3D printing enables the production of objects that combine materials in hitherto infeasible ways, with the potential of varying their use with a granularity of up to individual print-resolution voxels. By combining printing materials, such as powders, fluid agents, etc., in volumetrically different ways, a limited number of materials can be used to yield a great variety of object properties, such as stiffness, strength, density, translucency and color. A key challenge is to ensure that an input object with volumetrically- specified properties is appropriately transformed to yield per-voxel recipes for how to combine a printing system’s materials. To ensure that such a transformation is performed in a way that maintains volumetric control with up to voxel precision, the present paper introduces a content processing pipeline that has individual printed voxel contents as its basic building blocks and that controls their placement in a natively volumetric domain. This pipeline is an evolution of the HANS print control paradigm. First results, applied to control color of 3D printed objects are reported.

1. © Copyright 2017 HP Inc.
A Multi-Material, Volumetric, Voxel-By-Voxel Content
Processing Pipeline for Color and Beyond
Peter Morovič*, Ján Morovič*, Ingeborg Tastlº, Melanie Gottwalsº, Gary Dispotoº
*HP Inc., Barcelona, Catalonia, Spain, ºHP Inc., Palo Alto (CA), USA
Presented at CIC 25, 14 September 2017, Lillehammer, Norway

2. © Copyright 2017 HP Inc.
Outline
• Pub Quiz
• Volumetric probability control domain
• Halftoning
• Building resources
• Results

3. © Copyright 2017 HP Inc.
HANS3D printed part
using first continuous
color & mechanically
robust resources in
December ’14
at HP Labs Palo Alto
Pub quiz question:
How and when was
this printed?

4. © Copyright 2017 HP Inc.
Case study: a chair (or a robot)

5. © Copyright 2017 HP Inc.
Atomic states: Mvecs
Label Cyan Magenta Yellow NIRD
Blank 0 0 0 0
N 0 0 0 1
Y 0 0 1 0
YN 0 0 1 1
M 0 1 0 0
MN 0 1 0 1
MY 0 1 1 0
MYN 0 1 1 1
C 1 0 0 0
CN 1 0 0 1
CY 1 0 1 0
CYN 1 0 1 1
CM 1 1 0 0
CMN 1 1 0 1
CMY 1 1 1 0
CMYN 1 1 1 1
N Y M MY
C CY CM CMY
Mvecs allow for
explicit/precise choice
of material
combination they
define the domain
• For set of agents + powders, the set of all their
possible combinations = set of atomic states: at-
voxel base materials
• For CMYN agents + single powder & binary use: set of
all base materials: 24 = 16 Mvecs (material vectors)
• Also: not just materials but anything that can be
controlled or specified per-voxel (temperature,
spectrum, powders, agents, …) is a dimension in the
Mvec domain!
M1 M2 M3 M4

6. © Copyright 2017 HP Inc.
Combining atomic states: Mvocs
• The ‘bill of materials’ over a unit volume:
Material Volume Coverages - Mvocs
*The probability distribution of materials
Mvocs allow for explicit/
precise control of the
proportions of material
combinations (Mvecs)
used over a volume

7. © Copyright 2017 HP Inc.
Combining Mvocs
• Volume-proportional combinations of
relative uses of materials, or:
convex combinations (via
barycentric coordinates) of convex
combinations of materials
• Volumetric transitioning of proportions
+ guarantee of no materials other than
those used in vertices involved in the
combination → smoothness of
transitioning ‘for free’

8. © Copyright 2017 HP Inc.
Building a mapping: Color to Mvocs
• Knowing what object property is achieved by
what Mvoc → build LUTs simply by putting
known object properties in correspondence
with Mvocs and interpolating by volumetric
convex combinations in-between
• Simple color example: hand-assign Mvocs
found to give certain colors to eight
vertices of RGB cube - other RGBs get
Mvocs from tetrahedral interpolation between 8
defined vertices (at most 4 at a time)

9. © Copyright 2017 HP Inc.
Halftoning objectives
• Given an Mvoc that determines probabilities of individual Mvecs
(materials) → distribute Mvecs over the volume they are
assigned to such that Mvoc proportions hold

10. © Copyright 2017 HP Inc.
PARAWACS3D
• PARAWACS3D: Single 3D matrix based halftoning (Parallel Random Weighted Area Coverage
Selection) - at location [x, y, z] Mvoc is compared against a value from a matrix ← all [x, y, z]
locations of a volume at once
• Using a 3D matrix allows for explicit control of 3D relationships (complementarity,
connectivity, level density, clustered, dispersed…)

11. © Copyright 2017 HP Inc.
The RGB cube
• First continuous color sample with prototype-grade mechanical properties
← within HP and outside
• Hand-built resources ← smoothness ‘for free’ without printing and measuring
any samples, linearity not (applied via 1D curves)
• But! A pipeline that is not color-specific
[object properties → Mvocs → Mvecs]

12. © Copyright 2017 HP Inc.
Structural Halftoning
Spatial Structure
Vector (STL)
Sliced Spatial
Structure
3D Structured
blue-noise (12b)
Print-ready 3DHT
of RGB Cube

13. © Copyright 2017 HP Inc.
Conclusions
• Takeaways about HANS3D:
• 3D-native, volumetric control of voxel contents
• Any [object property to volumetric voxel
probability] mapping possible
• Super-set of any other possible approach
(everything can be expressed as a volumetric
probability distribution of voxel contents + spatial
arrangement)
• Next steps
• Applying to other properties (visual, mechanical,
electrical, chemical, optical, …) and multiple
properties: e.g. a “strong red”, “translucent
yellow”, “pining blue” …

14. © Copyright 2017 HP Inc.
Takk så mye!
• Africa Real
• Annarosa Multari
• Andrew Fitzhugh
• Albert Serra
• David Gaston
• Hou T Ng
• Jay Gondek
• Juan Manuel Garcia Reyero
• Keith Moore
• Lihua Zhao
• Ramon Pastor
• Sascha de Peña
🎂