[whatwg] Canvas arcTo

[Philip Taylor]

As implemented, the operation of arcTo in Firefox (2, 3) and Opera
(9.2, 9.5) is utterly unrelated to the spec and arguably crazy. At
least Opera has the right spirit and tries drawing arcs between
points, though they're the wrong points and they're always
semicircles. Safari nearly matches the spec, and it's still sensible
when it disagrees with the spec, so that's the only one that's
relevant to consider. There are some examples at
<http://canvex.lazyilluminati.com/misc/arcto.html>.

"If the point (x2, y2) is on the line defined by the points (x0, y0)
and (x1, y1) then the method must do nothing, as no arc would satisfy
the above constraints." - why would no arc satisfy the constraints? If
P0, P1, P2 are collinear and non-coincident, then (I think) any of the
(infinitely many) circles which have the given radius and touch
tangential to the line P0->P2 will satisfy the constraints (i.e. being
tangential to P0->P1 at some point and to P1->P2 at some point).

When P0->P1 and P1->P2 are parallel and the same direction, Safari
just draws the line P0->P1. When they are parallel but opposing
directions, it instead draws a line from P0 to a point infinitely far
from P0 in the direction P1->P2. That is sensible in both cases since
it's equal to the limit as the two lines tend towards parallelism.

If P0=P1 (and either P2=P1 or P2!=P1) then Safari does nothing at all
and does not add any points to the subpath (or, equivalently, it does
add the point P1 to the subpath, which has no effect since the line
P0->P1 has zero length). If P1=P2 and P0!=P1, then it adds the point
P1 to the subpath. Both of these seem generally sane - there's no
sensible limit as the points tend towards coincidence, so there's no
real correct answer, and drawing the straight line P0->P1 seems an
adequate thing to do.

"Negative or zero values for radius must cause the implementation to
raise an INDEX_SIZE_ERR exception." - why not allow zero? You just get
an arc at P1 with zero length, with the start and end tangent points
both at P1, so the effect would be a straight line from P0 to P1,
without needing to handle it as a special case. Safari works like
that.

So, I think the following definition would cover all the cases and match Safari:

"""
The arcTo(x1, y1, x2, y2, radius) method must do nothing if the
context has no subpaths. If the context does have a subpath, then the
behaviour depends on the arguments and the last point in the subpath.

Let the point (x0, y0) be the last point in the subpath. If x0=x1 and
y0=y1, then the method must do nothing. Otherwise, if x1=x2 and y1=y2,
or if the line defined by the points (x0, y0) and (x1, y1) is parallel
and in the same direction as the line defined by the points (x1, y1)
and (x2, y2), then the method must connect the point (x0, y0) to the
point (x1, y1) by a straight line and add the point (x1, y1) to the
subpath.

Otherwise, if the line defined by the points (x0, y0) and (x1, y1) is
parallel and in the opposite direction to the line defined by the
points (x1, y1) and (x2, y2), then the method must connect the point
(x0, y0) to the point obtained by extending an infinite distance from
(x0, y0) in the direction of the line defined by (x1, y1) and (x2,
y2), and add that new point to the subpath.

Otherwise, let The Arc be the shortest arc given by the circumference
of the circle that has one point tangent to the line defined by the
points (x0, y0) and (x1, y1), another point tangent to the line
defined by the points (x1, y1) and (x2, y2), and that has radius
radius. The points at which this circle touches these two lines are
called the start and end tangent points respectively. The method must
connect the point (x0, y0) to the start tangent point by a straight
line, then connect the start tangent point to the end tangent point by
The Arc, and finally add the start and end tangent points to the
subpath.

Negative values for radius must cause the implementation to raise an
INDEX_SIZE_ERR exception.
"""

-- 
Philip Taylor
excors at gmail.com