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no worries thanks for your input
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Do you want to reform geometry because of True Type fonts handling is a complex task, don't you?
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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The Grand Negus wrote: Real math is a highly-developed but obtuse system that we're trying to apply, with partial and scattered success, in a discrete universe.
Actually math is not only higly-developed, it's great!
The Grand Negus wrote: The point is that a tool should make the accomplishment of a job easier, not harder
Math is not a tool is a science. You can only say it is one of the best Tool we have to make a bit of light into the obscure Universe.
Anyway, good luck and enjoy yourself with you workplan.
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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Thanks 
Anyway, Math it's not guilty if the Graphic Library is buggy!
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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The Grand Negus wrote: But that's my point. The graphic library isn't buggy
Yes, it is.
The Grand Negus wrote: it's just having trouble deciding which pixels belong to a line
This is task showing library misbehaviour (note that it's a library task, not a math one).
The Grand Negus wrote: by definition, has no width
This is the mathematical side of the argument, where all goes fine!
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 
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The Grand Negus wrote: Works very well" only in very limited circumstances. The formula for the volume of a cylinder, for example, is simple enough; but put a few bumps on the thing and there is no comprehensible formula to describe it. Equations are great for schoolbook cylinders, but they're no good for tree trunks. The universe is an algorithm, not an equation.
It works very well not in limited circumstances but for the circumstances for which it was designed ie to describe the real world in mathematical terms. All advances in mathematics have taken us a step (a very small step) nearer to describing the world fully. I would suggest that our current understanding of mathematics barely scratches the surface!
As for your cylindrical example - the formula for the volume of a cylinder is precisely that, if you want to find the volume of a cylinder with bumps on it or a tree trunk then you would need a formula for that - but first and more importantly you need a method of describing the object, this is probably the most difficult part! Until you can define precisely the nature of the data set 'tree trunks' you can't possibly hope to find the formula to convert a member of the data set 'tree trunks' into a member of the data set 'volume'. The same of course applies to any 'real world' object, and by that I mean tree, house, worm car etc and not the mathematical real world, real numbers integers, cylinders, squares etc.
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(1) Yes I understand
(2) As a mathematical curiosity I might look at the possiblilty of an integer geometry in my spare time
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I think that any work in this area is doomed to irrelevance unless you take perception into account, it appears to me that this is where much of the current work is happening. To explain what I mean, take a block of pixels and look at all possible arrangements of colours, some of these will be perceived to contain recognizable patterns, such as lines, the letter 'A' etc. The boundaries of these sets will be fuzzy (like the graphics). The goal of any improved rendering technique should be to achieve the highest perception scores from users, and not concentrate simply on algorithmic details of rendering on a pixellated screen.
The Grand Negus wrote: The goal is to show that by starting with shapes and operations native to a discrete coordinate system, computer graphics can be both conceptually simpler and more easily implemented than with the traditional mathematical approach.
Whilst admirable goals from a programming perspective, the bigger picture surely must be perception dominated.
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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The Grand Negus wrote: where the formulas are minimal data structures for describing those shapes (in our Plain English programming language); and where the algorithms for drawing, filling, translating, rotating, and scaling are also presented in Plain English.
Defining a whole new geometry in so called 'plain english' (programming language or not) just isn't going to be feasible. The geometry must be defined in mathematical terms either using existing notation or creating new notation (mathematicians are very fond of this!). The reason for this is obvious, y=mx+c is easier to understand (for me anyway) than "the value along the y axis is equal to the value along the x axis multplied by another value m representing the slope of the line added to a constant which is the y value where the line crosses the y axis"
Once defined in the correct notation it may then be translated into the plain english version but to be honest I would have to wonder why when in C (ugly or not) we can write y=m*X+c; and be finished.
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Well I've never been called lukewarm before! I have a problem with the 'plain english' its your 'baby' I don't know enough about it to know what it can do - if its that good why isn't everyone using it? I haven't made any deliberate attempt to give you any grief - I'm passionate enough about my work to question everything (EVERYTHING) I don't understand - asking questions is how research is done, I don't care if the questions are uncomfortable or don't agree with your way of thinking. You might be right I don't know - but I have to ask the questions!!
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Defining the problem in familiar terms is one way of asking the question 'How do we solve this?'. I went on to say we can then go on and express the problem in terms of plain english, I'm not dismissing plain english just tyring already to work out the problem in term I already understand - the question is this particular case is to myself, how to I work this out?
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The Grand Negus wrote: algorithms are not limited in the ways that formulas are
Formulae are necessarily limited - thats the point surely? Also most algorithms depend on formulae to work (whatever language they might be written in), theres no getting away from them!
