Rotation and TranslationMechanisms for Tabletop Interaction

Mark S. Hancock, Frédéric D. Vernier, Daniel Wigdor, Sheelagh Carpendale, Chia Shen

MITSUBISHIELECTRIC

Changes for the better

Rotation and translation techniquescan be better understood by comparing thedegrees of freedoms of input to output

Motivation

DownhillBack-Country (Telemark)

Motivation

• Downhill bindings– Attached at rear

•Telemark bindings–Free at rear

Motivation

Degrees of Freedom

The minimum number of independent variables that describes the possible movement in a system.

Degrees of Freedom

• Input (physical movement):– Single-point or multi-point (per person)– 2D surface or physical 3D space

• Output (virtual movement):– Position (2D)– Angle (1D)

Rotation & Translation

Can

you

read

this

?C

an y

ou

read

this

?

Methods ofRotation & Translation

Explicit Specification

• Input– x, y, θ, etc.– 1 DOF

• Output– x, y, θ, etc.– 1 DOF

• Input DOF = Output DOF

Independent Translation

• Input– x & y– 2 DOF

• Output– x & y– 2 DOF

• Input DOF = Output DOF

Independent Translation

T

C

O

T’

C’

Independent Rotation

• Input– x & y– 2 DOF

• Output– θ– 1 DOF

• Input DOF > Output DOF

Independent Rotation

C

T

T’

Ө

C

T

T’

Ө

Automatic Orientation

• Input– x & y– 2 DOF

• Output– r, θ– 2 DOF

• Input DOF = Output DOF

Automatic Orientation

T

O

T’

C

θ

Integral Rotation & Translation

• Input– x & y– 2 DOF

• Output– x, y, & θ– 3 DOF

• Input DOF < Output DOF

Integral Rotation & Translation

Ө

Ө T

T’

C

C’

C

Two-Point Rotation & Translation

T2 T’1

T1 T’2

T2

Ө

• Input– x1, y1, x2, y2

– 4 DOF

• Output– x, y, θ– 3 DOF

• Input DOF > Output DOF

Two-Point Rotation & Translation

T2 T’1

T1 T’2

T2

Ө

Degrees of Freedom

T2 T’1

T1 T’2

T2

Ө

1DOF → 1DOF 2DOF → 2DOF 2DOF → 2DOF

2DOF → 1DOF 4DOF → 3DOF 2DOF → 3DOF

Explicit Specification Independent Translation Automatic Orientation

Independent Rotation 2-Point Integrated

Impact ofDegrees of Freedom

Coordination & Communication

• Use rotation & translation to communicate

• Must support both:– Need all 3 DOF output

Coordination & Communication

T2 T’1

T1 T’2

T2

Ө

Communication-Friendly

Communication-Unfriendly

Consistency

• Consistent– Output = f(Input)– Output DOF ≤ Input DOF

• Inconsistent– Output ≠ f(Input)– Output DOF > Input DOF:

Consistency

ConsistentInconsistent

Completeness

• Complete– Output DOF ≥ Entire space

• Incomplete– Output DOF < Entire space

Completeness

Complete

Incomplete

GUI Integration

• Restricted Areas– Input DOF = Output DOF

• Works!

GUI Integration

Input DOF < Output DOF(Larger area desirable)

Input DOF > Output DOF(Difficult to constrain)

Role of Snapping

• Input DOF > Output DOF– e.g. Ruler: 2DOF Input, 1DOF Output– e.g. Independent Rotation, 2-Point

Role of Snapping

• Snap to polar-grid• Snap to rectilinear grid• Snap to one another

• Snap:– Position– Orientation– Both

Design Questions

• What DOF of output is necessary?

• What DOF of input is available?

• How can the input DOF be mapped to the output DOF?

• If the mapping involves a change in DOF, how will this affect interaction?

Conclusion

• Downhill bindings– Less DOF input– Good for downhill

•Telemark bindings–More DOF input–Good for uphill climbs

Conclusion

Alpine Touring (AT) Bindings

Rotation and translation techniquescan be better understood by comparing thedegrees of freedoms of input to output

Mark S. Hancock (msh@cs.ucalgary.ca)

Frédéric D. Vernier (frederic.vernier@limsi.fr)

Daniel Wigdor (dwigdor@dgp.toronto.edu)

Sheelagh Carpendale (sheelagh@cpsc.ucalgary.ca)

Chia Shen (shen@merl.com)

Thank you!