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Procedural meshes post: more rambling on POV-Ray

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Chris Hodapp 2021-08-10 12:33:12 -04:00
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@ -40,15 +40,12 @@ about 1999 in PolyRay and POV-Ray... though my [[../../images/portfolio/1999-12-
from 1999]] are mostly garbage. POV-Ray is probably what led me to from 1999]] are mostly garbage. POV-Ray is probably what led me to
learn about things like procedural geometry and textures, especially learn about things like procedural geometry and textures, especially
implicit surfaces and parametric surfaces, as its scene language is implicit surfaces and parametric surfaces, as its scene language is
full of constructs for that. The images below are some of my POV-Ray full of constructs for that. Below is one of my procedural POV-Ray
scenes from way back in 2005, with the first two done completely with scenes from experimenting back in 2005, and though I hadn't heard of
its implicit surfaces. Context Free at that point (if it even existed) I was already trying
to do similar things in a sort of ad-hoc way.
{{< gallery >}}
{{< figure page="images" resource="portfolio/2005-07-05-spiral-isosurface2.jpg">}}
{{< figure page="images" resource="portfolio/2005-07-08-vaguely-celtic-metalwork.jpg">}}
{{< figure page="images" resource="portfolio/2005-08-23-shear6.jpg">}} {{< figure page="images" resource="portfolio/2005-08-23-shear6.jpg">}}
{{< /gallery >}}
Naturally, this led me to wonder how I might extend Context Free's Naturally, this led me to wonder how I might extend Context Free's
model to work more generally with 3D geometry, and let me use it to model to work more generally with 3D geometry, and let me use it to
@ -105,7 +102,7 @@ mesh looks great, but I quickly ran into a problem: OpenSCAD scales
pretty poorly with this level of complexity - and as far as that goes, pretty poorly with this level of complexity - and as far as that goes,
this geometry is even fairly mild. This really isn't surprising, as this geometry is even fairly mild. This really isn't surprising, as
tools like this were made for practical applications in CAD, and not tools like this were made for practical applications in CAD, and not
so much for my silly explorations in generative art. so much for my silly explorations in procedural art.
But wait! *Implicit surfaces* handle almost all of this well! (Or see But wait! *Implicit surfaces* handle almost all of this well! (Or see
any of the related-but-not-identical things around this, e.g. [[https://en.wikipedia.org/wiki/Function_representation][F-Reps]] any of the related-but-not-identical things around this, e.g. [[https://en.wikipedia.org/wiki/Function_representation][F-Reps]]
@ -121,17 +118,16 @@ Keeter's work with [[https://www.libfive.com/][libfive]] and [[https://www.mattk
wonderfully elegant, and I'll probably have many other posts on them. wonderfully elegant, and I'll probably have many other posts on them.
(TODO: Link to my CS6460 stuff) (TODO: Link to my CS6460 stuff)
Many renderers can render implicit surfaces directly. POV-Ray is one Many renderers can render implicit surfaces directly. [[https://www.shadertoy.com/][Shadertoy]] is
of them - see [[https://www.povray.org/documentation/view/3.6.1/300/][Isosurface Object]] which a few of my examples above full of user-created examples of ad-hoc realtime rendering of implicit
use. The appleseed renderer can sort of do it via a [[https://github.com/appleseedhq/appleseed/blob/master/sandbox/examples/cpp/distancefieldobject/distancefieldobject.cpp][custom object via surfaces, mostly in the form of sphere tracers, done completely in
a plugin]]. [[https://www.shadertoy.com/][Shadertoy]] is also full of user-created examples of ad-hoc [[https://en.wikipedia.org/wiki/OpenGL_Shading_Language][GLSL]]. Keeter's work on [[https://www.mattkeeter.com/research/mpr/][MPR]] is all about realtime rendering of a
realtime rendering of implicit surfaces, mostly in the form of sphere similar sort, but in a much more scalable way. The [[https://appleseedhq.net/][appleseed]] renderer
tracers, done completely in [[https://en.wikipedia.org/wiki/OpenGL_Shading_Language][GLSL]]. Keeter's work on [[https://www.mattkeeter.com/research/mpr/][MPR]] is all about can do it via a [[https://github.com/appleseedhq/appleseed/blob/master/sandbox/examples/cpp/distancefieldobject/distancefieldobject.cpp][custom object via a plugin]]. POV-Ray, as mentioned
realtime rendering of this sort in a much more scalable way. before, also handles them nicely with its [[https://www.povray.org/documentation/view/3.6.1/300/][Isosurface Object]]. That is
what I used below in yet another of my 2005 experiments:
# TODO: Why not move the spiral isosurface from POV-Ray here, and give {{< figure page="images" resource="portfolio/2005-07-05-spiral-isosurface2.jpg">}}
