Generalized Matryoshka Computational Design of Nesting … · 2017. 10. 13. · Generalized Matryoshka Computational Design of Nesting Objects. Title: matryoshka-pdf Created Date:

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Alec JacobsonUniversity of Toronto

Generalized MatryoshkaComputational Design of Nesting Objects

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Previous work enables computational design of reconfigurables

7[Garg et al. 2016]

Previous work enables computational design of reconfigurables

8[Garg et al. 2016]

Previous work enables computational design of reconfigurables

9[Garg et al. 2016]

[Zvyozdochkin & Malyutin 1890]

We present a method to generalize Matryoshkato arbitrary shapes

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We present a method to generalize Matryoshkato arbitrary shapes

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Nesting requires strict enclosure…

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loose enclosure

Nesting requires strict enclosure…

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enclosure

Nesting also requires removal

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enclosed, but not removable loose enclosure

Nesting also requires removal

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enclosed, but not removable

cut

loose enclosure

Nesting also requires removal

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enclosed, but not removable loose enclosure

Nesting also requires removal

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enclosed, but not removable enclosed and removable loose enclosure

We present highly parallelizable methods to…

• determine feasibility of nesting,

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We present highly parallelizable methods to…

• determine feasibility of nesting,• find maximum scale,

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We present highly parallelizable methods to…

• determine feasibility of nesting,• find maximum scale, and• optimize nesting scale

over some or all parameters

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Our optimization utilizes rigid motionfor tighter nesting

39% 53% 63%

fixed position+rotation fixed rotation free22

Our optimization utilizes rigid motionfor tighter nesting

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39% 53% 63%

fixed position+rotation fixed rotation free

Our optimization utilizes rigid motionfor tighter nesting

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39% 53% 63%

fixed position+rotation fixed rotation free

We define valid self-nesting

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A

AGiven:1. shape ,

We define valid self-nesting

Given:1. shape ,2. similarity transform ,

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A

A

T T (A)

We define valid self-nesting

Given:1. shape , 2. similarity transform ,3. cut plane , and

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AT (A)T

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PP

We define valid self-nesting

Given:1. shape , 2. similarity transform ,3. cut plane , and4. removal trajectories

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AT (A)T

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PP

We define valid self-nesting

Given:1. shape , 2. similarity transform ,3. cut plane , and4. removal trajectories directions

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AT (A)T

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PP

We define valid self-nesting

Must have:1. , and2. no collisions along

either direction after cutting by

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AT (A)

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P

T (A)⇢

A P

We define valid self-nesting

Must have:1. , and2. no collisions along

either direction after cutting by

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AT (A)

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P

T (A)⇢

A PDefinition depends on choice of cut plane and removal directions.

Some configurations admit perfect self-nesting

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convex shapes?

Some configurations admit perfect self-nesting

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convex shapes?enclosure is easy ….

Some configurations admit perfect self-nesting

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convex shapes?enclosure is easy ….but removal depends on cut plane!

[Zvyozdochkin & Malyutin 1890]

invalid

valid36

invalid

valid37

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Perfect self-nesting requires visibility of cut plane at all points along removal directions

Our tool exploresnesting of arbitrary solid 3D shapes

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Our tool exploresnesting of arbitrary solid 3D shapes

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Our tool exploresnesting of arbitrary solid 3D shapes

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We cast this as a computational design problem

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Manual design with traditional tools would be tortuous

We cast this as a computational design problem

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Manual design with traditional tools would be tortuous

We cast this as a computational design problem

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Manual design with traditional tools would be tortuous

We cast this as a computational design problem

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Manual design with traditional tools would be tortuous

Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Take a clue from order-independent transparency by “depth peeling”

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Take a clue from order-independent transparency by “depth peeling”

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Take a clue from order-independent transparency by “depth peeling”

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Take a clue from order-independent transparency by “depth peeling”

[Everitt 2001, Bavoil et al. 2007][Baldacci et al. 2016]

[Shade et al. 1998][Inui & Ohta 2007][Faure et al. 2008]

[Kim et al. 2002][Myszkowski et al.1995, Knott & Pai 2003, Heidelberger et al. 2004]

[Goldfeather et al. 1986, Kelley et al. 1994, Hable & Rossignac 2005]

a.k.a. K-Buffer, Layered Depth Imagestransparencyshape diameterimage-based renderingCNC millingintersection volumeswept volumescollision detectionCSG operations

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Take a clue from order-independent transparency by “depth peeling”

[Everitt 2001, Bavoil et al. 2007][Baldacci et al. 2016]

[Shade et al. 1998][Inui & Ohta 2007][Faure et al. 2008]

