#Eigenmath user guide code

stl (stereolithography) files for output to a 3d-printing system.ĬGAL's Nef Polyhedron is not the only type of Polyhedron representation inside of CGAL. Then it is converted to an 'ordinary polyhedron'.

The actual coordinates of the polygons that make up that 'cage' shape are calculated by CGAL by calculating the intersections and unions of the 'half spaces' involved. It is a cube with a sphere subtracted from it. Let's take example 4 from OpenSCAD's example programs.

#Eigenmath user guide code

Why would you go to all this trouble? Why not just use plain old 'points in space' and triangle faces and be done with it? Well, Nef Polyhedrons have certain properties that make boolean operations on them work better than boolean operations between meshes-in theory.ĬGAL's Nef Polyhedron code calculates the resulting 3 dimensional points of the new shapes generated when you perform CSG operations. In other terms, you have created a polyhedron by doing boolean operations on 'half spaces' - halves of the universe. This 'intersection' forms a cuboid - from the outside it just looks like a box. Now lets just imagine the 'inside' of all of these planes - and now imagine that you do an 'intersection' operation on them - like a venn diagram or any other boolean operation on sets. Now imagine you take several of these planes, and arrange them, for example, as if they were walls of a room, and a ceiling and a floor. Now, imagine you can 'mark' one side to be the 'inside' and the other side to be the 'outside'. A rough explanation of the theory goes like this: imagine you can create a 'plane' that divides the universe in half. But the main data structures are the Nef and the 'ordinary' Polyhedra.Īccording to wikipedia's Nef Polyhedron article, Nef Polyhedrons are named after Walter Nef, who wrote a book on Polyhedrons named 'Beiträge zur Theorie der Polyeder' published in 1978 by Herbert Lang, in Bern, Switzerland. It also uses various other functions like Triangulation &c. OpenSCAD uses two main features of CGAL - the Nef Polyhedra and the 'ordinary' Polyhedra. It calculates the actual 'point sets' of 3d objects, which enables the output of 3d formats like STL. It contains a large collection of Geometry algorithms and methods by which objects can be represented. Freenix 2005 paper, more detail on Goldfeather, Normalization, etc.ĬGAL is the Computational Geometry Algorithm Library.Freenix 2005 slideshow on OpenCSG, Goldfeather, and Normalization.It can help you to learn about the various OpenCSG rendering options.

OpenCSG has it's own example source code that comes with the program. The number of objects during normalization is limited and can be changed in OpenSCAD preferences. Occasionally the normalization process 'blows up' and freezes the machine, making CGAL rendering the only way to view an object. The Normalized CSG tree is then passed to OpenCSG for rendering. OpenSCAD does this normalization itself, as can be seen in the log window during OpenCSG previews. Normalization forms the primitive objects into a 'tree' where each 'leaf' consists of a 'positive' and 'negative' object. For example, if your code says to start with a cube, subtract a sphere, add a diamond, add a cylinder, add two more spheres, and subtract a donut, this is not 'normalized'. OpenCSG also requires that the objects be 'normalized'. The algorithms work by breaking down CSG operations into parts, and then rendering the parts into an OpenGL graphics buffer using special features such as an off-screen OpenGL Framebuffer Object (or Pbuffers), as well as making extensive use of the OpenGL Stencil Buffer and Depth Buffer. The two main algorithms it uses are SCS and Goldfeather, selectable in OpenSCAD from the 'preferences' menu. OpenCSG is based largely around special algorithms that can 'fake' the presentation of Computational Solid Geometry operations (subtraction, intersection, union) on a 2d screen. Discussions on the mailing list have mentioned the possibility of the OpenCASCADE library instead of CGAL, for example. It doesn't matter what 'backend' is used for it's geometry as long as it works properly and provides useful functions. In theory, though, the backend libraries could be replaced. CGAL on the other hand is a Geometry library that actually calculates intersections & unions of objects, allowing for. OpenCSG uses special tricks of OpenGL graphics cards to quickly produce 2-d 'previews' of Computational Solid Geometry operations. OpenSCAD, as of 2011, relies heavily on two other projects: the OpenCSG library and the CGAL geometry library.