograph so that the interior rectangle is precisely positioned and sized. 1) I know the size of the photo, 2) I know the coordinates of the rectangle's corners in the photo 3) I know the coordinates where I want the rectangle's corners to be after the transformation. I need to know the new coordinates of the photo's corners to achieve #3. I don't know if you got the offlist answer you asked for, but it's probably a question worth answering on-list too. Basically what you need to do is to invert a transformation matrix. So you need to start by constructing the matrix M used to transform the original rectangle R = (0,-H,W,0) to the distorted rectangle: that is (using homogeneous coordinates (the kind used in Flash's own Matrix object)), M maps (0,0,1) to (x1,y1,1), (0,-H,1) to (x2,y2,1), (W,-H,1) to (x3,y3,1) and (W,0,1) to (x4,y4,1). This matrix *ought* to be given by: ( (x1-x2)/H (x4-x1)/W x1) ( (y1-y2)/H (y4-y1)/W y1) ( 0 0 1 ) I say 'ought' because if your camera has a non-parallel distortion, this matrix may fail to correctly transform the fourth point to (x3,y3,1). If that's true, there's no matrix that will work (all matrix transformations are affine, meaning they transform parallel lines into parallel lines). Once you have this matrix M, you can invert it to get M'(If you can't do that, I can explain how) and apply M' to the corners of your image to get your un-transformed rectangle. Best Danny ___ Flashcoders@chattyfig.figleaf.com To change your subscription options or search the archive: http://chattyfig.figleaf.com/mailman/listinfo/flashcoders Brought to you by Fig Leaf Software Premier Authorized Adobe Consulting and Training http://www.figleaf.com http://training.figleaf.com ___ Flashcoders@chattyfig.figleaf.com To change your subscription options or search the archive: http://chattyfig.figleaf.com/mailman/listinfo/flashcoders Brought to you by Fig Leaf Software Premier Authorized Adobe Consulting and Training http://www.figleaf.com http://training.figleaf.com
