On 2014-06-02, 9:59 AM, Rik Cabanier wrote:
On Mon, Jun 2, 2014 at 9:05 AM, Nick Alexander <nalexan...@mozilla.com <mailto:nalexan...@mozilla.com>> wrote: On 2014-06-02, 4:59 AM, Robert O'Callahan wrote: On Mon, Jun 2, 2014 at 3:19 PM, Rik Cabanier <caban...@gmail.com <mailto:caban...@gmail.com>> wrote: isIdentity() indeed suffers from rounding errors but since it's useful, I'm hesitant to remove it. In our rendering libraries at Adobe, we check if a matrix is *almost* identity. Maybe we can do the same here? One option would be to make "isIdentity" and "is2D" state bits in the object rather than predicates on the matrix coefficients. Then for each matrix operation, we would define how it affects the isIdentity and is2D bits. For example we could say translate(tx, ty, tz)'s result isIdentity if and only if the source matrix isIdentity and tx, ty and tz are all exactly 0.0, and the result is2D if and only if the source matrix is2D and tz is exactly 0.0. With that approach, isIdentity and is2D would be much less sensitive to precision issues. In particular they'd be independent of the precision used to compute and store store matrix elements, which would be helpful I think. I agree that most mathematical ways of determining a matrix (as a rotation, or a translation, etc) come with isIdentity for free; but are most matrices derived from some underlying transformation, or are they given as a list of coefficients? You can do it either way. Here are the constructors: http://dev.w3.org/fxtf/geometry/#dom-dommatrix-dommatrix So you can do: var m = new DOMMatrix(); // identity = true, 2d = true var m = new DOMMatrix("translate(20 20) scale(4 4) skewX"); // identity = depends, 2d = depends var m = new DOMMatrix(otherdommatrix; // identity = inherited, 2d = inherited var m = new DOMMatrix([a b c d e f]); // identity = depends, 2d = true var m = new DOMMatrix([m11 m12... m44]); // identity = depends, 2d = depends If the latter, the isIdentity flag needs to be determined by the constructor, or fed as a parameter. Exactly how does the constructor determine the parameter? Exactly how does the user? The constructor would check the incoming parameters as defined: http://dev.w3.org/fxtf/geometry/#dom-dommatrixreadonly-is2d http://dev.w3.org/fxtf/geometry/#dom-dommatrixreadonly-isidentity
Thanks for providing these references. As an aside -- it worries me that these are defined rather differently: is2d says "are equal to 0", while isIdentity says "are '0'". Is this a syntactic or a semantic difference?
But, to the point, the idea of "carrying around the isIdentity flag" is looking bad, because we either have that A*A.inverse() will never have isIdentity() == true; or we promote the idiom that to check for identity, one always creates a new DOMMatrix, so that the constructor determines isIdentity, and then we query it. This is no better than just having isIdentity do the (badly-rounded) check.
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