# its formula and explain a little? Or - should this be for another
# post?
Many renderers don't handle implicit surfaces at all. Blender's Many renderers don't handle implicit surfaces at all. Blender's
renderers, [[https://www.cycles-renderer.org/][Cycles]] and [[https://docs.blender.org/manual/en/latest/render/eevee/introduction.html][Eevee]], are among them. Using implicit surfaces renderers, [[https://www.cycles-renderer.org/][Cycles]] and [[https://docs.blender.org/manual/en/latest/render/eevee/introduction.html][Eevee]], are among them. Using implicit surfaces
@ -140,24 +136,36 @@ handle - typically a polygon mesh.
This leads to a pretty big issue: turning implicit surfaces to good This leads to a pretty big issue: turning implicit surfaces to good
meshes for rendering /is a huge pain/. If you don't believe me, meshes for rendering /is a huge pain/. If you don't believe me,
believe Matt Keeter in [[https://www.mattkeeter.com/research/mpr/keeter_mpr20.pdf][his paper]] when he says, "There is significant believe Matt Keeter in [[https://www.mattkeeter.com/research/mpr/keeter_mpr20.pdf][his paper on MPR]] when he says, "There is
literature on converting implicit surfaces into meshes for significant literature on converting implicit surfaces into meshes for
visualization. Having implemented many of these algorithms, we've visualization. Having implemented many of these algorithms, we've
found it extremely difficult to make them robust." I'd love to tell found it extremely difficult to make them robust." I'd love to tell
you that I saw this advice before wasting my time trying to turn you that I saw this advice before wasting my time trying to turn
implicit surfaces to meshes, first with various libraries and then implicit surfaces to meshes, first with various libraries and then
with ad-hoc conversions and optimizations of my own, but I didn't. I with ad-hoc conversions and optimizations of my own, but I didn't.
may have other posts talking about my failures here, but for now, take For comparison, POV-Ray raytraced the above example comfortably on a
it on faith that this is why I gave up trying to use implicit surfaces machine with 512 MB of RAM, and that's at 4000x3000 resolution - while
for this project. (TODO: Make those posts.) I've had very limited success at turning this particular implicit
surface to a polygon mesh good enough to produce anywhere near a
comparable render, and that fits in 32 GB of RAM.
I may have other posts talking about my failures here, but for now,
take it on faith: things like this are why I gave up trying to use
implicit surfaces for this project. (TODO: Make those posts.)
# TODO: Perhaps make a note here on explicit vs. implicit, maybe try
# to explain generative/procedural/algorithmic/parametric?
#
# https://en.wikipedia.org/wiki/Parametric_equation#Computer-aided_design -
# note explicit vs. implicit vs. parametric.
With these limitations in mind, around 2018 June I had started jotting With these limitations in mind, around 2018 June I had started jotting
some ideas down. The gist is that I wanted to create some ideas down. The gist is that I wanted to create
"correct-by-construction" meshes from these recursive grammars. By "correct-by-construction" meshes from these recursive grammars. By
that, I meant: incrementally producing the desired geometry as a mesh, that, I meant: incrementally producing the desired geometry as a mesh,
triangle-by-triangle, in such a way that guaranteed that the resultant polygon-by-polygon, in such a way that guarantees that the resultant
mesh had the desired detail level, was a manifold surface, and that it mesh has the desired detail level, is a manifold surface, and that it
was otherwise a well-behaved mesh (e.g. no degenerate triangles, no is otherwise a well-behaved mesh (e.g. no degenerate triangles, no
self-intersection, no high-degree vertices, no triangles of extreme self-intersection, no high-degree vertices, no triangles of extreme
angles) - rather than attempting to patch up the mesh after its angles) - rather than attempting to patch up the mesh after its
creation, or subdividing it to the necessary detail level. For creation, or subdividing it to the necessary detail level. For