Junction meshing for lattice structures

Abstract

Methods, systems, and apparatus, including medium-encoded computer program products, for designing three dimensional lattice structures include, in one aspect, a method including: calculating a radius of incidence for respective pairings of beams of different sizes that converge at a junction in a lattice; determining a maximized radius of incidence for each of the beams based on the radii of incidence for the pairings with that beam; comparing the maximized radii of incidence to find a global radius for the junction; calculating local intersection points and global intersection points, respectively, for each of the beams with a local sphere defined by the maximized radius of incidence for that beam and with a global sphere defined by the global radius for the junction; and generating meshing with sockets for the beams at the junction using the local intersection points and the global intersection points.

What is claimed is: 
     
         1 . A method comprising:
 receiving, at a physical structure designing computer, input specifying one or more regions of a three dimensional (3D) model in which to generate a non-uniform lattice;   generating, by the physical structure designing computer, the non-uniform lattice in the one or more regions of the 3D model, the generating comprising
 (i) creating different sized beams that meet at junctions to form the non-uniform lattice, and 
 (ii) meshing at least a portion of the junctions in the non-uniform lattice by, for each junction of multiple junctions in the at least a portion of the junctions,
 (a) calculating, for each pair of beams that meet at a center point of the junction, a distance between the center point and a point of intersection of the pair of beams, 
 (b) determining a maximized distance for each beam from distances from the center point calculated for respective points of intersection between the beam and remaining beams at the junction, 
 (c) finding a largest maximized distance for the beams that meet at the center point of the junction, and 
 (d) calculating, using the largest maximized distance and respective maximized distances for the beams that meet at the center point of the junction, 3D mesh for sockets that receive the beams for the junction to form a mechanically robust structure at the junction; and 
 
   storing, by the physical structure designing computer, the non-uniform lattice in a document on a non-transitory computer-readable medium, wherein the document is usable by a computer controlled manufacturing machine to manufacture a physical structure comprising the non-uniform lattice.   
     
     
         2 . The method of  claim 1 , wherein generating the non-uniform lattice comprises:
 varying junction placement within the non-uniform lattice; and   varying a number of intersecting beams that meet at each junction in the non-uniform lattice.   
     
     
         3 . The method of  claim 2 , wherein creating the different sized beams that meet at junctions to form the non-uniform lattice comprises:
 varying a thickness of the different sized beams; and   varying a cross section profile of the different sized beams.   
     
     
         4 . The method of  claim 3 , wherein determining the maximized distance for each beam from the distances from the center point comprises:
 finding a largest of the distances from the center point; and   adding a margin amount to the largest distance to generate the maximized distance.   
     
     
         5 . The method of  claim 1 , wherein calculating the 3D mesh for sockets that receive the beams for the junction comprises:
 stereographically projecting intersections of the beams with a sphere, which is defined by the largest maximized distance from the center point, to create two dimensional (2D) projections of the beams;   generating triangulation between the 2D projections; and   mapping connectivity of the triangulation to intersection points of corner lines of the beams with spheres, which are respectively defined by the respective maximized distances from the center point, to form the sockets that receive the beams for the junction.   
     
     
         6 . The method of  claim 5 , wherein generating the triangulation comprises using Constrained Delaunay Triangulation (CDT) on the 2D projections. 
     
     
         7 . The method of  claim 1 , wherein calculating the 3D mesh for sockets that receive the beams for the junction comprises:
 calculating a 3D convex hull using, as input, intersection points of corner lines of the beams with a sphere, which is defined by the largest maximized distance from the center point, to create triangulation in a 3D space about the junction; and   mapping connectivity of the triangulation to intersection points of corner lines of the beams with spheres, which are respectively defined by the respective maximized distances from the center point, to form the sockets that receive the beams for the junction.   
     
     
         8 . The method of  claim 7 , wherein calculating the 3D convex hull comprises using end points of the beams as the input in addition to the intersection points of the corner lines of the beams. 
     
     
         9 . The method of  claim 1 , wherein calculating the 3D mesh for sockets that receive the beams for the junction comprises:
 generating 3D socket edges between the beams from intersection points of corner lines of the beams with a sphere, which is defined by the largest maximized distance from the center point; and   generating each 3D beam socket point, of multiple beam socket points connected by the 3D socket edges, by finding a maximum of one or more distances from the center point calculated for respective one or more points of intersection between the beam to attach at the 3D beam socket point and one or more other beams with at least one socket point connected to the 3D beam socket point by an edge in the 3D socket edges.   
     
     
         10 . The method of  claim 9 , wherein calculating the 3D mesh for sockets that receive the beams for the junction comprises:
 generating one or more subdivision points for each of the 3D socket edges to increase a number of edges in the 3D mesh for the sockets and to improve material efficiency of the junction, wherein each subdivision point is located in a 3D space about the junction based on (i) two 3D beam socket points connected through a 3D socket edge being divided by the subdivision point, and (ii) a distance from the center point of a midpoint of a shortest distance between two beam corner lines that connect to the two 3D beam socket points.   
     
