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Main menu Main menu move to sidebar hide Navigation Main page Contents Current events Random article About Wikipedia Contact us Contribute Help Learn to edit Community portal Recent changes Upload file Special pages Print/export Download as PDF Printable version In other projects Wikimedia Commons Wikidata item Search Search Appearance Donate Create account Log in Personal tools Donate Create account Log in Contents move to sidebar hide (Top) 1 Workings Toggle Workings subsection 1.1 Ray tracing 2 Applications 3 Conversion from meshes to CSG 4 Notable applications with CSG support Toggle Notable applications with CSG support subsection 4.1 Generic modelling languages and software 4.2 Ray tracing and particle transport 4.3 Computer-aided design 4.4 Gaming 4.5 Others 5 References Toggle the table of contents Constructive solid geometry 19 languages Afrikaans Bosanski Català Čeština Deutsch Español Eesti Français Bahasa Indonesia Italiano 日本語 한국어 Nederlands Norsk bokmål Polski Português Русский Українська 中文 Edit links Article Talk English Read Edit View history Tools Tools move to sidebar hide Actions Read Edit View history General What links here Related changes Upload file Permanent link Page information Cite this page Get shortened URL Print/export Download as PDF Printable version In other projects Wikimedia Commons Wikidata item Appearance move to sidebar hide From Wikipedia, the free encyclopedia Creating a complex 3D surface or object by combining primitive objects CSG objects can be represented by binary trees, where leaves represent primitives, and nodes represent operations. In this figure, the nodes are labeled ∩ for intersection , ∪ for union , and — for difference . Constructive solid geometry ( CSG ; formerly called computational binary solid geometry ) is a technique used in solid modeling . Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, [ 1 ] potentially generating visually complex objects by combining a few primitive ones. [ 2 ] [ 3 ] In 3D computer graphics and CAD , CSG is often used in procedural modeling . CSG can also be performed on polygonal meshes , and may or may not be procedural and/or parametric. CSG can be contrasted with polygon mesh modeling, boundary representation , and box modeling . Workings [ edit ] The simplest solid objects used for the representation are called geometric primitives . Typically they are the objects of simple shape: cuboids , cylinders , prisms , pyramids , spheres , cones . [ 1 ] The set of allowable primitives is limited by each software package. Some software packages allow CSG on curved objects while other packages do not. An object is constructed from primitives by means of allowable operations , which are typically Boolean operations on sets : union (OR), intersection (AND) and difference (NOT), as well as geometric transformations of those sets. [ 1 ] A primitive can typically be described by a procedure which accepts some number of parameters ; for example, a sphere may be described by the coordinates of its center point, along with a radius value. These primitives can be combined into compound objects using operations like these: Union Merger of two objects into one Difference Subtraction of one object from another Intersection Portion common to both objects Combining these elementary operations, it is possible to build up objects with high complexity starting from simple ones. Ray tracing [ edit ] Rendering of constructive solid geometry is particularly simple when ray tracing . Ray tracers intersect a ray with both primitives that are being operated on, apply the operator to the intersection intervals along the 1D ray, and then take the point closest to the camera along the ray as being the result. Applications [ edit ] CSG operations being applied in the context of rays in a ray tracer Constructive solid geometry has a number of practical uses. It is used in cases where simple geometric objects are desired, [ citation needed ] or where mathematical accuracy is important. [ 4 ] Nearly all engineering CAD packages use CSG (where it may be useful for representing tool cuts, and features where parts must fit together). The Quake engine and Unreal Engine both use this system, as does Hammer (the native Source engine level editor), and Torque Game Engine / Torque Game Engine Advanced . CSG is popular because a modeler can use a set of relatively simple objects to create very complicated geometry. [ 3 ] When CSG is procedural or parametric, the user can revise their complex geometry by changing the position of objects or by changing the Boolean operation used to combine those objects. One of the advantages of CSG is that it can easily assure that objects are "solid" or water-tight if all of the primitive shapes are water-tight. [ 5 ] This can be important for some manufacturing or engineering computation applications. By comparison, when creating geometry based upon boundary representations , additional topological data is required, or consistency checks must be performed to assure that the given boundary description specifies a valid solid object. [ 1 ] A convenient property of CSG shapes is that it is easy to classify