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Editorial Team
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Asked: 2026-05-31T11:45:10+00:00

SVG’s elliptical arc curve path command takes 9 parameters: implicit current X and Y,

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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?

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1 Answer

  1. Editorial Team

    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).

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