Computational Tools for 3D Printing
Ariel Shamir
Bernd Bickel
Wojciech Matusik

Part 2: Appearance Fabrication for 3D Printing
Bernd Bickel

The Appearance Of Objects

Aspects of Appearance• Shape (geometry)• Surface structure (meso-geometry)• Material (reflectance)– color, gloss, anisotropy,scattering properties, translucency,…

• Effects take place at different scales• Modelled using different representations

macro
meso
micro

Appearance Fabrication Pipelinemodelcreation-

ManualAcquisition fromreal-word objects

manipulation-

Intuitive
Expressivefabrication-

Physically realizable(image: [Li et al. 2013])

Direct Specification• Decompose into regions• Assign one material foreach region

Functional Specification

Appearance Properties

TextureFrom Functional 2 Direct Specification

Base Materials
Fabrication

Mapping /Optimization
OutputTarget Object

From Functional 2 Direct Specification
Choice of base materials

ComputeTarget Object?
?

Material Distribution+Small-scale Geometry?

Fabrication - Challenges• Get a high quality match between virtual and realmodel• Simulation of printed appearance– Choice of representation– Speed– Accuracy• Solve inverse problem– Problem parametrization– Optimization– Physical fabrication constraints

Existing 3D Color Printing Devices
Powder-binder/
Laminated[3D Systems Zprinter 650]

FDM
[http://mcortechnologies.com/]

Poly-jet[Stratasys Connex 3]

Hydrographic[FDMColor Mixing]
PrintingMany other methods exist…
• Milling: [Weyrich et al. 2007], [Weyrich et al. 2009], [Alexa and Matusik
2010], [Regg et al. 2010]• Etching: [Levin et al. 2013]• Printing on sheets: [Malzbender et al. 2012] (printing reflectance functions
on a mirrorlet array substrate); [Wetzstein et al. 2011] [Holroyd 2011] [Baranet al. 2012] (layered attenuators); [Matusik et al. 2009] (printing spatiallyvarying reflectance)• Free-form lenses: [Siedow 2008] [Finckh et al. 2010] [Papas et al. 2011] [Kiseret al. 2013] [Schwartzburg et al. 2014]• Thermoforming: [Schüller et al. 2016]• 3D printing + flatbed printer: [Lan et al. 2013] (directional reflectance)• Holograms: [Mann 1995]• …
potential combination with 3D printing possible but not part of this course

Overview
TextureSubsurface Scattering
Powder-binder/
Laminated

proprietaryLayer Shifting[Reiner et al. 2014]
Error Diffusion withtranslucent materials[Brunton et al. 2015]
Hydrographic Printing[Panozzo et al. 2015][Zhang et al. 2015]

FDM
Subsurface Scattering[Hasan et al. 2010][Dong et al. 2010]

Poly-jetHydrographicPrintingOverview
TextureSubsurface Scattering
Powder-binder/
Laminatedproprietary

Layer Shifting[Reiner et al. 2014]
Error Diffusion withtranslucent materials[Brunton et al. 2015]
Hydrographic Printing[Panozzo et al. 2015][Zhang et al. 2015]

FDM
Subsurface Scattering[Hasan et al. 2010][Dong et al. 2010]

Poly-jetHydrographicPrinting

Low-cost consumer 3D printers• Continous (two-tone) imagery[Reiner et al. 2014]

Active Color Mixing[James Chang; http://www.3ders.org/]

Layer Shifting

Dual-Color Mixing for Fused Deposition Modeling Printers
Reiner, T., Carr, N., Měch, ., Stava, O., Dachsbacher, C., Miller, G.
Computer Graphics Forum (Proc. Eurographics), 33(2), 2014

[Reiner et al. 2014]

Layer Shifting - Impression of a Gradient[Reiner et al. 2014]

22

Results[Reiner et al. 2014]

Results[Reiner et al. 2014]

Overview
TextureSubsurface Scattering
Powder-binder/
Laminatedproprietary

Layer Shifting[Reiner et al. 2014]
Error Diffusion withtranslucent materials[Brunton et al. 2015]
Hydrographic Printing[Panozzo et al. 2015][Zhang et al. 2015]

FDM
Subsurface Scattering[Hasan et al. 2010][Dong et al. 2010]

Poly-jetHydrographicPrinting

Polyjet 3D Printers
Stratasys J750
X-axis: 600 dpi; Y-axis: 600 dpi
up to 6 base resins
Challenges:• Multi-jet printing allows exactly
one material per voxel• Amount of data – typical prints
require billions of voxels• Translucent colored tints

Error Diffusion with Translucent Materials[Brunton et al. 2015]

Reproducing Albedo Texture• Problem: Multi-jet printing allows exactly
one material per voxel• Approach: Halftoning a signal defined on a surface

3D printed model([Brunton et al. 2015])

Brunton, A., Arikan, C. A., & Urban, P. (2015).
Pushing the Limits of 3D Color Printing: Error Diffusion
with Translucent Materials.
ACM Transactions on Graphics 35(1): Article 4

Background: 2D Error Diffusion

1 # 24 1 1
Example of a simple kernel
where "#" denotes the pixelcurrently being processed.
[https://en.wikipedia.org/wiki/File:Neighborhood_watch_bw.png]

Layered Halftoning
1

2,34,5

6

Material assignments• Streaming-friendly algorithm
1. Object surface mapped to voxels slice-wise
2. Sample texture, assign color to surface voxels
3. Map sRGB values to printer tonal values via ICC profile
4. Push tonal values from surface voxels to interior voxels
5. Extract “layers” or voxel iso-shells of distance to surface
6. Halftone layers independently[Brunton et al. 2015]

