Computational Fabrication: Bridging the Productivity Gap between 3D Printing and Subtractive Manufacturing. Mohammad M. Hossain

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1 Computational Fabrication: Bridging the Productivity Gap between 3D Printing and Subtractive Manufacturing Mohammad M. Hossain

2 Freeform CNC fabrication Robust surface offsetting Compact Voxel Structure

3 Additive vs Subtractive Fabrication Image Source: Shapeways Image Source: Siemens

4 Fabrication Pipeline: From CAD to CNC Input Mesh Axes Configuration G-codes CNC Machine Machined Part

5 Fabrication time Productivity Gap: Milling vs 3D Printing Part programming time

6 Freeform CNC fabrication Robust surface offsetting Compact Voxel Structure

7 CAM Tool-path Planning in 2D Image Source: MIT Fabrication Course

8 CAM Tool-path Planning in 3D

9 Triangle Offsetting in 2D Given a triangle and an offset distance r, expand or shrink the triangle: 2r a b c

10 Triangle Offsetting in 3D For each Vertex For each Edge For each Triangle Sphere Cylinder Prism

11 Triangle Offsetting: Alternative Approach

12 Generic Offsetting: Alternative Approach Image Source: MIT Fabrication Course

13 High Flop per dollar High Memory B/W Productivity CUDA Scalability Massive Computing Parallelism

14 Freeform CNC fabrication Robust surface offsetting Compact Voxel Structure

15 Grid Data Structures Tiles Voxel Block Uniform Grid Tiled Grid

16 Octree Data Structure Quadtree (2D analogue to 3D Octree)

17 Hybrid Illustration Image Source: DreamWorks Studios

18 Hybrid Dynamic Tree (HDT) HDT: combination of tiled grid and octree Level 1 Level 2 (16 x 2 3 x 16) 3 = 2,048 3 Root Grid [16 x 16 x 16] Octree Level 3 Leaf Grid [16 x 16 x 16]

19 Building Blocks: Leaf Grid

20 HDT Memory Pools C Root Cell C C 0 C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 1 0 Root Grid C 1 C 5 Octree Cell C 1 1 C 1 3 C 1 5 C 1 2 C 1 4 C 1 6 C 1 7 C 5 0 C 5 1 C 5 2 C 5 3 C 5 4 C 5 5 C 5 6 C 5 7 Element Pool Leaf Pool

21 HDT Demonstration

22 HDT Construction Steps (1) Triangle Mapping Map each triangle to the root cells that intersect it. Only check the root cells that overlap the bounding box of the triangle.

23 HDT Construction Steps (2) HDT Branching Each cell splits into eight child cells. Each child tests intersection with the set of triangles overlapped with its parent cell.

24 HDT Construction Steps (3) Leaf Processing At target resolution, a cell is decomposed into a block (Leaf Grid) of voxels. Each voxel state is coded in 2 bits: INSIDE, OUTSIDE or ON the surface. Each thread in a CUDA block of size processes 16 voxels, coded in 2 bits 16 = 4 bytes.

25 HDT Benchmarks Triangles 230, ,104 57,792 38,000 Resolution HDT Height Leaf Grid (x 10 3 ) HDT Cell (x 10 3 ) HDT Active Voxels (x 10 6 ) Bits / voxel

26 Storage Comparisons Per active voxel total storage in HDT o With leaf dimension of (data) + 2 (topology) = 34 bits o With leaf dimension of 8 16 (data) + 8 (topology) = 24 bits

27 Time (sec) HDT Construction Times at

28 HDT Construction Speedups at Triangles Mapping HDT Branching Leaf Processing Overall Speed-up

29 Freeform CNC fabrication Robust surface offsetting Compact Voxel Structure

30 Volume Offsetting in CNC Manufacturing Target Part Expanded Part Contact Volume Union of expanded part and shrunk stock Part in Stock Shrunk Stock

31 Iterative Volume Offsetting

32 Convolution based Offsetting o Input A volume represented in hybrid dynamic tree (HDT). An offset distance (+ve expand, -ve shrink) o Output An expanded (or shrunk) volume represented in HDT. o Implementation A convolution based algorithm that uses a stencil kernel to define the spatial neighborhood in 3D space.

33 Convolution Offsetting Demonstration A ring structuring element or template (magnified) 2D Cross-section (of a cube) to be swept with the ring template Dilated cross-section (green) overlaid with the input (red)

34 Time (sec) Offsetting Results at Head Dragon Turbine Candle Holder mm 2mm 3mm 4mm Offset Distance

35 Optimization via Kernel Decomposition Offset 1 voxel [# 4] Offset 2 voxels [# 12] Offset 3 voxels [# 24]

36 Offsetting Time (sec) Normalized Average Error Kernel Decomposition Results Dragon Horse Armadillo Candle Holder Dragon Horse Armadillo Candle Holder Offset 40 voxels x 1 Offset 20 voxels x 2 Offset 10 voxels x 4 Offset 5 voxels x voxels x 2 10 voxels x 4 5 voxels x 8

37 Milled Parts

38 Ball Joint: CNC fabricated VS 3D Printed

39 Executive Summary CNC programming can be as easy as 3D Printing. o Hybrid Dynamic Tree (HDT) is highly storage-efficient; up to 2.5x compact than state-of-the-art VDB approach. o HDT is well-suited for accelerated algorithm development on GPUs. o Both HDT and Convolution Offsetting algorithm is highly scalable to a GPU-cluster deployment.

40 Team Mohammad M Hossain David R Lynn James S Collins Dr. Thomas Tucker Dr. Thomas Kurfess Dr. Richard Vuduc

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