Constructive solid geometry - Revision history

Apm at 08:30, 5 May 2024

2024-05-05T08:30:47Z

← Older revision		Revision as of 10:30, 5 May 2024
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	[[Category:Pages with algorithms]]		[[Category:Pages with algorithms]]
	[[Category:Programming]]		[[Category:Programming]]
			[[Category:Software]]

Apm: added Category:Programming

2023-07-11T10:58:31Z

added Category:Programming

← Older revision		Revision as of 12:58, 11 July 2023
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	[[Category:Pages with algorithms]]		[[Category:Pages with algorithms]]
			[[Category:Programming]]

Apm: /* Related / '''Digital control over matter''' * '''Materializable programs''' * Software

2023-06-21T06:36:21Z

Related: * '''Digital control over matter''' * '''Materializable programs''' * Software

← Older revision		Revision as of 08:36, 21 June 2023
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	----		----
	* [[Atomic orbitals]] – the implicit formulas can be used for F-Rep surface evaluation <br>Note that these are single electron solutions. There are no exact solutions for multi electron atoms. <br>The charge of the nucleus that is seen by an electron is gradually shielded towards the nucleus due to the other electron(s).		* [[Atomic orbitals]] – the implicit formulas can be used for F-Rep surface evaluation <br>Note that these are single electron solutions. There are no exact solutions for multi electron atoms. <br>The charge of the nucleus that is seen by an electron is gradually shielded towards the nucleus due to the other electron(s).
			----
			* '''[[Digital control over matter]]'''
			* '''[[Materializable programs]]'''
			* [[Software]]

	= External links =		= External links =

Apm: /* Related */ bold

2023-06-20T16:57:54Z

Related: bold

← Older revision		Revision as of 18:57, 20 June 2023
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	= Related =		= Related =

	* [[List of programmatic 3D modelling tools]]		* '''[[List of programmatic 3D modelling tools]]'''
	* [[Data decompression chain]]		* [[Data decompression chain]]
	* [[Computer algebra system]]		* [[Computer algebra system]]

Apm: /* Code: DSL libraries for CSG, CSG software, ... */ factored out to List of programmatic 3D modelling tools

2023-06-20T16:57:39Z

Code: DSL libraries for CSG, CSG software, ...: factored out to List of programmatic 3D modelling tools

← Older revision		Revision as of 18:57, 20 June 2023
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	* [https://en.wikipedia.org/wiki/Octree Octree]		* [https://en.wikipedia.org/wiki/Octree Octree]

	~~== Code: DSL libraries for CSG, CSG software, ... ==~~

	* B-Rep – [[OpenSCAD]] – '''[https://openscad.org/ OpenSCADs website]''' – <small>(uses [https://www.cgal.org CGAL under the hood] – C/C++)</small> <br>
	~~Interestingly OpenSCAD ...~~
	* ... is a 100% pure/denotative/side-effect-free by design. But as of 2021 it ...
	* ... is ''not'' a higher order functional language with functions as "first class citizens".
	~~There are quite a few copycat projects of OpenSCAD around. <br>~~
	~~Unfortunately they all seem to fail to implement a hard guarantee on code purity – (inheriting impurity from their substrate language). <br>~~
	~~Beyond OpenSCAD of the software artifacts listed here only implicitcad can give hard guarantees on purity (there enforced by types). <br>~~
	~~Related: [[Relations of APM to purely functional programming]]~~
	~~----~~
	* B-Rep – [http://evanw.github.io/csg.js/ csg.js] – (javascript library)
	* F-Rep – [https://libfive.com/ libfive (formerly AO)] [https://github.com/libfive/libfive (on github)] — (guile scheme software)
	* F-Rep – [https://github.com/fogleman/sdf Foglemans SDF library] — (python library)
	* F-Rep – [https://implicitcad.org/ implicitcad] – (haskell DSL)
	* F-Rep – [https://www.thingiverse.com/thing:40210 MiniSageCAD experiment on Thingiverse] (implemented in the sage computer algebra system)
	~~----~~
	* F-Rep (2D) – rendering engine of the enso programming language (rust library)
	* F-Rep SDF-code on shadertoy – many examples there <br>– [https://www.shadertoy.com/view/Xds3zN Raymarching - Primitives ~ by iq] <br>– [https://www.shadertoy.com/results?query=tag%3Dsdf shadertoy: tag=sdf]

	[[Category:Pages with algorithms]]		[[Category:Pages with algorithms]]

Apm: /* Related / link to yet unwritten List of programmatic 3D modelling tools

2023-06-20T16:54:59Z

Related: link to yet unwritten * List of programmatic 3D modelling tools

← Older revision		Revision as of 18:54, 20 June 2023
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	= Related =		= Related =

			* [[List of programmatic 3D modelling tools]]
	* [[Data decompression chain]]		* [[Data decompression chain]]
	* [[Computer algebra system]]		* [[Computer algebra system]]

