Is SVG elliptical arc curve path command overdetermined?

2
votes

SVG's elliptical arc curve path command takes 9 parameters: implicit current X and Y, rx (x-radius), ry (y-radius), x-axis-rotation, large-arc-flag, sweep-flag, x (endpoint-x), y (endpoint-y). Lets ignore the two "flag" parameters that I believe to be unimportant for my question. Then 7 parameters remain.

Now my question is: is the ellipse overdetermined or not? I just believe that it is, because providing too small rx and ry and an endpoint which is too far the the current point will result in no solution. Thinking this way, only a subset of parameter space forms valid arches, hence the ellipse is overdetermined.

On the other hand, I'm not a geometry expert and I know that SVG is a well-thought-out standard, suggesting that I am wrong. Am I or not?

1
pathsvgcommandellipsegeometric-arc
I was wrong and now I see why. rx and ry parameters are actually not absolute, but relative, they determine ratio. Sadly, I am unable to find this in the standard. – Tregoreg
The standards are very difficult to follow – Chasbeen
It might say somewhere that where parameters are inconsistent that defauts are used to override.. – Chasbeen

1 Answers

2
votes

Per http://www.w3.org/TR/SVG/implnote.html#ArcOutOfRangeParameters

If rx, ry and φ are such that there is no solution (basically, the ellipse is not big enough to reach from (x1, y1) to (x2, y2)) then the ellipse is scaled up uniformly until there is exactly one solution (until the ellipse is just big enough).