My understanding of 3D printers is that they need specific directions for the path that the print head takes. I know Solidoodle assumes you're starting with .stl (triangle mesh) files and recommends using Skeinforge to create the printer head path files (http://www.solidoodle.com/how-to-2/how-to-print/). It looks like .stl files are pretty standard for the 3D printing community (http://www.thingiverse.com/). I do have J code to create .stl files for the Platonic solids. Are you working with a specific printer and software that requires the binary 3D array format you describe?
-----Original Message----- From: programming-boun...@jsoftware.com [mailto:programming-boun...@jsoftware.com] On Behalf Of Skip Cave Sent: Tuesday, June 26, 2012 4:03 AM To: Programming@jsoftware.com Subject: Re: [Jprogramming] The 3D printer problem For our 3D printer problem, we first look at how to create a data structure which will define a mesh of triangles, which in turn, defines a 3D solid. Then we can see about defining nouns that will compute the interior points in the solid, which would fall in each scanning plane. At first glance, it would seem that one could make a simple list of triples, where a triple is a vector with three numbers that represent the x, y, and z coordinates of a single vertex in the triangle mesh. This data structure would be a simple 3xN array where each triple represents one vertex in the triangle mesh. This seems quite efficient, except for the fact that with this data structure, discovering which verticies belong to which triangles is a non-trivial problem. The data structure needs to somehow indicate which vertices go with which triangles, to avoid any additional computational complexities. The obvious way to keep triangle data in the structure is to simply define a 3 by 3 by N matrix. Each three-element row vector in the matrix representing one point in 3D space and thus one vertex in the triangle mesh. Each 3x3 array represents three vertices, which defines exactly one triangle in the mesh, and the N 3x3 arrays then represent the N triangles in the mesh. Since all the triangles will be sharing vertices with other triangles, this scheme will be somewhat inefficient. This is because the same vertex may be in several triangles, and thus repeated in several different 3x3 matrices. However, this is probably the easiest data structure to deal with computationally, but its inefficiency may become problematic for large triangle meshes. Wikipedia presents additional proposals for triangle mesh data structures. The Wikipedia article "Triangle Mesh" ( http://en.wikipedia.org/wiki/Triangle_mesh), defines two other triangle mesh data structures, including the "Triangle Strip" and the "Index Array" structures, both of which reduce the vertex redundancy from the general case I defined previously. However, with J, it is likely much easier to deal with the fully-redundant 3x3xN matrix, as that structure should keep extra data manipulation to a minimum. This now allows us to define our first solid, the right tetrahedron I described in my first post, using our new data structure. t1 =. 4 3 3 $ 0 0 0 100 0 0 0 100 0 0 0 100 t1 0 0 0 100 0 0 0 100 0 0 0 100 0 0 0 100 0 0 0 100 0 0 0 100 0 0 0 100 0 0 0 100 0 0 0 100 Where t1 is the data structure for our tetrahedron. Now we are ready to try to build the point classification algorithm, which will take some work, in order to convert Feito's algorithm to J. Any suggestions would be appreciated.. Skip On Tue, Jun 26, 2012 at 1:40 AM, Skip Cave <s...@caveconsulting.com> wrote: > So far, no one has replied to my 3D printer problem post. Meanwhile, I > have been researching the problem, and I have found what looks like a > reasonable algorithm that could be applied to the solution. The > algorithm is described in a paper by F.R. Feito and others, entitled > "An Efficient Point Classification Algorithm for Triangle Meshes". > > The paper is located at: http://elliscave.com/cc/sfrto05.pdf. > > The C code implementing the algorithm is at: > http://wwwdi.ujaen.es/~gigjaen/recursos/inclusionmesh.htm > > This algorithm gives us a head start on the problem. We still need to > find the points in each of the 100 scan planes that fall within the solid. > However, one of the first steps will be to decide how to structure the > data for the triangle mesh in a "J" way, which will represent the > solid, and still lend itself to the coming computations. That will be > my next step in this problem space. > > Skip > > > On Mon, May 21, 2012 at 8:46 AM, Skip Cave <s...@caveconsulting.com>wrote: > >> A key problem for all 3D printers is to convert a defined solid into >> a set of horizontal slices (planes) through the solid. Each slice >> will represent one scan-pass of the printer head for the 3D printer >> as it builds up the solid, one layer at a time. >> >> >> Each slice through the solid should be defined as a binary 2D surface >> array, with a binary one in the array indicating that specific point >> on the plane is inside the solid, and a binary zero in the array >> indicating that the point in the plane is outside the solid. A one in >> the scan plane array indicates that the printer should deposit some >> material at this point in the plane, and a zero indicates that the >> printer should not deposit any material at this point in the plane. >> >> >> For this problem, we will define a solid using a set of points in 3D >> space. The points define the vertices on the surface of the solid. >> The edges of the solid are defined as the lines between the points. >> The faces of the solid are defined by the set of points which are in the same plane. >> In the general case, the faces of the solid's surface can be made as >> numerous and as small as required, to form the required shape. >> >> >> Our solids will be defined in a 3 dimensional space, with points in >> the space represented by an x,y,z triple. Thus a solid tetrahedron >> can be represented by four points in the space. >> >> >> The four points 0,0,0 100,0,0 0,100,0 and 0,0,100 define a simple >> right tetrahedron. This will be the first solid that we want to print >> with our 3D printer. >> >> >> We define a horizontal scan surface for our printer as the plane >> defined by the three points 0,0,0 100,0,0 0,100,0. There is no >> reason to define the scan surface array any larger than the solid >> itself, so the scan surface array can be a 100 x 100-point binary array. >> >> >> Each point in a scan-surface array must indicate whether it is inside >> or outside the solid shape. If the point is inside the solid, a >> binary one will tell the printer to deposit material at this point. >> If the point is outside the solid, a binary zero will tell the >> printer to not deposit any material there. >> >> >> For our 3D printer, we need to generate 100 of these binary scan >> surface arrays, one for each resolution step as the printer moves up >> through the solid space. These 100 scan surface arrays define where >> the 3D printer will deposit material on each layer, to form our >> tetrahedron. The 3D printer will start with the lowest layer of the >> scan arrays, and build the material up from there. >> >> >> The problem is to define a J verb that will generate the one hundred >> 100x100 2D binary arrays (essentially building a 100x100x100 3D >> binary matrix), which represents the 100 horizontal slices through >> the solid. That binary matrix will indicate to the 3D printer where >> to place the material to create the solid. >> >> >> Once you have generated the 100x100x100 binary array for the >> tetrahedron, test your function out by generating a similar scan >> surface array for the solid created by the intersection of two tetrahedrons: >> >> >> Tetrahedron 1: 50,0,0 0,50,0 50,50,0 25,25,100 >> >> Tetrahedron2: 0,50,0 0,0,50 0,50,50 100,25,25 >> >> >> For further challenges, see if your J function can generate the set >> of 3D printer scan surface arrays for the four other Platonic solids >> besides the tetrahedron. Here are the J definitions for all the Platonic solids: >> http://tinyurl.com/bry2yxc You probably will want to scale these >> solids up by a factor of 10 or so. >> >> >> In general, your J function should be able to generate binary scan >> surface arrays for a 3D printer given any arbitrary solid, defined by >> a set of points in 3-space. Actually, besides the points, for complex >> solids you may need a vector indicating which side of each surface or >> face is the inside of the solid. >> >> >> Skip >> >> >> > > > -- > Skip Cave > Cave Consulting LLC > Phone: 214-460-4861 > > -- Skip Cave Cave Consulting LLC Phone: 214-460-4861 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
