From: /#!/JoePea <trusktr@gmail.com>

Date: Mon, 4 Jan 2016 17:15:03 -0800

Message-ID: <CAKU1PAUNuHW3HHCYpv95oHHruS31BWHFg9C=r8wUKa7+w2xA4g@mail.gmail.com>

To: public-fx@w3.org

Date: Mon, 4 Jan 2016 17:15:03 -0800

Message-ID: <CAKU1PAUNuHW3HHCYpv95oHHruS31BWHFg9C=r8wUKa7+w2xA4g@mail.gmail.com>

To: public-fx@w3.org

It seems like Famous 0.3.x (https://github.com/Famous/famous) does less calculations, and ends with the same results. When rotating around Z, using Famous' `Transform.rotateZ(45 * Math.PI/180)`, we get the same value for m11 as we do with `DOMMatrix.rotate(45)`. Here's what Famous is doing: https://github.com/Famous/famous/blob/develop/src/core/Transform.js#L284-L306 We see the value for m11 is calculated as ``` x * x * (1 - Math.cos(theta)) + Math.cos(theta) ``` (inferred by replacing all the variables with their actual calculations). In DOMMatrix, the value for m11 is calculated as ``` 1-2*(y*y + z*z)*Math.pow(Math.sin(angle/2 * Math.PI/180), 2) ``` . If we assume radians in the calculation, that is ``` 1-2*(y*y + z*z)*Math.pow(Math.sin(theta/2), 2) ``` , which can be written as ``` 1-2*(y*y + z*z)*Math.sin(theta)*Math.sin(theta) ``` . Now, comparing the two, we see that the Famous Transform calculation has 6 steps and the DOMMatrix calculation has 9 steps, so the Famous Transform calculations may be faster. If we simplify each calculation (Trnsform and DOMMatrix m11 rotation, assuming we are rotating around the Z axis), then both formulas become, respectively: ``` Math.cos(theta) ``` and ``` 1-2*Math.sin(theta/2)*Math.sin(theta/2) ``` There might be room for improvement on the calculations specified in the spec, depending on which trig identities we choose. This would be good considering we want graphic calculations to be as fast as possible. /#!/JoePeaReceived on Tuesday, 5 January 2016 01:16:10 UTC

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