how to best transform with lipschitz<=1.0 ?
category: code [glöplog]
Is there a database of transformations in 2d and 3d that have a lipschitz_constant <=1.0 other than hg_sdf???
Whats The Best method to turn a transformation that has lipschitzes >1.0 to More useful variants with lipschitz<= 1
Are zhere any reliable general methods for that for orthogonal 3d Space?
Calculating a transformations lipschitz constant to later divide by it is often too complex and accumulates rounding errors.
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Application :
In raymarching You transform a Point p to measure distances to transformed(p)
P is generally a 3d vector.
The problem is that too many types of transformations lead to overestimating distances through transformation of p.
In a raymarcher This overestimation leads to pseudo-Random Quantum teleportation through defined solid geometry surfaces. Its bearable unless You dare to calculate occlusion and reflection on surfaces. Quantum teleportation and reflection Are not good friends.
Simple example is a twisting transformation that rotates p around an axis.
This transform too often has a lipschitz constant >1.
Another transform with lipschitz>1.0 is The transform for fisheye perspectives.
You Can calculate The lipschitz of them but it is roughly as computationally complex than distance(p) , and it adds one constant that You later need to divide a vec3 by, once for eacd transform with lipschitz>1.0 .
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Bonus Point for fractal transforms with lipschitz<=1.0
Whats The Best method to turn a transformation that has lipschitzes >1.0 to More useful variants with lipschitz<= 1
Are zhere any reliable general methods for that for orthogonal 3d Space?
Calculating a transformations lipschitz constant to later divide by it is often too complex and accumulates rounding errors.
-----
Application :
In raymarching You transform a Point p to measure distances to transformed(p)
P is generally a 3d vector.
The problem is that too many types of transformations lead to overestimating distances through transformation of p.
In a raymarcher This overestimation leads to pseudo-Random Quantum teleportation through defined solid geometry surfaces. Its bearable unless You dare to calculate occlusion and reflection on surfaces. Quantum teleportation and reflection Are not good friends.
Simple example is a twisting transformation that rotates p around an axis.
This transform too often has a lipschitz constant >1.
Another transform with lipschitz>1.0 is The transform for fisheye perspectives.
You Can calculate The lipschitz of them but it is roughly as computationally complex than distance(p) , and it adds one constant that You later need to divide a vec3 by, once for eacd transform with lipschitz>1.0 .
----
Bonus Point for fractal transforms with lipschitz<=1.0
