Geometry Help - Rectangular Polar Transformation (From Cartesian or To Cartesian) [SOLVED OR NEARLY SOLVED]

Software G'MIC
1

At the moment, I do have the rectangular polar transform almost ready after I solved some quirks, but one issue do remain - After I move the point from which the transform use as a reference for output, the result goes out of bound.

To explain what is Rectangular Polar Image

image
image994×498 7.07 KB

Your output is generated from reading pixels going from the direction of these line. The greater the Y-Axis, the farther away from the center it’s going to be. When Y is 1, then the output would show that pixel to be located at the bottom of the image.Treat the X line as pixel scanning, and it is what determines the angle from the center when Y is greater than 0.

Transform Input/Output

To show how the result would look like when the transform affects a image when the centerpoint is located at 0,0 - let’s use a sample image:

Target Image

image

Transformed Image

image

The current G’MIC implementation

rep_polar_rectangular_transform:
skip ${1=.5},${2=.5}
f "
begin(
    point_x=$1*w;
    point_y=$2*h;
    inv_point_x=w-point_x;
    inv_point_y=h-point_y;
    cut_ang_s0=atan2(point_y,inv_point_x)*180/pi;
    cut_ang_s1=180-atan2(point_y,point_x)*180/pi;
    cut_ang_s2=180+abs(atan2(inv_point_y,point_x)*180/pi);
    cut_ang_s3=360-abs(atan2(inv_point_y,inv_point_x)*180/pi);
    distanceaway(value)=(
        if(value==0,w-point_x?w-point_x:1,
        if(value==1,h-point_y?h-point_y:1,
        if(value==2,point_x?point_x:1,
        if(value==3,point_y?point_y:1
        );
        );
        );
        );
    );
);
surface_angle=(x/w)*360;
sur_180=surface_angle-180*floor(surface_angle/180+(10^-8));
sur_90=sur_180>90?180-sur_180:sur_180;
if(surface_angle>cut_ang_s0&&surface_angle<=cut_ang_s1,side=1, #Top#
if(surface_angle>cut_ang_s1&&surface_angle<=cut_ang_s2,side=2, #Right#
if(surface_angle>cut_ang_s2&&surface_angle<=cut_ang_s3,side=3, #Bottom#
side=0; #Left#
);
);
);
orientation=side%2;
mdist=orientation?90-sur_90:sur_90;
mdist=1/cos((mdist/180)*pi);
dix=(point_x+cos((surface_angle/180)*pi)*distanceaway(side)*mdist*y/h)*((w-1)/w);
diy=(point_y+sin((surface_angle/180)*pi)*distanceaway(side)*mdist*y/h)*((h-1)/h);
i(dix,diy,z,c,1);
"

That being said, what exactly I’m doing wrong when using point location change. Why it goes out of bound?

EDIT: I fixed it for $1. Not for $2. That means result will be correct with $2=.5. If not, then result will be incorrect.

EDIT: I finally determine the cause of my issue has to do with the mdist line. I would need to figure how to create a gradient based on angle found. After that, this command would work.

3

Solved or almost solved!

Last post for this thread. Decided to not to try to solve micro-shifting, and call it a day with these command. You can consider it solved, but if micro-shifting is a big issue on preserved details, then consider it nearly solved, but I can’t do it.