The Grand Negus wrote: First because there are too many strong but unnecessary ties to conventional math
Just because conventional math is used doesn't make it wrong - theres no need to reinvent the wheel 'just because', we can still use the useful features of the wheel like the fact that its round and still come up with something new. A new geometry will still need to use addition, multiplication etc to work.
The Grand Negus wrote: the paper stops short of practical applications
Of course it does - the guy is an academic!
If a system like you propose were developed, how do you imagine it is integrated into existing applications? Microsoft for example aren't going to incorporate it into Word just because its better and faster that any other method (if they did things like that we would all be running MS Linux by now!)
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The Grand Negus wrote: Less than 10% of the routines in our 25,000 line development system involve formulas of any kind
I disagree - most algorithms will contain a formula of one kind or another even if it is simply "add 1 to the current position" its still a formula. Prove me otherwise!
The Grand Negus wrote: your contention that "most algorithms depend on formulae to work" is simply not true
Maybe if you had used more your development would have been a little more efficient!
The Grand Negus wrote: It's not addition and multiplication we object to; it's real numbers
And how in your 'graphics system' do you expect to be able to represent circles without Pi? Calculate the hypotenuse of a triangle without square roots? Do anything interesting at all without Sine and Cosine? Not easy without real numbers - of course you could scrap everything mankind has ever learned about mathematics since the dawn of time and start again, either that or approximate Pi to 3...
The Grand Negus wrote: "impedance mismatch"
You use this term all the time - when I was at school it was a term used by electronic engineers, I assume that you mean this in a different sense - maybe a certain kind of academic trying to communicate with us ordinary folk might be an "impedance mismatch"
The Grand Negus wrote: Teachers will be able to use the information, together with our Plain English development system, to introduce the next generation of "mathematicians" to this kind of constructivist thinking
My son briefly played with this kind of 'educational' software, Logo was it? For about 10 minutes before he got bored and moved on along with his friends to real programming C++, HTML etc, he's 10 now. The last thing kids these days are interested in is plain english - have you heard them speak?! Now think of a language based on emoticons and you might be on to a winner! (actually there's an idea...)
The Grand Negus wrote: "apparently intelligent"(tm) PAL 3000 machine
Dare I ask what PAL stands for?
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The Grand Negus wrote: You're not the guy for this project
You're kidding, right?
The Grand Negus wrote: I did. 90% of the routines in our development are void of anything that resembles a formulaic approach
Since when did quoting a single unsubstantiated figure constitute a proof? Maybe an example would help?
The Grand Negus wrote: and it can reproduce itself, on a bottom-of-the-line Dell, in less than three seconds
For what purpose?
The Grand Negus wrote: On page 97 of our reference manual there is an illustration of a sine-wave constructed from an integer-only polygon smoothed using integer-only math
Since I do not have access to your manual this can't be considered an example - again I only have your unsubstantiated claim that it is proof. I have no doubt however that you can draw very pretty pictures using only integers, but that still doesn't help you rotate a cube 33 and a third degrees around the X axis - a very real graphic 'problem'.
The Grand Negus wrote: We define a real programming language as one that can be used to conveniently and efficiently reproduce itself
Like C you mean?
The Grand Negus wrote: You should have asked about the difference between an "apparently intelligent" machine, and an "artificially intelligent" one
I know this one - 'artificial intelligence' applies to the machine, 'apparent intelligence' applies to the user of the machine, right?
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The Grand Negus wrote: I propose that lines be described using something like "left 2 up 1" (in whatever syntax is appropriate), because lines defined like that can be precisely plotted on the screen;
Sounds like you may be wanting to use vectors to form lines. Such as in some advance CAD systems.
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Whats all this got to do in a C# forum?
If a newcomer writes a question for languages/subjects other than C# he is banged straight.
Shouldnt this topic be discussed in more appropriate forums?
Arti
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Please ignore my previous reply.
I accidentally got linked with this forum instead of C#.
Apologies for the inconvinience caused.
Arti
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Steve_pqr wrote: t works very well not in limited circumstances but for the circumstances for which it was designed ie to describe the real world in mathematical terms. All advances in mathematics have taken us a step (a very small step) nearer to describing the world fully.
hey boy, that's physics, not math itself.
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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Correct - but you don't get far in physics without math, and without physics math is just an intellectual excercise, you draw the line between them, I suspect it won't be a straight one!! (probably a fractal)
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I want to make my project (witch I did it with Matlab) I want to make it runs on any PC without the need of Matlab program to be on this PC.
in other words...I want to make my project an (.exe) file.
how can I do that please???
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