From: Simon Sapin <simon.sapin@kozea.fr>

Date: Tue, 10 Jan 2012 17:15:33 +0100

Message-ID: <4F0C6425.5030600@kozea.fr>

To: www-style@w3.org

Date: Tue, 10 Jan 2012 17:15:33 +0100

Message-ID: <4F0C6425.5030600@kozea.fr>

To: www-style@w3.org

Hi, I am in the process of implementing margin boxes from CSS3 Paged Media in WeasyPrint. One particular pain point is Section 6.3.2 Margin Box Variable Dimension Computation Rules. This section describes *what* is the desired behavior, but leaves the implementer with no clue as to *how* to do it. For comparison, the next section on Fixed Dimension is much closer to an algorithm. http://dev.w3.org/csswg/css3-page/#margin-dimension First, has anyone implemented this and is willing/able to share the algorithm under an appropriate license for use in other UAs? To give a quick overview: 3 margin boxes that share the same side are laid-out together in one direction. The problem can be seen as a system of: * 0 to 9 variables (properties with a computed value of 'auto') * 0 to 6 linear inequality constraints (lower and/or upper bounds on widths) * 1 or 2 linear equality constraints (the total sum if fixed; the middle box must be centered if it "exists") * a quadratic goal function that must be minimized (sum of squared margins) This kind of problem is known as quadratic programming: http://en.wikipedia.org/wiki/Quadratic_programming General solvers exist, but they are based on iterative algorithms that can be slow and only give an approximate solution. Also, they’re often based on a whole numeric/scientific package. A big dependency for a CSS UA that has otherwise no need for such solvers. Furthermore, I believe that a general solver is not required. For any set of input, I can tell without iterating what the output should be. (In other words, the algorithm could be made of conditionals, without loops.) I only have a hard time writing that algorithm. 9 properties that may or may not be auto give 2^9 = 512 cases. These can be reduced by symmetry but there are still a lot of cases with different behaviors, especially when rule 2 applies. (When the middle box exists and must be centered.) Implementing CSS is generally not trivial, but I find this particular section especially troublesome. I’ve been at it for weeks. Did I miss something obvious? Regards, -- Simon SapinReceived on Tuesday, 10 January 2012 16:19:30 UTC

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