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Do you want to reform geometry because of True Type fonts handling is a complex task, don't you? :-D
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler. -- Alfonso the Wise, 13th Century King of Castile.
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Many different kinds of geometry already exist, providing your 'geometric rules' are applied consistently to a closed data set (for example the set of all integers) then I guess you could 'create' any kind of geometry you wanted. I'm not sure I agree with you on the argument behind this - conventional exists as a way of describing the real world and it works very well. It 'fails' when applied to fonts (for example) because of the restrictions applied to the data set (Real numbers) by the discrete device used to display the fonts and not because the geometry is wrong! As a mathematician I'd be glad to look at this for you - providing we can agree on payment terms ;)