note 95472 added to function.imageantialias

There's a minor edit bug in those lines in the fast algorithm ("20 times faster"): imageLine( $img, $cx + $ix, $cy + $iy - 1, $cx + $ix, $cy + $ix, $fill ); imageLine( $img, $cx + $ix, $cy - $iy + 1, $cx + $ix, $cy - $ix, $fill ); imageLine( $img, $cx - $ix, $cy + $iy - 1, $cx - $ix, $cy + $ix, $fill ); imageLine( $img, $cx - $ix, $cy - $iy + 1, $cx - $ix, $cy - $ix, $fill ); imageLine( $img, $cx + $iy - 1, $cy + $ix, $cx + $ix, $cy + $ix, $fill ); imageLine( $img, $cx + $iy - 1, $cy - $ix, $cx + $ix, $cy - $ix, $fill ); imageLine( $img, $cx - $iy + 1, $cy + $ix, $cx - $ix, $cy + $ix, $fill ); imageLine( $img, $cx - $iy + 1, $cy - $ix, $cx - $ix, $cy - $ix, $fill ); the reference to "$ix" in the parameters of each call (just before the ", $fill " parameter) should be sometimes "$iy". This algorithm uses the Bresenham midpoint algorithm for circles, but computing successive pixels positions ($ix, $iy) incrementally in the first octant, relative to the circle center ($cx, $cy), then applying the 8 symetries by swapping them or changing signs. A similar algorithm exists for ellipses: it uses quadrants symetries instead of octants when the ellipse focal axis is aligned or orthogonal to the two image axis, be subdividing each quadrant in two regions (deminited by the point on the arc where the tangent has a unitary slope). For general ellipses (rotated arbitrarily in the plane), there are also 4 quadrants symetries, but they are a bit more complex to compute, as you need to compute the rotations, for this reason you'll only be able to use 2 symetries, but the incremental algorithm still exists: you may think that this would be based on the evaluation of the sum of lengths from the two focal points, which is contant; however the sum of two distance cannot be squared so easily (you would need to compute the square of both distances, then take their respective square root before adding them and testing the difference with the exact length. A cleaner solution uses NURBS (Non-Uniform Rational B-splines) because they are numerically stable and still very fast to compute (you only need some floatting point for the knot constants that separate each quadrant, which is then computed using a simple quadratic parametric equation of the ellipse instead of the implicit equation, given that the quadratic (polynomial) equation has first and scond derivatives that are easy to bound in order to get the needed precision and reduce the number of unnecessary pixel plots : such the parametric eqaution will draw points along the arc with a movement speed varying between 1 and 4 subpixel distance per incremental step, but in fact only between 1 and 2 subpixels when you subdivide the quadrant in two regions). Alternatively, you may also draw an antialised "straight" ellipse with a double resolution, and then rotate the antiliased image while also rescale it at half size, and at the same time combining it to the target: depending on implementations (and computing language used), it may be faster (but it may require more memory for the intermediate image at scale 2)... ---- Server IP: 69.147.83.197 Probable Submitter: 79.82.50.170 ---- Manual Page -- http://www.php.net/manual/en/function.imageantialias.php Edit -- https://master.php.net/note/edit/95472 Del: integrated -- https://master.php.net/note/delete/95472/integrated Del: useless -- https://master.php.net/note/delete/95472/useless Del: bad code -- https://master.php.net/note/delete/95472/bad+code Del: spam -- https://master.php.net/note/delete/95472/spam Del: non-english -- https://master.php.net/note/delete/95472/non-english Del: in docs -- https://master.php.net/note/delete/95472/in+docs Del: other reasons-- https://master.php.net/note/delete/95472 Reject -- https://master.php.net/note/reject/95472 Search -- https://master.php.net/manage/user-notes.php