It should perhaps be explained that the joining arc must be outside the convex hull locally around the terminating points, which condition holds for the ccw arc only.
Chris -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Philip Taylor Sent: Saturday, February 02, 2008 11:21 PM To: Kristof Zelechovski Cc: WHATWG Subject: Re: [whatwg] Canvas line styles comments On 02/02/2008, Kristof Zelechovski <[EMAIL PROTECTED]> wrote: > You considered the convex hull of the original lines to get that paradox; > I had the stroke path segments in mind. > (Stroke path segments are the path equivalent of the stroked curve > when the stroke operator is not allowed and must be replaced by the fill > operator). > Each line corresponds to two parallel stroke path segments; > two of them intersect and the other two get joint with an arc. > One of the possible arcs is in the convex hull of those stroke path > segments. If the two lines are very short, their stroke paths will (if I understand correctly) look like .-. | | | | | | .-----|-*-------. '-----|-|-------' | | | | '-' where the * is the join point and the short lines are the two parallel stroke path segments of each line. Then the convex hull is nearly a square rotated by 45 degrees, like .-. /| |'- / | | '- / | | '-. .-----|-*-------. '-----|-|-------' '. | | .-' '-.| |_.-' '-' and so an arc with radius lineWidth/2 from the rightmost point going clockwise to the upmost point will not be contained entirely within that nearly-square. So neither arc is within the convex hull. -- Philip Taylor [EMAIL PROTECTED]
