Geometric Modeling Topics

Transcription

1 Geometric Modeling Topics George Allen,

2 Outline General background Convergent modeling Multi-material objects Giga-face lattices Page 2

3 Boundary Representation (b-rep) Topology Is the glue that holds trimmed surfaces together Representation of an object by storing its boundary (i.e. its surfaces) Face on the left as you walk along a fin Topology Objects Body Region Shell Face Loop Fin Edge Vertex Page 3

4 Topology and Geometry -- Largely Independent Topology Objects Body Edge Region Shell Face Geometry Objects Surface Loop Topology Fin Surface1 Face1 Face2 Surface2 Edge Curve Fin1 Fin2 Vertex Connectivity Shape Edge 3D Curve Geometry Page 4

5 Parasolid B-Rep Body Types Solid body Sheet body Cellular body -- regions with common faces Page 5 Wire body Non-manifold body Mixed dimension body

6 Outline General background Convergent modeling Multi-material objects Giga-face lattices Page 6

7 Convergent Modeling: Two New Types of Geometry in Parasolid Surfaces Plane Circular cylinder Circular cone Sphere Torus NURB surface Surface of revolution Extruded surface Offset surface Rolling ball fillet surface Mesh (new) Curves Line Circle Ellipse NURB curve Parameter-space curve Intersection curve Polyline (new) Intersection curve New surface type: mesh (a connected collection of triangles) New curve type: polyline (piecewise linear) Still a boundary representation, but using some new geometry types Many operations are independent of surface type, so they just work Current limitation: a body s faces must be all mesh, or all curvy/classic NURBS surface Cylindrical surface Circle Mesh surface Cylindrical surface Circle Mesh surface Mesh surface Polyline Page 7

8 Mesh Surfaces Are More General than Classic Ones A traditional surface is a warped rectangle. Mathematically, it is globally parameterized by a mapping u, v S(u, v) from 0,1 0,1 into R 3 Mesh surfaces are much more general. They are not necessarily rectangular. Their parameterizations are local. v u, v S(u, v) u Each of these is a single face. No matter how you bend and warp a rectangle, you can t make shapes like this Page 8

9 Speedup in Reverse Engineering Workflows Traditional Workflow Removes the surfacing step from many workflows Sources of facet data Scanning FE models CAM IPW models JT and STL files Physical Scan Surface Offset Detail Application areas: Automotive (clay scans) Medical 3D printing New Convergent Workflow Facetted models already work in many downstream apps (e.g. CAM, FEM,...) Physical Scan Offset Detail Page 9

10 Medical Application Boolean operation directly on scanned mesh data, without constructing surfaces CAD model Boolean subtract Bone scan Page 10

11 But,... I Need Smooth Surfaces I need smooth surfaces to machine dies You probably don t. If you give surfaces to a CAM algorithm, the first thing it will do is tesselate them. Fine tesselation Coarse tesselation I need G3 surfaces for good reflections You probably don t If the tesselation is fine enough, the reflections will look good. Smooth surfaces help to reduce data size, but are not necessary for good shape quality. Page 11

12 Parametrics/Associativity Parametric/associative editing works as with classic geometry Powerful editing operations. Some examples are: Change offset distance Change rib widths Replace outer mesh by a NURBS surface Mesh Cone Cylinder Mesh Page 12

13 Outline General background Convergent modeling Multi-material objects Giga-face lattices Page 13

14 Multi-Material Objects the Chunky Case Multiple distinct regions, each with its own homogeneous material Easy: use Parasolid cellular body capability A cellular body has internal faces that partition it into several regions A different material could be assigned to each region Cellular bodies supported better than general non-manifold ones Possible workaround just use an assembly of touching bodies Metal region embedded within a plastic region Page 14

15 Multi-Material Objects -- the Graded Case Some 3D printers can produce continuous variation in composition Material composition varies continuously as a function of x, y, z location in space Huge benefit a new design parameter New problem current CAx systems all assume that material is homogeneous Mixing at the droplet level Page 15

16 Some Possible Approaches to Graded Materials Fake it (in simple cases) Field functions: f x, y, z = x 2 + y 2 Tetrahedral interpolation (the 3MF approach) Page 16

17 Mass Properties with Variable Density New algorithm needed in Parasolid prototype shown here ρ = C.G. C.G. ρ = Density = 1.00 (constant) Weight = C.G. = (1.05, 0, 4.27) Density varies from 1.00 to 0.25 Weight = C.G. = (0.64, 0, 3.34) Page 17

18 Outline General background Convergent modeling Multi-material objects Giga-face lattices Page 18

19 Lattices Produced by Additive Manufacturing Coarse Medium Fine Coarse -- No Problem Just use curvy b-reps, same as today. Everything works Medium Big Problem A lattice with a few billion faces. Too fine to use a b-rep, but too coarse to be considered homogeneous. Probably need some new approach. Very fine Smaller Problem The lattice structure is so fine that the material can essentially be considered homogeneous. Many things just work. Mfg still a problem. Page 19

20 Lattice Data Size Problems cells Number of cells in a lattice can be very large: 1 m 3 part with cell size of 1 mm cells 10 bytes per cell 10 gigabyte of data Size problems if we try to create an explicit (evaluated) representation of the entire lattice Curvy b-reps are too big Facetted b-reps are too big But... many b-rep-based algorithms do not need the entire lattice b-rep all at once So, we can generate the b-rep lazily/locally, only when and where it s needed Page 20

21 Handling Giga-face Lattices -- Some Ideas Use implicit (unevaluated) representations, like programs or skeletal graphs Generate explicit (evaluated) reps like b-reps locally and lazily when/where needed Type = regular rectangular Repeats: nx = 4 ; ny = 2 Spacing: dx = 5 ; dy = 10 Ball_diameters = 2 Rod_diameters = 1 Evaluate lazily/locally Evaluate lazily/locally Parameters & Logic The recipe for the lattice Rules/logic for generating it Skeleton Graph Ball centers Ball connectivity Ball_diameters = 2 Rod_diameters = 1 Explicit Reps Curvy b-rep Faceted b-rep Voxels Page 21

22 Store the Recipe (Program), Not the Geometry A parametric model **is** a program, so nothing new A very concise way to represent a complex repetitive model. 40 lines of code Evaluate lazily/locally Complex rod-ball lattice for 3D printing Large balls at one end Smaller balls at other end Page 22

23 Summary Convergent modeling A new surface type (mesh) Works just like classic surfaces Dramatic speedups in reverse engineering New modeling technology for AM Graded materials Giga-face lattices Both require fundamental changes New reps have to work in all applications Page 23

24 Related presentations Peter Kerwin What s New in Parasolid Andreas Saar, Jon Stevenson, Brad Rothenberg additive manufacturing Mike Zink What s New in JT Thank You george.allen@siemens.com Page 24