Apm: /* The issues with B-Rep boolean operations */ fixed section title according to new insights

2023-06-20T16:51:32Z

The issues with B-Rep boolean operations: fixed section title according to new insights

← Older revision		Revision as of 18:51, 20 June 2023
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	* multiplicative negation (commonly known as multiplication with minus one) turns a volumes inside out and vice versa – with that and the above one can construct differences		* multiplicative negation (commonly known as multiplication with minus one) turns a volumes inside out and vice versa – with that and the above one can construct differences

	=== The issues with B-Rep boolean operations ===		=== The issues with triangle meshes (piecewise linear B-Rep) in boolean operations ===

	~~In B-rep~~ boolean operations are much more difficult. <br>		With triangulated surface meshes boolean operations are much more difficult. <br>
	Involving intersecting surface descriptions like triangle meshes, treatment of degenerate edge cases, and possible local re-meshing. <br>		Involving intersecting surface descriptions like triangle meshes, treatment of degenerate edge cases, and possible local re-meshing. <br>

	In the open source 3D modelling program blender that is being more aimed at visually pleasing results than good watertight meshes for manufacturing. <br>		In the open source 3D modelling program blender that is being more aimed at visually pleasing results than good watertight meshes for manufacturing. <br>
	Using automatic ~~B-Rep~~ booleans is generally advised against (in favor of high effort manual tinkering) as it screws up the texture mapping. <br>		Using automatic booleans on triangle meshes is generally advised against (in favor of high effort manual tinkering) as it screws up the texture mapping. <br>
	All that manual tinkering on already triangulated meshed gets lost though when intersection and such need to be changed. <br>		All that manual tinkering on already triangulated meshed gets lost though when intersection and such need to be changed. <br>
	This is going strongly against reversible [[non-destructive modeling]].		This is going strongly against reversible [[non-destructive modeling]].

Apm: added = F-Rep vs B-Rep =

2023-06-20T16:48:55Z

added = F-Rep vs B-Rep =

← Older revision		Revision as of 18:48, 20 June 2023
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	Constructive solid geometry (CSG) is a form of volumetric modelling where complex geometries can be built up		Constructive solid geometry (CSG) is a form of volumetric modelling where complex geometries can be built up
	by combining simple geometries via boolean functions. <br>		by combining simple geometries via boolean functions. <br>

			= F-Rep vs B-Rep =

			* F-Rep … functional representations – implicit functions specifying a volume<br> Signed distance functions SDFs are a subset.
			* B-rep … boundary representation – description of 2D surfaces in 3D space<br> May be parametric, piecewise parametric, or even piecewise linear (aka triangulation)

	= Why functional representation is desirable =		= Why functional representation is desirable =

Apm: /* F-Rep is higher level than (polygonal modelling) B-Rep */ some fixes getting closer to new insights

2023-06-20T16:38:09Z

F-Rep is higher level than (polygonal modelling) B-Rep: some fixes getting closer to new insights

← Older revision		Revision as of 18:38, 20 June 2023
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	The extremely useful of creating convex hulls seems not implementable <small>(aside from a few special cases maybe)</small>		The extremely useful of creating convex hulls seems not implementable <small>(aside from a few special cases maybe)</small>

	== F-Rep is higher level than ~~(polygonal modelling)~~ B-Rep ==		== F-Rep is higher level than piecewise linear B-Rep ==

	[[File:Libfive p-orbital Screenshot 20201110 001820.png\|400px\|thumb\|right\|Positive lobe of a p-orbital (single electron solution for the Schrödinger equation) this can be done via F-rep but not via SDF. Related [[Atomic orbitals]].]]		[[File:Libfive p-orbital Screenshot 20201110 001820.png\|400px\|thumb\|right\|Positive lobe of a p-orbital (single electron solution for the Schrödinger equation) this can be done via F-rep but not via SDF. Related [[Atomic orbitals]].]]
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	Functional representation (F-Rep) is on a higher abstraction level than triangulation based boundary representation (B-Rep).		Functional representation (F-Rep) is on a higher abstraction level than triangulation based boundary representation (B-Rep).
	That is		That is
	* F-Rep can be triangulated to B-Rep to arbitrary precision		* F-Rep can be triangulated to piecewise linear B-Rep to arbitrary precision
	* Going from B-Rep to F-rep requires a bit of artistic creativity filling in the blanks		* Going from B-Rep to F-rep requires a bit of artistic creativity filling in the blanks

Apm: /* Boolean operations */ === The issues with B-Rep boolean operations ===

2023-06-06T12:31:15Z

Boolean operations: === The issues with B-Rep boolean operations ===

@@ Line 84: / Line 84: @@
 * '''minimum or maximum function corresponds to intersection and union''' (respectively or reverse respectively deepening if inside is positive
 * multiplicative negation (commonly known as multiplication with minus one) turns a volumes inside out and vice versa – with that and the above one can construct differences
 == Coordinate transformations ==