     
         11 . A non-transitory computer-readable medium encoding computer program instructions operable to cause a physical structure designing computer to perform operations comprising:
 receiving, at the physical structure designing computer, input specifying one or more regions of a three dimensional (3D) model in which to generate a non-uniform lattice;   generating, by the physical structure designing computer, the non-uniform lattice in the one or more regions of the 3D model, the generating comprising
 (i) creating different sized beams that meet at junctions to form the non-uniform lattice, and 
 (ii) meshing at least a portion of the junctions in the non-uniform lattice by, for each junction of multiple junctions in the at least a portion of the junctions,
 (a) calculating, for each pair of beams that meet at a center point of the junction, a distance between the center point and a point of intersection of the pair of beams, 
 (b) determining a maximized distance for each beam from distances from the center point calculated for respective points of intersection between the beam and remaining beams at the junction, 
 (c) finding a largest maximized distance for the beams that meet at the center point of the junction, and 
 (d) calculating, using the largest maximized distance and respective maximized distances for the beams that meet at the center point of the junction, 3D mesh for sockets that receive the beams for the junction to form a mechanically robust structure at the junction; and 
 
   storing, by the physical structure designing computer, the non-uniform lattice in a document on a non-transitory computer-readable medium, wherein the document is usable by a computer controlled manufacturing machine to manufacture a physical structure comprising the non-uniform lattice.   
     
     
         12 . The non-transitory computer-readable medium encoding the computer program instructions of  claim 11 , wherein generating the non-uniform lattice comprises:
 varying junction placement within the non-uniform lattice; and   varying a number of intersecting beams that meet at each junction in the non-uniform lattice.   
     
     
         13 . The non-transitory computer-readable medium encoding the computer program instructions  claim 12 , wherein creating the different sized beams that meet at junctions to form the non-uniform lattice comprises:
 varying a thickness of the different sized beams; and   varying a cross section profile of the different sized beams.   
     
     
         14 . The non-transitory computer-readable medium encoding the computer program instructions of  claim 13 , wherein determining the maximized distance for each beam from the distances from the center point comprises:
 finding a largest of the distances from the center point; and   adding a margin amount to the largest distance to generate the maximized distance.   
     
     
         15 . The non-transitory computer-readable medium encoding the computer program instructions  claim 11 , wherein calculating the 3D mesh for sockets that receive the beams for the junction comprises:
 stereographically projecting intersections of the beams with a sphere, which is defined by the largest maximized distance from the center point, to create two dimensional (2D) projections of the beams;   generating triangulation between the 2D projections; and   mapping connectivity of the triangulation to intersection points of corner lines of the beams with spheres, which are respectively defined by the respective maximized distances from the center point, to form the sockets that receive the beams for the junction.   
     
     
         16 . The non-transitory computer-readable medium encoding the computer program instructions  claim 15 , wherein generating the triangulation comprises using Constrained Delaunay Triangulation (CDT) on the 2D projections. 
     
     
         17 . The non-transitory computer-readable medium encoding the computer program instructions  claim 11 , wherein calculating the 3D mesh for sockets that receive the beams for the junction comprises:
 calculating a 3D convex hull using, as input, intersection points of corner lines of the beams with a sphere, which is defined by the largest maximized distance from the center point, to create triangulation in a 3D space about the junction; and   mapping connectivity of the triangulation to intersection points of corner lines of the beams with spheres, which are respectively defined by the respective maximized distances from the center point, to form the sockets that receive the beams for the junction.   
     
     
         18 . The non-transitory computer-readable medium encoding the computer program instructions  claim 17 , wherein calculating the 3D convex hull comprises using end points of the beams as the input in addition to the intersection points of the corner lines of the beams. 
     
     
         19 . The non-transitory computer-readable medium encoding the computer program instructions  claim 11 , wherein calculating the 3D mesh for sockets that receive the beams for the junction comprises:
 generating 3D socket edges between the beams from intersection points of corner lines of the beams with a sphere, which is defined by the largest maximized distance from the center point; and   generating each 3D beam socket point, of multiple beam socket points connected by the 3D socket edges, by finding a maximum of one or more distances from the center point calculated for respective one or more points of intersection between the beam to attach at the 3D beam socket point and one or more other beams with at least one socket point connected to the 3D beam socket point by an edge in the 3D socket edges.   
     
     
         20 . The non-transitory computer-readable medium encoding the computer program instructions  claim 19 , wherein calculating the 3D mesh for sockets that receive the beams for the junction comprises:
 generating one or more subdivision points for each of the 3D socket edges to increase a number of edges in the 3D mesh for the sockets and to improve material efficiency of the junction, wherein each subdivision point is located in a 3D space about the junction based on (i) two 3D beam socket points connected through a 3D socket edge being divided by the subdivision point, and (ii) a distance from the center point of a midpoint of a shortest distance between two beam corner lines that connect to the two 3D beam socket points.