Hi Luc! Thank you for your answer. I tried it an it works. But isn't there an easier way to build a polyhedron? Do I relly need this projection and line stuff?
Best regards, Martin -------- Original-Nachricht -------- > Datum: Sat, 25 Aug 2012 14:03:33 +0200 > Von: Luc Maisonobe <luc.maison...@free.fr> > An: Commons Users List <user@commons.apache.org> > Betreff: Re: [math] How to use the BSP Tree? > Le 25/08/2012 12:17, Martin Ennemoser a écrit : > > Hi! > > Hi Martin, > > > > > I have a polyhedron in 3D space that consists of a triangle mesh. Now I > want to use the BSP tree to classify wheter a point is inside or outside of > the polyhedron. > > The problem is that I don't know how to construct a BSP tree with my > polyhedron vertices. The user guide only gives provides little information. > > Maybe someone could give me with a short code example. > > You can look for example at the junit tests. One example is testIssue780 > in the PolyhedronsSetTest class in package > org.apache.commons.math3.geometry.euclidean.threed. The algorithm used > by the test is the following: > > 1) set up the points coordinates for all vertices of the polyhedron > 2) set up the mesh triangles by using an indirection array > of indices (i.e. somthing like triangle 1 uses points 1, 2 and 3, > triangle 2 uses point 4, 5 and 1, traingle 3 uses ...) > 3) for each triangle, create a facet using the following stages: > 3a) create a 3D plane from the three points > 3b) create 2D points by projecting the 3D points into the plane > 3c) create three 2D lines by joining all pairs of projected 3D points > 3c) create a 2D PolygonSet using the 2D lines > 3d) create a 3D SubPlane using the plane and the 2D PolygonSet > 4) create the PolyhedronSet using all 3D SubPlanes > > The main trick is the 2D/3D projection that occurs at each facet. > > Beware that when you create a Region from a collection of boundary > elements (i.e. creating a PolygonSet from lines or creating a > PolyhedronSet from facets), the elements in the boundary must be > oriented, as they define which half space will be the interior and which > half space will be the exterior. The convention we use is that the > interior is on the minus side of the hyperplane. For lines, the plus > side is the half space on the right when traveling along the line in > ascending coordinate direction. This implies that if you define a square > polygon, you should define the boundary in counterclockwise direction if > you want the interior to be the finite square (on the left as you travel > in counterclockwise direction along the boundary) and the exterior to be > the infinite plane minus the central square (on the right as you travel > in counterclockwise direction along the boundary). If you define the > boundary in the opposite direction (i.e clockwise), the interior will be > the infinite region and the exterior will be the finite square. If you > define your boundary with some elements in one direction and other > elements in the opposite direction, this will fail. For planes in 3D, > the plus half space is towards plane normal. > > best regards, > Luc > > > > > Thank you! > > > > --------------------------------------------------------------------- > > To unsubscribe, e-mail: user-unsubscr...@commons.apache.org > > For additional commands, e-mail: user-h...@commons.apache.org > > > > > > > --------------------------------------------------------------------- > To unsubscribe, e-mail: user-unsubscr...@commons.apache.org > For additional commands, e-mail: user-h...@commons.apache.org > --------------------------------------------------------------------- To unsubscribe, e-mail: user-unsubscr...@commons.apache.org For additional commands, e-mail: user-h...@commons.apache.org