[Kim et al. 2002][Myszkowski et al.1995, Knott & Pai 2003, Heidelberger et al. 2004]

[Goldfeather et al. 1986, Kelley et al. 1994, Hable & Rossignac 2005]

a.k.a. K-Buffer, Layered Depth Imagestransparencyshape diameterimage-based renderingCNC millingintersection volumeswept volumescollision detectionCSG operations

Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Bad “codes”:• blue before orange• orange before green• orange before front-facing blue

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

Feasible!• all green

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Step 1: we determine feasibility in real-timeby exploiting orthographic rendering

Feasible!• all green

“ping-pong” with 2 buffersGL_SAMPLES_PASSED

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Step 2: binary search to maximize scale

Assume momentarily that shape is convex

Fix cut plane, center of mass, rotation

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Step 2: binary search to maximize scale

Assume momentarily that shape is convex

Fix cut plane, center of mass, rotation

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Step 2: binary search to maximize scale

Assume momentarily that shape is convex

Fix cut plane, center of mass, rotation

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Step 2: binary search to maximize scale

Assume momentarily that shape is convex

Fix cut plane, center of mass, rotation

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Step 2: binary search to maximize scale

Assume momentarily that shape is convex

Fix cut plane, center of mass, rotation

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Step 2: binary search to maximize scale

Assume momentarily that shape is convex

Fix cut plane, center of mass, rotation

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Step 2: binary search to maximize scale

For non-convex shapes binary search is conservative,

but in practice optimal

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Step 2: binary search to maximize scale

For non-convex shapes binary search is conservative,

but in practice optimal

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Step 2: binary search to maximize scale

For non-convex shapes binary search is conservative,

but in practice optimal

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Step 2: binary search to maximize scale

For non-convex shapes binary search is conservative,

but in practice optimal

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Step 2: binary search to maximize scale

For non-convex shapes binary search is conservative,

but in practice optimal

Step 3: optimize over all parameters

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70%

0%

70%

maximize scale subject to nesting constraint

non-convex energy landscape

Step 3: optimize over all parametersvia particle swarm optimization

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k parameter vector as point in nD

Step 3: optimize over all parametersvia particle swarm optimization

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k parameter vector as point in nD

update each iteration according to “velocity”

Step 3: optimize over all parametersvia particle swarm optimization

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pull velocity toward personal best and global best of swarm

k parameter vector as point in nD

Step 3: optimize over all parametersvia particle swarm optimization

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random perturbations

k parameter vector as point in nD

Naive P-Swarm would treat scale as just another parameter (coordinate)…

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… instead optimize over all others,

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all other parameters

… instead optimize over all others,

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… instead optimize over all others, and search for max scale

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… instead optimize over all others, and search for max scale

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abort search early if upper bound < best

Our optimization enables fully automatic Matryoshka generation…

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Automatic Upright Custom Cut Plane

63%60% 56%

fully optimized

… or partially constrained interactive design

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Automatic Upright Custom Cut Plane

63%60% 56%fixed upright orientation

… or partially constrained interactive design

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Automatic Upright Custom Cut Plane

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+ fixed cut plane

Tool performs fast enough for interaction

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Tool performs fast enough for interaction

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We validate our results via 3D printing

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We validate our results via 3D printing

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We validate our results via 3D printing

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We validate our results via 3D printing

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We validate our results via 3D printing

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We validate our results via 3D printing

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We validate our results via 3D printing

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We validate our results via 3D printing

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We validate our results via 3D printing

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We validate our results via 3D printing

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We accommodate printer tolerances by nesting within an offset surface

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Our tools trivially generalize to nesting disparate shapes

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Limitations & Future Work• no global optimum guarantee

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Limitations & Future Work• no global optimum guarantee• search assumption too conservative

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Limitations & Future Work• no global optimum guarantee• search assumption too conservative• thin shapes don’t rigidly nest well

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Limitations & Future Work• no global optimum guarantee• search assumption too conservative• thin shapes don’t rigidly nest well• deformable nesting?

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Limitations & Future Work• no global optimum guarantee• search assumption too conservative• thin shapes don’t rigidly nest well• deformable nesting?

1. deform during design

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Limitations & Future Work• no global optimum guarantee• search assumption too conservative• thin shapes don’t rigidly nest well• deformable nesting?

1. deform during design2. nest soft physical objects

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Acknowledgements…David LevinNSERC Discovery Grants (RGPIN-2017-05235 & RGPAS-2017-507938)Connaught Fund (NR-2016-17)Adobe Systems Inc.Kevin Gibson, Masha Shugrina, Michael Tao, and Alex Tessier

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Alec [email protected]

Generalized MatryoshkaComputational Design of Nesting Objects