On 17/05/07, Philip Taylor <[EMAIL PROTECTED]> wrote:
On 16/05/07, Ian Hickson <[EMAIL PROTECTED]> wrote:
> For arc() and arcTo() the definition seems complete, but I'm not familiar
> enough with graphics theory to know what quadraticCurveTo() and
> bezierCurveTo() need. Could you suggest some text?
I'd probably just add the equations of the curves kind of like:
"""
The quadraticCurveTo(cpx, cpy, x, y) method must do nothing if the
context has no subpaths. Otherwise it must connect the last point in
the subpath to the given point (x, y) by a quadratic curve with
control point (cpx, cpy), and must then add the given point (x, y) to
the subpath. The curve must cover the points $C(t) = (1-t)^2 P_0 + 2 t
(1-t) P_1 + t^2 P_2$ with t ranging from 0 to 1, where P_0 is the last
point in the subpath, P_1 is the control point (cpx, cpy), and P_2 is
the point (x, y).
The bezierCurveTo(cp1x, cp1y, cp2x, cp2y, x, y) method must do nothing
if the context has no subpaths. Otherwise, it must connect the last
point in the subpath to the given point (x, y) using a Bézier curve
with control points (cp1x, cp1y) and (cp2x, cp2y). Then, it must add
the point (x, y) to the subpath. The curve must cover the points $C(t)
= (1-t)^3 P_0 + 3 t (1-t)^2 P_1 + 3 t^2 (1-t) P_2 + t^3 P_3$ with t
ranging from 0 to 1, where P_0 is the last point in the subpath, P_1
is the control point (cp1x, cp1y), P_2 is the control point (cp2x,
cp2y), and P_3 is the point (x, y).
"""
(Also s/bezier/Bézier/)
Actually, since I now better understand what "Bézier curve" means, I'd
say something more like
"""
The quadraticCurveTo(cpx, cpy, x, y) method [...] must connect the
last point in the subpath to the given point (x, y) using a quadratic
Bézier curve with control point (cpx, cpy) [...]
The bezierCurveTo(cp1x, cp1y, cp2x, cp2y, x, y) method [...] must
connect the last point in the subpath to the given point (x, y) using
a cubic Bézier curve with control points (cp1x, cp1y) and (cp2x, cp2y)
[...]
"""
and probably not bother with giving equations, since "quadratic Bézier
curve" and "cubic Bézier curve" are sufficiently well-known and
well-defined (unlike the old "quadratic curve" which seems to be an
undefined or differently-defined term, and the old "Bézier curve"
which is a whole family of curves of varying degrees).
--
Philip Taylor
[EMAIL PROTECTED]