#@cli rep_polrectrans_inv : eq. to 'rep_polar_rectangular_transform_inverse'. : (+)
rep_polrectrans_inv: rep_polar_rectangular_transform_inverse $*
#@cli rep_polar_rectangular_transform_inverse : -1>=_xpos<=1,-1>=_ypos<=1,_from_preserved_details={ 0=false | 1=true }
#@cli : Transform rectangular polar images into cartesian coordinates.
#@cli : (eq. to 'rep_polrectrans_inv').\n
#@cli : Warning: Without preservation of details, artifacts is a lot more visible.
#@cli : Default values: '_xpos=0','_ypos=0','_preserve_details=1'
rep_polar_rectangular_transform_inverse:
skip ${1=0},${2=0},${3=1}
if $1<-1||$1>1 error "($1>=-1&&$1<=1)=0" fi
if $2<-1||$2>1 error "($2>=-1&&$2<=1)=0" fi
if $3
    repeat $! l[$>]
        ov={[im,iM]}
        {w/2-h/2},{h/2},{d},{s},"
        begin(
            ww=w#0;
            hh=h#0;
            ox=ww/2-hh/2;
            oy=hh/2;
            sd=max(ww,hh)/min(ww,hh);
            sxf=ox<oy?sd:1;
            syf=ox<oy?1:sd;
            cx=.5+$1*.5;
            cy=.5+$2*.5;
            px=cx*ww;
            py=(1-cy)*hh;
            sxl=(ww/2)/px;
            sxr=(ww/2)/(ww-px);
            syt=(hh/2)/py;
            syb=(hh/2)/(hh-py);
        );
        xx=(x/(w-1))*ww;xx+=(xx/(ww-1)-.5)*-1;
        yy=(y/h)*hh;
        xl=-1+(xx/ww)*2*sxl;
        xr=1-(1-xx/(ww-1))*2*sxr;
        yt=-1+(yy/hh)*2*syt;
        yb=1-(1-yy/(hh-1))*2*syb;
        nxx=xx>px?xr:xl;
        nyy=yy>py?yb:yt;
        ay=max(abs(nxx),abs(nyy));
        ax=(atan2((yy/hh-(1-cy))*syf,(xx/ww-cx)*sxf)+pi)/(2*pi);
        i(#0,ax*ww,ay*hh,z,c,1,1);
        "
        n $ov
        k.
    endl done
else
    ov={[im,iM]}
    f "
    begin(
        sd=(max(w,h)/min(w,h));
        sx=w>h?sd:1;
        sy=w>h?1:sd;
        ww=w-1;
        hh=h-1;
        cx=.5+$1*.5;
        cy=.5+$2*.5;
        px=cx*w;
        py=(1-cy)*h;
        sxl=(w/2)/px;
        sxr=(w/2)/(w-px);
        syt=(h/2)/py;
        syb=(h/2)/(h-py);
    );
    xl=-1+(x/w)*2*sxl;
    xr=1-(1-x/w)*2*sxr;
    yt=-1+(y/h)*2*syt;
    yb=1-(1-y/h)*2*syb;
    xx=x>px?xr:xl;
    yy=y>py?yb:yt;
    ay=max(abs(xx),abs(yy));
    xx=(x/w)-cx;
    yy=(y/h)-(1-cy);
    ax=(atan2(yy*sy,xx*sx)+pi)/(2*pi);
    i(ax*ww,ay*hh,z,c,2,1);
    "
    n $ov
fi
#@cli rep_polrectrans : eq. to 'rep_polar_rectangular_transform'. : (+)
rep_polrectrans: rep_polar_rectangular_transform $*
#@cli rep_polar_rectangular_transform : -1>=_xpos<=1,-1>=_ypos<=1,_preserve_details={ 0=false | 1=true }
#@cli : Transform image into rectangular polar coordinates.
#@cli : (eq. to 'rep_polrectrans').\n
#@cli : Default values: '_xpos=0','_ypos=0','_preserve_details=1'
rep_polar_rectangular_transform:
skip ${1=0},${2=0},${3=1}
if $1<-1||$1>1 error "($1>=-1&&$1<=1)=0" fi
if $2<-1||$2>1 error "($2>=-1&&$2<=1)=0" fi
repeat $! l[$>]
    ov={[im,iM]}
    if $3 r {(w+h)*2},200%,100%,100%,1 fi #Resize to perimeter for width and double the height for height to preserve all the details in the original image using nearest-neighbor#
    f "
    begin(
        point_x=(($1*-1)*.5+.5)*w;
        point_y=($2*.5+.5)*h;
        inv_point_x=w-point_x;
        inv_point_y=h-point_y;
        cut_ang_s0=abs(atan2(inv_point_y,inv_point_x)*180/pi); #Find angle requirement to meet side#
        cut_ang_s1=180-abs(atan2(inv_point_y,point_x)*180/pi); #Find angle requirement to meet side#
        cut_ang_s2=180+abs(atan2(point_y,point_x)*180/pi);     #Find angle requirement to meet side#
        cut_ang_s3=360-abs(atan2(point_y,inv_point_x)*180/pi); #Find angle requirement to meet side#
        distanceaway(value)=(
            if(value==0,w-point_x, #Left#
            if(value==1,h-point_y, #Top#
            if(value==2,point_x,   #Right#
            if(value==3,point_y    #Bottom#
            );
            );
            );
            );
        );
    );
    surface_angle=(x/w)*360; #Convert into angle surface using x-coordinate#
    if(surface_angle>cut_ang_s0&&surface_angle<=cut_ang_s1,side=1, #Top#
    if(surface_angle>cut_ang_s1&&surface_angle<=cut_ang_s2,side=2, #Right#
    if(surface_angle>cut_ang_s2&&surface_angle<=cut_ang_s3,side=3, #Bottom#
                                                           side=0; #Left#
                                                                );
                                                                );
                                                                );
    mdist=abs(side%2?1/sin((surface_angle/180)*pi):1/cos((surface_angle/180)*pi));    #Find multiplier to distance based on angle to edge boundary#
    dix=(point_x+cos((surface_angle/180)*pi)*distanceaway(side)*mdist*y/h)*((w-1)/w); #x-coordinate#
    diy=(point_y+sin((surface_angle/180)*pi)*distanceaway(side)*mdist*y/h)*((h-1)/h); #y-coordinate#
    i(w-(dix+1),h-(diy+1),z,c,2); #Output using pixel coordinate with linear interpolation#
    "
    cut $ov
endl done