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# Freehand Drawing System based on Geometric Constraints - PowerPoint PPT Presentation

Freehand Drawing System based on Geometric Constraints. Kaisuke Nakajima Joint work with Takeo Igarashi. User Interface Research Group The University of Tokyo. Two Parts of the Talk. Introduction to Pegasus [Igarashi, UIST 1997 & CHI 1998] Improvement attempts My current study

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### Freehand Drawing Systembased on Geometric Constraints

Kaisuke Nakajima

Joint work with Takeo Igarashi

User Interface Research Group

The University of Tokyo

• Introduction to Pegasus

• [Igarashi, UIST 1997 & CHI 1998]

• Improvement attempts

• My current study

• Any comments greatly appreciated! 

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

• Diagrams

• In documents, slides, …

• By drawing editors

• Difficult to satisfy geometric relations!

Flip

Move

• In this case, grids works well, but…

Another Example

draw a perpendicular line,

but grid prevents desired placements.

rotates it, but fails to get precise angle.

COPY

Better strategy:

copy the slope  rotate 90 degrees

Grid

Flip

Copy

Rotate

Why Difficult?

The user must plan detailed strategy.

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

+ Beautify

Our Idea

• Sketching is easy!

• Sketch  Beautify

• Interactive Beautification[Igarashi, UIST 1997]

Interactive Beautification

Interactive Beautification

Satisfied

Constraints

Beautify.

Interactive Beautification

Beautify.

Beautify.

But free strokes are ambiguous.

Generate multiple candidates

 Let the user select

In this way,the user can constructprecise geometric diagramswithout any editing commands!!

### Prototype System Pegasus

Live Demo

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

[Pavlidis 1985] ...

Batch-based

too many errors!

More Interaction (+ multiple candidates)

[Apple Newton] [SmartSketch] ...

Local context

Local context

Global context

[Sutherland 1963] [Nelson 1985] ...

• Previous work

• Explicitly specify constraints

• Our approach

• Infer constraints

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

Constraint Inference

Multiple constraints

Constraint Solver

Multiple candidates

Candidate Evaluation

Primary candidate

Beautification Algorithm

Reference segments

(array of (X0, Y0, X1, Y1))

New stroke

(x0, y0, x1, y1)

Output

Possible constraints

(linear equations of (x0, y0, x1, y1))

Constraint Inference

Perpendicular

const * (x1 – x0) + const * (y1 – y0) = 0

Edge Connection

x0 = const, y0 = const

etc.

(x1, y1)

(x0, y0)

• How?

• Supported constraints

if (distance(point1, point2) < 30)

infer constraint(point1 == point2);

Possible constraints

(linear equations of (x0, y0, x1, y1))

Output

Beautification candidates

(array of (x0, y0, x1, y1))

Constraint Solver

Perpendicular

Same Length

Edge Connection

Horizontal

Candidate nearest to the original stroke

 Primary candidate

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

To confirm the intuition !

“It’s difficult for novice users

to use commands”

“Interactive beautification is good”

How fast?

Precision

Beautiful?

Two Measures

• 18 subjects

• 3 diagrams, 3 editors (9 sessions / person)

• Draw ... SmartSketch(Future Wave), Drawing Editor.

• Pegasus…Our Prototype system.

On AMiTY (a pen computer)

B)

C)

A)

Parallel-1

Symmetric-1

Parallel-1

Parallel-2

Symmetric-2

Parallel-2

Connected

(all Vertices)

Perpendicular

Equal Interval

Vertical and Horizontal

Connected

(all Vertices)

Connected (all Vertices)

Rapidness

Averaged drawing time

for three diagrams

The ratio of sessions where

all constraints are satisfied

### Results

100

600

500

80

400

60

300

40

200

in both rapidness and precision.

20

100

0

0

Draw

Pegasus

Draw

Pegasus

• Pegasus cannot do everything

• But: certainly useful in its target domain

Paint

Geometric diagrams,

rapidly & precisely!

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

• Only lines

• Too many candidates

• Forgets constraints

 Support curves

• Circles, ellipses, arcs,

Bézier curves

• (Experimental demo)

• Challenges with curves

• More ambiguity

• Shape recognition

• Constraint inference

• Complex constraints: how to represent?

• e.g. line tangent to piecewise Bézier curve

• Complex constraints: how to solve efficiently?

• Exponential growth of candidate solutions

Overlapping…

 Constraint switching interface

• Visualize conflicting constraints

• Enable manual switching

• Challenges

• How to detect conflicting constraints efficiently?

•  Remember constraints

• Maintain them during manipulation

• Chorus [Hosobe 2001]

Skewed 

Stretch!

Stretch!

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

• Pegasus: freehand drawing system

• User study showed promising results

• Geometric constraints play an important role in sketch beautification

• Further improvements to be made

• Papers & demos available at

http://www-ui.is.s.u-tokyo.ac.jp/