[whatwg] Canvas line styles comments

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: whatwg-bounces@lists.whatwg.org
[mailto:whatwg-bounces at lists.whatwg.org] 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 <giecrilj at stegny.2a.pl> 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
excors at gmail.com

Received on Sunday, 3 February 2008 00:59:46 UTC