Representation Issues in Data Exchange for RP-LM Sara McMains U.C. Berkeley

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

Data Translation Easiest for the designer: –Format that includes all design constructs B-reps –Tesselated –Trimmed NURBS CSG Sweeps Voxels Parametric Surface equations

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

Data Translation Easiest for the manufacturer: –Simplest possible format Lowest common denominator This is why STL is still being used!

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

ASCII or Binary? ASCII –Data exchange always imperfect Humans will end up examining files Binary –Compact –Computers store binary numbers Simple fractional decimals cannot be exactly represented as floating point values

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

Sources of Cracks in STL Round-off –Instancing with geometric transformations

Require Shared Vertices Specify vertex coordinates only once All geometry that shares vertex references same vertex Compact for transmission Forces designer to think about connectivity

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

Sources of Cracks in STL –Boolean trim curves

Boolean Trim Curves Intersection curve higher order than input Mapped back onto input patches –Approximated in parametric space –Won’t match exactly on two patches Connectivity of trimmed patches should be specified explicitly

File Repair Techniques: Local Triangulate between unmatched facet edges –Bohn and Wozny ’92 –Barequet and Sharir ’95 Merges edges for small cracks, Triangulate remaining holes –Barequet and Kumar ’97 Adding triangles may introduce intersections; Best match problem NP complete

File Repair Techniques: Global Build a Binary Space Partitioning tree, identify solid regions, output boundary –Murali & Funkhouser ’97 Scalability issues

Better STL Generation Curved patch to STL conversion without gaps: Match discretized trim curves, User-supplied tolerances –Dolenc ’93 –Sheng & Meier ’95 Prevent intersections when triangulating

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

Nesting Information Should nesting of shells be transmitted? –Designer intent –But how is nesting generated? Computed from b-rep? –What if it disagrees with geometry? Who do you believe - geometry or topology?

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

Units Require units! Lack of units invites educated guesses Default unit not good enough –Assumptions may differ –Require explicit specification Force assumptions to be visible

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

Input Captured in Layers E.g. –CT scans –Digitized input Can we manufacture these layers directly? Do we want to?

Matched Layer Thicknesses

Unmatched Layer Thicknesses

Surface Reconstruction Interpolate between input slices –Interpolation smooths boundary –Additional processing can further smooth coarse input –Complete freedom to re-orient surface Faster build times

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit

Implicit Booleans Implicit unions

Implicit Booleans Implicit unions

Implicit Booleans Implicit differences (2D example)

Implicit Booleans Implicit differences (2D example)

Implicit Booleans Implicit differences (2D example)

Implicit Booleans Implicit differences (2D example)

Implicit Booleans Implicit differences (2D example)

Implicit Booleans Implicit differences (2D example)

Implicit Booleans Implicit differences (2D example)

Implicit Booleans Self-intersections (2D example)

Implicit Booleans Self-intersections (2D example)

Implicit Booleans Self-intersections (2D example)

Implicit Booleans Even if exchange format doesn’t include explicit Booleans, implicit Booleans will arise Manufacturers won’t categorically reject Need semantics for implicit Booleans

non-2-manifold Scope: Solids Optimize for 2-manifolds –2 directed “edge-uses” per undirected edge Should also support non-manifold solids 2-manifold

Pseudo-2-Manifolds Geometry not 2-manifold Represented topology is 2-manifold

RP-LM Data Exchange Designer Read Validate Scale Position/orient Slice Rasterize Manufacturer Network Translate Write Transmit