Error Diffusion with Translucent Materials• Consistent traversal algorithm, which maps 2D error diffusion filters onto surface• Layered halftoning, performing error diffusion on multiple layers[Brunton et al. 2015]

Results[Brunton et al. 2015]

Results[Brunton et al. 2015]

Overview
TextureSubsurface Scattering
Powder-binder/
Laminatedproprietary

Layer Shifting[Reiner et al. 2014]
Error Diffusion withtranslucent materials[Brunton et al. 2015]
Hydrographic Printing[Panozzo et al. 2015][Zhang et al. 2015]

FDM
Subsurface Scattering[Hasan et al. 2010][Dong et al. 2010]

Poly-jetHydrographic
Printing

Subsurface Scattering

Base Materials
Fabrication

Optimize stackof base materials

VolumetricModel

OutputTarget Material[Hasan et al. 2010]

Inverse Problem

min 𝑓2−Allforward unknown
problem stacking

targetreflection[Hasan et al. 2010]

A Combinatorial Search Problem• Node: A stacking of blocks• Edge: Addition of a block tothe bottom of a stacking

NodeEdge

Need efficientpruning strategies!
Root node:
empty stacking[Hasan et al. 2010]

Pruning Strategy 1: “Too Bright”

any material

If reflection is too high, no added material at the bottom
will decrease it. We can prune the node.

[Hasan et al. 2010]

Pruning Strategy 2: “Too Dark”

100% whiteIf even 100% white does not increase reflection enough, wedeem the search node too dark and prune it.
[Hasan et al. 2010]

Heterogeneous Scattering?

Convert heterogeneous problem to many homogeneous ones

[Hasan et al. 2010]

Heterogeneous Problem: Factorization• Song et al [2009]: BSSRDF factorization for artistic editing• Approximation:– Transport between x and y only depends on local material columns𝑥𝑃𝑥 (𝑟)𝑟𝑦𝑅(𝑥, 𝑦)𝑅 𝑥, 𝑦 ≈𝑃𝑦 (𝑟)𝑃𝑥 𝑟 𝑃𝑦 (𝑟)[Hasan et al. 2010]

Fabricating Heterogeneous Materials
Stone

Chess Board

Marble+…+[Hasan et al. 2010]

Heterogeneous Materials: Arbitrary Geometry
Chess Board+Marble+Stone+…+[Hasan et al. 2010]

Overview
TextureSubsurface Scattering
Powder-binder/
Laminated

proprietary

Layer Shifting[Reiner et al. 2014]
Error Diffusion withtranslucent materials[Brunton et al. 2015]
Hydrographic Printing[Panozzo et al. 2015][Zhang et al. 2015]

FDM
Subsurface Scattering[Hasan et al. 2010][Dong et al. 2010]

Poly-jetHydrographicPrintingTexturing as a Post-ProcessHydrographic Printing
Intersecting

FreeAttached

1.
2.
3.
4.

Film-Object Collision
Lowering
Quasi-static Elasticity
Labels update[Panozzo et al. 2015]

Computational Approches to Hydrographic Printing

Texture Mapping Real-World Objects with Hydrographics
Daniele Panozzo, Olga Diamanti, Sylvain Paris, Marco Tarini,
Evgeni Sorkine, Olga Sorkine-Hornung
Symposium of Geometry Processing, 2015

parametrization based (quasi-static) approach

Computational Hydrographic Printing

Yizhong Zhang, Chunji Yin, Changxi Zheng, Kun Zhou
ACM Transactions on Graphics (SIGGRAPH), 2015

dynamic simulation
film-model registration and multiple dips[Zhang et al. 2015]

Conclusion• From Functional 2 Direct Specification– Small-scale geometry– Material distribution• Solve inverse problem– Problem parametrization– Optimization– Physical fabrication constraints• Hardware– More materials– Better resolution, surface structure difficult to control

Thank you!
Acknowledgements
Philipp Urban, Alan Brunton, Tim Weyrich, Nathan Carr, Daniele Panozzo, and Hongzhi Wu for providing slides/imagematerial.

References••••••Hullin, M. B., Ihrke, I., Heidrich, W., Weyrich, T., Damberg, G., & Fuchs, M. (2012). Computational fabrication anddisplay of material appearance. InEurographics 2013-State of the Art Reports (pp. 137-153). The Eurographics
Association.
Brunton, A., Arikan, C. A., & Urban, P. (2015). Pushing the Limits of 3D Color Printing: Error Diffusion with Translucent
Materials. In ACM Transactions on Graphics (TOG) (Vol 35(, No. 1, Article 4).
Zhang, Y., Yin, C., Zheng, C., & Zhou, K. Computational Hydrographic Printing. In ACM TOG, 34, 4.
Daniele Panozzo, Olga Diamanti, Sylvain Paris, Marco Tarini, Evgeni Sorkine, Olga Sorkine-Hornung. Texture Mapping
Real-World Objects with Hydrographics.
Symposium of Geometry Processing, 2015
Reiner, T., Carr, N., Měch, R., Št'ava, O., Dachsbacher, C., & Miller, G. (2014, May). Dual‐color mixing for fused
deposition modeling printers. In Computer Graphics Forum (Vol. 33, No. 2, pp. 479-486).
Hašan, M., Fuchs, M., Matusik, W., Pfister, H., & Rusinkiewicz, S. (2010, July). Physical reproduction of materials withspecified subsurface scattering. In ACM Transactions on Graphics (TOG) (Vol. 29, No. 4, p. 61).