Pixel corner at stellar disk edge misclassified as fully outside of the star

[d-giles]

In an edge case where the pixel is just touching the stellar disk on one corner, the pixeloverlaparea method misclassifies the pixel as completely outside the stellar disk

The original condition below is to blame, which I would guess originates from an arithmetic error (at least, I'm unable to derive the condition as given)

#radial distance squared minus 1
rsq = x0**2 + y0**2 - 1.

#calculate area of overlap between pixel and sky-projected stellar disk
if rsq > ((sqrt2*w)):
    #pixel is guaranteed to be fully outside the star
    area = 0.0
    #print "outside"

A fix for this condition is the following:

pix_r = (x0**2 + y0**2)**0.5
pix_rc = ((abs(x0)+w/2)**2 + (abs(y0)+w/2)**2)**0.5
if (pix_r >= 1+w/SQRT2) or (abs(x0) >= (1+w/2)) or (abs(y0) >= (1+w/2)):
    # pixel is guaranteed to be fully outside the star
    if verbose: print("Pixel outside")
    area = 0.0
    return area

A similar issue occurs when the pixel is within the stellar disk with a corner just shy of the edge, but this is not an issue since the condition is not met and no intersections default to being fully within the disk.

Demonstration of issue:

    w     = 0.5
    x0    = 1/sqrt2+w/2-.06
    y0    = 1/sqrt2+w/2
    rsq   = x0**2+y0**2-1
    pix_r = (x0**2+y0**2)**0.5

cGrid condition:

rsq    > sqrt2*w
0.7209 > 0.7071 - True, will not look for intersections

New condition:

pix_r  >= 1+w/sqrt2
1.3118 >= 1.3536 - False, will look for intersections

Area of overlap = 0.000542

Percent of full pixel = 0.682%