[whatwg] Canvas line styles comments

Kristof Zelechovski giecrilj at stegny.2a.pl
Sun Feb 3 00:59:46 PST 2008

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.


-----Original Message-----
From: whatwg-bounces at 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
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

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