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

Date: Sun, 28 Sep 2008 18:09:17 +0200

To: www-svg@w3.org

Message-Id: <200809281809.17673.Dr.O.Hoffmann@gmx.de>

Date: Sun, 28 Sep 2008 18:09:17 +0200

To: www-svg@w3.org

Message-Id: <200809281809.17673.Dr.O.Hoffmann@gmx.de>

David Woolley: >Can you provide a concrete example. I would have though that, if the >inverse didn't exist, there will always be points that don't have a >unique image when the transform is reversed. If the determinant of the transformation matrix is zero, 2-dimensional and 1-dimensional structures are mapped to 1-dimensional structures or points. Just looking at the result, it is not possible to reverse such transformation, it is not a bijective function, just surjective. For example matrix(0 0 0 0 e f), matrix(1 1 1 1 e f), matrix(0 1 0 1 e f), matrix(1 0 1 0 e f), matrix(1 1 0 0 e f), matrix(0 0 1 1 e f) etc with e,f numbers have no inverse. Or in an animateTransform of the type scale one may try values="-1;1" - without keyTimes at 50% of active duration obviously the scaling is zero, the determinant too, but before and later there is an inverse again. Or if someone uses values="-1 1;0 2;0 -2;1 -1" this is not only one moment, it is a complete time interval without an inverse, but using the new vector-effect non-scaling-stroke a structure remains visible as a line (or point). As an application, if one rotates (with animateTransform of type rotate) an element with vector-effect non-scaling-stroke and scales one dimension to zero, the result is an exact representation of an harmonic oscillator, else only available as approximation in SVG, resulting from some number crunching. An author can use this to check the accuracy of such an approximation for example. And obviously if an element with transform="<transform-ref>" is inside such a structure, it is intended, that it remains unchanged as 2-dimensional object. An implementation cannot use the not existing inverse to get it unchanged, it has to do it in another way (what is practically not a big problem, because the document itself contains much more information about the transformation and structure than the CTM, or the implementation can extract such objects with constrained transformations in general, before they are transformed and just put them back for rendering only). Doing tests about this feature, for me such degenerate cases would be the first thing to explore, whether an implementation crashes or fails with this feature of constrained transformation or not. The second thing would be a skewX/Y around +-90 degree ;o) OlafReceived on Sunday, 28 September 2008 16:54:43 GMT

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