From: Edward Lee <edilee@mozilla.com>

Date: Fri, 15 May 2009 00:43:03 -0500

Message-ID: <dc07ed930905142243y3ab88ac7wca318b0065472c6c@mail.gmail.com>

To: www-style@w3.org

Date: Fri, 15 May 2009 00:43:03 -0500

Message-ID: <dc07ed930905142243y3ab88ac7wca318b0065472c6c@mail.gmail.com>

To: www-style@w3.org

"The four values specify points P1 and P2 of the curve as (x1, y1, x2, y2). All values must be in the range [0, 1] or the definition is invalid." If the [0, 1] constraints were removed for y1 and y2, one could describe a curve that overshoots and/or undershoots then returns to the final destination. A simple example would be P1 = (0, 0); P2 = (1, 7/3) where it reaches 100% out at 50% time then overshoots and returns to 100% out at 100% time. The [0, 1] constraints for x1 and x2 would still need to remain to make sure there's no going backwards in time -- repeated input%; but there wouldn't be any problems of a repeated output%. Some values would need to be capped at a max/min, but things like length are fine. So the bézier curve is described by.. [ x ] = [ x1 * 3t(1-t)^2 + x2 * 3(1-t)t^2 + t^3 ], t = 0..1 [ y ] [ y1 * 3t(1-t)^2 + y2 * 3(1-t)t^2 + t^3 ] Removing the [0, 1] constraint for y1 and y2 won't change the fact that the start and end will always be 0 and 1 respectively. Keeping them for x1 and x2 retains the monotonically increasing curve from 0 to 1. EdReceived on Friday, 15 May 2009 06:27:17 GMT

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