Layered Manufacturing
of Thin-Walled Parts
Sara McMains, Jordan Smith,
Jianlin Wang, Carlo Séquin
UC Berkeley
Is Layered Manufacturing
really Rapid Prototyping?
2.5”, 15hrs
3.5”, 20hrs
3.0”, 25 hrs
• How can we speed up these manufacturing
technologies?
Raster Scan Technologies
•
•
•
•
Example: 3D Printing
Speed of roller limits the process
Build time = z-height
Speed up: pack build volume in xy with many parts
Vector Scan Technologies
• Example: FDM (Fused Deposition Modeling)
• Build time = volume scanned (material used)
• Our Goal: create a sturdy part that is visually equivalent
but uses less material, so that it builds faster
Building Solid Parts with QuickSlice
QuickSlice
3D B-Rep
STL
Slicer
SSL
Support
Roads
• Software interface to Stratasys 1650
FDM Machine
• Input: STL boundary representation
• Slices model into z-layer contours (SSL)
• Builds support structure
• Builds roads (nozzle fill path) (SML)
SML
FDM
QuickSlice Fast Build
3D B-Rep
STL
QuickSlice
Slicer
SSL
SML
Support
• Builds a semi-hollow
version of the solid
• n solid offset rings
• Center filled with a loose
crosshatch pattern
Fast
Roads
FDM
Fast Build Limitations
z
• Structurally conservative
• Only applied to slice
layers whose center area
is completely covered by
slices above and below it
• Gradually sloping
surfaces prevent its
application
• Worst case example
Can Approach Be More Aggressive?
3D B-Rep
Automated Process?
SML
FDM
• Our Goal:
– Create an automated process
– Input: the boundary representation of a desired solid geometry
– Output: a sturdy, physical part that is visually equivalent
while using less material
– Benefits: faster build times and material conservation
• Our Assets:
– QuickSlice software as a black box
– Specifically the loose fill crosshatched roads option
Idea #1: 3D Offset Pipeline
3D B-Rep
Polyhedron
Offset
STL
Quick
Slice
Assume we have true 3D offset surface at
the desired distance inward
• Solid-fill the volume between the
input and the offset surfaces
• Crosshatch-fill the volume within
the offset surface
Unfortunately, the 3D offset is
difficult to implement robustly!
SML
FDM
z
Idea #2: Approximate 3D Offset
3D B-Rep
QuickSlice
Slices
Slicer
Slicer
SSL
Support
Roads
SML
FDM
• Key ideas:
– Offsetting is much simpler in 2D than in 3D
– The manufacturing process eventually represents the part as a
stack in z of layers of 2D contours
• Start: slice polyhedron into desired set of 2D contours
• End: input SSL to QuickSlice to build support and roads
2D Contour Offset
3D B-Rep
Slices
Slicer
Contour
Offset
Offsets
QuickSlice
SML
FDM
S S R
SSL
• Data: layers of 2D contours
• Offset the 2D contours inward by a specified
distance = n layer thicknesses
• Near vertical walls, this is the correct 3D offset
• Approximation degrades as the walls approach
horizontal
2½D Polyhedron Offset
3D B-Rep
Slices
Slicer
Contour
Offset
Offsets
2½D
CSG
QuickSlice
SML
FDM
S S R
SSL
• Data: layers of 2D contours and offsets
• Adjust the loose fill areas in regions where
the vertical coverage above or below is
less than n layers thick
– Perform 2D boolean (CSG) combinations of
the contours and offsets of the ith layer with
the n layers above and below it
– We use OpenGL for the 2D booleans
Regularized Boolean Operations
•
•
•
•
Unregularized: op  { , , - }
Regularized: op*  { *, *, -* }
A op* B = Closure( Interior( A op B ) )
If A & B are 2D areas and C = A op* B then
C is a non-degenerate 2D area or 
A B
AB
A * B
1-Layer Thick 2½D Offset
A  Offset Si 
B  Si  Si 1   Si  Si 1 
C  Si  Offset Si 1   Offset Si 1 
Shell  A  B  C
z
1-Layer Thick 2½D Offset
A  Offset Si 
B  Si  Si 1   Si  Si 1 
C  Si  Offset Si 1   Offset Si 1 
Shell  A  B  C
z
1-Layer Thick 2½D Offset
A  Offset Si 
B  Si  Si 1   Si  Si 1 
C  Si  Offset Si 1   Offset Si 1 
Shell  A  B  C
z
n-Layer Thick 2½D Offset
A  Offset Si 
 n
 n

B'  Si  U Si k 1  Si  k   U Si k 1  Si k  
  k 1

 k 1
z
 n
 n

C '  Si  U Offset Si  k   U Offset Si k  
  k 1

 k 1
Shell  A  B'C'
n-Layer Thick 2½D Offset
A  Offset Si 
 n
 n

B'  Si  U Si k 1  Si  k   U Si k 1  Si k  
  k 1

 k 1
z
 n
 n

C '  Si  U Offset Si  k   U Offset Si k  
  k 1

 k 1
Shell  A  B'C'
n-Layer Thick 2½D Offset
A  Offset Si 
 n
 n

B'  Si  U Si k 1  Si  k   U Si k 1  Si k  
  k 1

 k 1
z
 n
 n

C '  Si  U Offset Si  k   U Offset Si k  
  k 1

 k 1
Shell  A  B'C'
Results: the Bolt Part
• QuickSlice Fast Build • 2½D Offset Method
– Time: 504 min (8:24)
– Filament used: 22.1 m
– Time: 232 min (3:52)
– Filament used: 7.6 m
QuickSlice took 2.71 times as long and
used 2.9 times as much filament
Conclusion
• We have implemented a robust 2D contour
offsetting program.
• We have conservatively approximated the 3D
polyhedron offset using 2D contour slices, 2D
offsets, and 2½D boolean operations.
• We have demonstrated a novel approach to
speeding up FDM manufacturing.
– Our approach decomposes the desired geometry into a
thin sturdy outer shell with a loosely filled center
volume.
– Our approach saves time and material as compared to
the built-in QuickSlice solution.
Thanks to our Sponsors
• NSF
– CyberCut
– CADRE:
• MOSIS++: A Distributed Manufacturing Resource
(EIA-9905140)
• Ford Motor Co.
2D Contour Offset Implementation
Input
Offset 0.1
Offset 0.2
• Difficulties arise from global interactions
• Robust approach based on Voronoi diagram
– Generalization of the approach described by
M. Held 1991
Voronoi Diagram of a Contour
• Input sites are both Vertices and
directed Edge Segments
• VD divides the plane into zones
s.t. every point in a zone is
closest to the corresponding
input site than to any other site
• Vertices of VD have an
associated signed distance
• VD is a signed distance function
Voronoi Mountain
z
z=0
• Create a height
• Offsetting by n
field by raising the
is the same as
vertices of VD in z
slicing the
by their signed
mountain with
distance
the plane z = n
Offset Slicing
z-monotone parabolic VD
edges
for each unvisited VD edge
if VD edge  z = n
Crawl VD CCW
around peak
CW around each VD
face
Dragon Curve Example
Input
Voronoi Diagram
Offset