Implicit surfaces

General questions about Indigo, the scene format, rendering etc...
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lycium
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Re: Implicit surfaces

Post by lycium » Sat Sep 15, 2012 12:02 am

galinette wrote:
lycium wrote:2. Render some 3D fractals with Indigo 8)
lycium wrote: the normal is everywhere the gradient of this potential function.
Hmmm... How do you define the gradient of a fractal? :roll:
With great difficulty, as you can imagine... actually, there are ways to do it analytically, without finite difference (as I do), however this needs per-equation analysis and I wanted it to work with "black box" point-sampled potential functions.

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galinette
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Re: Implicit surfaces

Post by galinette » Sat Sep 15, 2012 4:07 am

lycium wrote: With great difficulty, as you can imagine... actually, there are ways to do it analytically, without finite difference (as I do), however this needs per-equation analysis and I wanted it to work with "black box" point-sampled potential functions.
In the case of a fractal, the gradient does not exist mathematically! (derivatives doesn't exist)
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lycium
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Re: Implicit surfaces

Post by lycium » Sat Sep 15, 2012 4:09 am

Some clever mathematicians worked that out, and recently there's a nice blog series on doing this for the Mandelbulb as a particularly well analysed example: http://blog.hvidtfeldts.net/index.php/2 ... ximations/

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Re: Implicit surfaces

Post by galinette » Sat Sep 15, 2012 8:02 am

lycium wrote:Some clever mathematicians worked that out, and recently there's a nice blog series on doing this for the Mandelbulb as a particularly well analysed example: http://blog.hvidtfeldts.net/index.php/2 ... ximations/
That's an approximation based on finite resolution. True fractals have no definable normal (Not only it cannot be calculated analytically, it does not exist)

However, it seems quite interesting for making 3d images, that's true... Refining the fractal resolution below visible wavelength range would not mean anything anyway...

Don't tell me that clever mathematicians have found an exact decimal form of Pi, or a tesselation of a sphere with a finite number of triangles :D
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lycium
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Re: Implicit surfaces

Post by lycium » Sat Sep 15, 2012 8:35 am

We don't even have true real numbers and infinite image resolution, so why should we expect normals to true fractals? :lol:

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Re: Implicit surfaces

Post by PureSpider » Sat Sep 15, 2012 10:02 am

Translation for regular human beings: "BRAIN HADUOKEN!"

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CTZn
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Re: Implicit surfaces

Post by CTZn » Sat Sep 15, 2012 11:20 am

Haxors !!!
obsolete asset

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