From: Dr. Olaf Hoffmann <Dr.O.Hoffmann@gmx.de>

Date: Thu, 9 Apr 2009 13:40:26 +0100

To: www-style@w3.org

Message-Id: <200904091440.26421.Dr.O.Hoffmann@gmx.de>

Date: Thu, 9 Apr 2009 13:40:26 +0100

To: www-style@w3.org

Message-Id: <200904091440.26421.Dr.O.Hoffmann@gmx.de>

>There is a well known cubic-bezier *parametric* formula but it is a >function of P(t) [1] where 't' is 'time' or 'step' value but not that >'Input Percentage' as it is shown on the image. In parametric form >Bezier curves are uniquely determined so you can use them as X(t), Y(t) >but in Y(x) form Bezier function is ambiguous. > >Cheers. > >-- >Andrew Fedoniouk. This is the same (apart from the wrong wording percentage) as for SMIL/SVG animation with calcMode spline. There is no explicit time dependency of the value provided with the control points. Both time and the value are functions of a parameter running from 0 to 1. Because especially the function for the time has to be monoton due to our current understanding of spacetime and the abilities of viewers (which act in this spacetime), there are restrictions on the possible values of the control points to be in the range 0 to 1. To have something like a bouncing effect or a harmonic oscillation, the best approach is to use more than just one set of values and control points - what is possible with animation, but not with transitions, having only two values. However, for a motion for example, one still has to ensure, that the values list contains the extreme points, therefore at least with SMIL/SVG it is often simpler to use animateMotion to move something along an arbitrary 2D-path instead of calculating the motion in x and y direction independently and with splines. I think, there are other sets of (normed) polynomes for example (with an explicit time depencence) with the possibility of a none monoton behaviour for the values. With them it should be possible too to restrict the result to the range between the initial and the final value without the need of a monoton function. They might be useful for transitions, those cubic curves are however very useful for the general animation case. OlafReceived on Thursday, 9 April 2009 12:51:31 UTC

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