Radial lattice structures for additive manufacturing

1. A physical object created by additive manufacturing, the physical object comprising:

multiple beams connected with each other at junction points to form a lattice of the physical object;

wherein the beams of the lattice correspond to a duplicated three dimensional (3D) structure;

wherein the 3D structure has (i) first sets of junction points at a first location along an axis for the 3D structure, and (ii) second sets of junction points at a second location, which is different from the first location, along the axis for the 3D structure; and

wherein, when projected into a two dimensional (2D) plane normal to the axis, the first sets of junction points alternate with the second sets of junction points at successive radii positions away from the axis in the 2D plane normal to the axis.

2. The physical object of claim 1 , wherein the first sets of junction points and the second sets of junction points have projection locations in the 2D plane that correspond to an Archimedean spiral.

3. The physical object of claim 1 , wherein the first sets of junction points and the second sets of junction points have projection locations in the 2D plane that correspond to a piecewise spiral.

4. The physical object of claim 1 , comprising additional beams connected with the junction points.

5. The physical object of claim 1 , wherein the first sets of junction points and the second sets of junction points have projection locations in the 2D plane determined by one or more input parameters for a spiral.

6. The physical object of claim 5 , wherein the beams of the lattice are formed from only a portion of the duplicated 3D structure.

7. A method comprising:

creating nodes in a plane normal to an axis in accordance with a spiral, wherein proper subsets of the nodes occur at successive radii positions away from the axis in the plane normal to the axis;

repositioning every other one of the proper subsets, from at least a portion of the nodes, in a direction in 3D space along the axis;

creating a three dimensional (3D) structure in the 3D space, the 3D structure comprising beams placed between the repositioned and non-repositioned proper subsets;

duplicating the 3D structure one or more times to form a lattice in the 3D space; and

selecting at least a portion of the lattice for inclusion in a 3D model.

8. The method of claim 7 , wherein the spiral is a spiral with constant separation distance between successive turns of the spiral, and creating the nodes in the plane comprises:

creating the spiral;

replicating the spiral with rotation in the plane normal to the axis;

mirroring the replicated spiral; and

using intersection points of the replicated and mirrored spirals as the nodes in the plane normal to the axis.

9. The method of claim 8 , wherein the spiral is an Archimedean spiral.

10. The method of claim 7 , wherein the spiral is a piecewise spiral, and creating the nodes in the plane comprises:

creating a first portion of the nodes from a radial grid; and

creating a second portion of the nodes by connecting the first portion of the nodes in a crisscross pattern.

11. The method of claim 7 , comprising:

placing additional beams between the repositioned proper subsets to form the 3D structure in the 3D space; and

adding additional beams between the non-repositioned proper subsets to form the 3D structure in the 3D space.

12. The method of claim 7 , comprising selecting the portion of the nodes from which to reposition the proper subsets, selecting a portion of the lattice for inclusion in the 3D model, or both.

13. The method of claim 12 , wherein moving every other one of the proper subsets comprises moving each node a distance equal to an average of distances between the nodes in the plane normal to the axis.

14. A system comprising:

a non-transitory storage medium having instructions of a three dimensional (3D) modeling program stored thereon; and

one or more data processing apparatus configured to run the instructions of the 3D modeling program to (i) obtain an axis of rotation for a part of a 3D model of an object to be built using an additive manufacturing apparatus, (ii) receive values for at least one size parameter to govern lattice cell size and an angle parameter to govern a number of wedges about the axis of rotation, (iii) generate nodes in 3D space using the axis of rotation and the received values, (iv) add beams connecting the nodes to form a rotationally balanced lattice in the 3D space, and (v) provide at least a portion of the rotationally balanced lattice for inclusion in the part of the 3D model of the object.

15. The system of claim 14 , wherein the one or more data processing apparatus are configured to run the instructions of the 3D modeling program to generate the nodes in the 3D space using a spiral with constant separation distance between successive turns of the spiral.

16. The system of claim 15 , wherein the spiral is an Archimedean spiral.

17. The system of claim 14 , wherein the one or more data processing apparatus are configured to run the instructions of the 3D modeling program to generate the nodes in the 3D space using a radial grid extended in a direction of the axis of rotation.

18. The system of claim 17 , wherein the one or more data processing apparatus are configured to run the instructions of the 3D modeling program to add the beams by connecting nodes of the extended radial grid in a crisscross pattern.

19. The system of claim 18 , wherein the one or more data processing apparatus are configured to run the instructions of the 3D modeling program to add the beams by further connecting nodes of the extended radial grid along straight and circular edges of the extended radial grid.

20. The system of claim 14 , wherein the one or more data processing apparatus are configured to run the instructions of the 3D modeling program to receive (i) an integer input for the number of lattice cells around a circumference, (ii) a lattice cell size in the radial direction, (iii) a lattice cell size along the axis of rotation, and (iv) a minimum radius of an inner most boundary of the rotationally balanced lattice.

21. The system of claim 20 , wherein the received lattice cell size in the radial direction and the received lattice cell size along the axis of rotation are both held constant for all lattice cells of the rotationally balanced lattice.

22. The system of claim 14 , wherein the one or more data processing apparatus are configured to run the instructions of the 3D modeling program to enable selection of a portion of the rotationally balanced lattice for inclusion in the part of the 3D model of the object, and enable deformation of the rotationally balanced lattice either before or after the selection of the portion.

23. The system of claim 14 , further comprising the additive manufacturing apparatus, wherein the one or more data processing apparatus are configured to run the instructions of the 3D modeling program to generate the 3D model of the object with the rotationally balanced lattice included in the part of the 3D model.

24. The system of claim 14 , wherein the one or more data processing apparatus are configured to run the instructions of the 3D modeling program to enable selection of a lattice topology, wherein the added beams connecting the nodes correspond to the selected lattice topology, and the rotationally balanced lattice comprises a self-supporting, mechanically robust and efficient lattice structure that is manufacturable using additive manufacturing systems and techniques.