Re: Drawing Arcs
Re: Drawing Arcs
- Subject: Re: Drawing Arcs
- From: "Alastair J.Houghton" <email@hidden>
- Date: Sun, 6 Jul 2003 13:11:02 +0100
On Sunday, July 6, 2003, at 05:26 am, Jim Crafton wrote:
Hi again,
I am trying to draw an arc given the following where:
x1, y1, x2, y2 define the bounding rectangle of the arc. The arc
follows along the
ellipse that fits this rect
x3,y3 define the starting point which intersects with edge of arc and
the center of rect
x4,y4 define the ending point which intersects with edge of arc and
the center of rect
(for those with Win32 experience this is the same as Win32's Arc
function)
I notice that NSBezierPath can draw arcs that trace along a circle,
but not elliptical arcs. What's the best approach for tackling this?
You can use Bezier curves to approximate an arc; see
http://www.tinaja.com/cubic01.asp (in particular, see
http://www.tinaja.com/glib/bezarc1.pdf for a solution to the problem of
fitting a cubic Bezier curve to a circular arc; remember that an
elliptical arc is the same but for a constant factor). Also check out
the comp.graphics.algorithms FAQ, at
http://www.faqs.org/faqs/graphics/algorithms-faq/ (see section 4.04).
An alternative would be to approximate the arc with straight line
segments (similar to the standard algorithms for rendering Bezier
curves, in fact); for example, you could compute points on the arc
(using the parametric formula for an ellipse), and continue to
subdivide until you find a chord whose gradient is approximately
constant, then render it as a straight line segment.
The one thing you *can't* do is to use a transformation to distort a
circular arc, because in Quartz things like line width, dash patterns
etcetera are _geometric_ attributes (on most other systems, Win32
included AFAIK, such things are _cosmetic_ attributes, which means that
they are not affected by geometric transformation; Quartz is a more
advanced graphics subsystem and as such, line styles etcetera *are*
affected by any transformations in effect).
Kind regards,
Alastair.
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