can somebody please explain non-euclidean geometry? 14 replies

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Mr. Pedantic

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8th October 2006

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#11 11 years ago

Basically have lots of hyperbolic arches, ovals, things like that.




Granyaski Advanced Member

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29th May 2008

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#12 11 years ago

Well dude it's very very hard to explain....one of those things a 15 year old like me isn't trained to do these days... Just ask some professor of something along those lines or if your still boggled read alot about it(like wikipedia)and actually have a try at it,thats how I learned it




MrFancypants Forum Administrator

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7th December 2003

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#13 11 years ago

I think a way to achieve Lovecraft's idea of that ancient city would be to program filters that radically change geometry depending on where your character is in the 3d-world you create. Not sure if your 3d modelling progam is able to, but if you could change the air density, rr maybe add a number of invisible lenses that might do the trick. The result could be a bit like going through a hall of mirrors or what it looks like when a character is shown as drunk in old movies.




DawnOfDiablo666

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#14 11 years ago

dont make it too realistic, otherwise you'll go insane as the others in the story...




Revenge Advanced Member

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#15 11 years ago

The point of geometry is usually to define unique points in a space.

Euclidean geometry deals with conventional coordinates, i.e. (10, -4) being 10 steps to the right in the x-axis and 4 steps to the bottom on the y-axis*. Most graphs you'll have dealt with in basic maths use Euclidean geometry systems.

Non-Euclidean geometry encompasses everything that isn't Euclidean geometry (obviously). Examples could include polar coordinates, which defines a point in space using a distance from the origin (point (0, 0) in Euclidean geometry, or wherever you place the 'middle' of the space) and the angle in which this distance should be travelled with respect to the origin in order to get to that point. A polar coordinate could be (10, 5r) where 10 is the distance and 5r is the value 5 degrees is in radians (look up radians on Wikipedia if you don't know what they are because it's too long to explain). They're called polar coordinates because they operate in circles around a centre, or pole. Much like our own North Pole. Imagine trying to plot the North Pole on a conventional map using Euclidean geometry - there's too much curvature of the Earth to be able to follow map directions easily. It's much easier to say 'walk x metres in that direction', which is essentially what polar coordinates tell you to do.

Another example of non-Euclidean geometry are spherical coordinates, which are an extension of polar coordinates but for 3D spaces instead of 2D. These define a distance and two angles, i.e. the angle on the y-axis and the angle on the z-axis.

...But in my experience the best and simplest method of geometry for linear things is Euclidean. If you're doing modelling, which is inherantly non-linear, then usually non-Euclidean coordinate systems are easier to deal with once you're over the learning curve.

*Well, whether or not it's to the right and to the bottom depends on how you want to define your axies, but rest assured the x, y and potentially z axies must all be perpendicular to one another.




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