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.galinette wrote:lycium wrote:2. Render some 3D fractals with IndigoHmmm... How do you define the gradient of a fractal?lycium wrote: the normal is everywhere the gradient of this potential function.
Implicit surfaces
Re: Implicit surfaces
Re: Implicit surfaces
In the case of a fractal, the gradient does not exist mathematically! (derivatives doesn't exist)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.
Eclat-Digital Research
http://www.eclat-digital.com
http://www.eclat-digital.com
Re: Implicit surfaces
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/
Re: Implicit surfaces
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)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/
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
Eclat-Digital Research
http://www.eclat-digital.com
http://www.eclat-digital.com
Re: Implicit surfaces
We don't even have true real numbers and infinite image resolution, so why should we expect normals to true fractals?
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