arbitrary points as being either inside or outside the shape created by CSG. The point is simply classified against all the underlying primitives and the resulting Boolean expression is evaluated. [ 6 ] This is a desirable quality for some applications such as ray tracing . [ 6 ] Conversion from meshes to CSG [ edit ] With CSG models being parameterized by construction, they are often favorable over usual meshes when it comes to applications where the goal is to fabricate customized models. For such applications it can be interesting to convert already existing meshes to CSG trees. This problem of automatically converting meshes to CSG trees is called inverse CSG . A resulting CSG tree is required to occupy the same volume in 3D space as the input mesh while having a minimal number of nodes. Simple solutions are preferred to ensure that the resulting model is easy to edit. Solving this problem is a challenge because of the large search space that has to be explored. It combines continuous parameters such as dimension and size of the primitive shapes, and discrete parameters such as the Boolean operators used to build the final CSG tree. Deductive methods solve this problem by building a set of half-spaces that describe the interior of the geometry. These half-spaces are used to describe primitives that can be combined to get the final model. [ 7 ] Another approach decouples the detection of primitive shapes and the computation of the CSG tree that defines the final model. This approach exploits the ability of modern program synthesis tools to find a CSG tree with minimal complexity. [ 8 ] There are also approaches that use genetic algorithms to iteratively optimize an initial shape towards the shape of the desired mesh. [ 9 ] Notable applications with CSG support [ edit ] Generic modelling languages and software [ edit ] HyperFun PLaSM Ray tracing and particle transport [ edit ] PhotoRealistic RenderMan POV-Ray Computer-aided design [ edit ] See also: CAD software AutoCAD Autodesk Inventor Autodesk Fusion 360 BRL-CAD CATIA FreeCAD NX CAD SolveSpace Onshape OpenSCAD PTC Creo Parametric (formerly known as Pro/Engineer ) Realsoft 3D Rhino Solid Edge SolidWorks Tinkercad Vectorworks Gaming [ edit ] Dreams Godot [ 10 ] GtkRadiant LittleBigPlanet Roblox Unity , via free or paid plug-ins from the Unity Asset Store . UnrealEd Valve Hammer Editor Others [ edit ] 3Delight Aqsis (as of version 0.6.0) [ 11 ] Blender – primarily a surface mesh editor, but capable of simple CSG using meta objects and using the Boolean modifier on mesh objects. CGAL – a library of geometric algorithms and data structures, in particular Boolean operations on polygonal meshes. Clara.io Geant4 Magica CSG [ 12 ] MCNP SketchUp Womp [ 13 ] References [ edit ] ^ a b c d Foley, James D. (1996), "12.7 Constructive Solid Geometry", Computer Graphics: Principles and Practice , Addison-Wesley Professional, pp.  557– 558, ISBN   9780201848403 , ^ Roth, Scott (1982). "Ray Casting for Modeling Solids". Computer Graphics and Image Processing . 18 (2): 109– 144. doi : 10.1016/0146-664X(82)90169-1 . ^ a b Bloomenthal, Jules; Bajaj, Chandrajit (1997), "5.2.5 Intersection with CSG Trees", Introduction to Implicit Surfaces , Morgan Kaufmann, pp.  178– 180, ISBN   9781558602335 . ^ Foley (1996) , p. 559. ^ van Rossen, Sander; Baranowski, Matthew (2011), "Real-time constructive solid geometry", in Ansari, Marwan (ed.), Game Development Tools , CRC Press, pp.  79– 96, ISBN   9781439867723 . ^ a b Glassner, Andrew S. (1989), An Introduction to Ray Tracing , Morgan Kaufmann, p. 80, ISBN   9780122861604 . ^ Buchele, Suzanne F.; Crawford, Richard H. (2004). "Three-dimensional halfspace constructive solid geometry tree construction from implicit boundary representations". Computer-Aided Design . 36 (11): 1063– 1073. doi : 10.1016/j.cad.2004.01.006 . ^ Du, Tao; Inala, Jeevana Priya; Pu, Yewen; Spielberg, Andrew; Schulz, Adriana; Rus, Daniela; Solar-Lezama, Armando; Matusik, Wojciech (2018). "InverseCSG: automatic conversion of 3D models to CSG trees" . ACM Trans. Graph . doi : 10.1145/3272127.3275006 . ^ Fayolle, Pierre-Alain; Pasko, Alexander A. (2016). "An evolutionary approach to the extraction of object construction trees from 3D point clouds" (PDF) . Computer-Aided Design . 74 : 1– 17. doi : 10.1016/j.cad.2016.01.001 . ^ Godot Engine - Godot gets CSG support ^ Gregory, Paul (February 12, 2002). "Major release" . Retrieved May 20, 2020 – via SourceForge. ^ Magica CSG website ^ Womp website Retrieved from " https://en.wikipedia.org/w/index.php?title=Constructive_solid_geometry&oldid=1333815575 " Categories : Computer-aided design 3D computer graphics Euclidean solid geometry Hidden categories: Articles with short description Short description is different from Wikidata All articles with unsourced statements Articles with unsourced statements from November 2014 This page was last edited on 19 January 2026, at 22:30  (UTC) . Text is available under the Creative Commons Attribution-ShareAlike 4.0 License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy . Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. , a non-profit organization. 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