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Freehand Drawing System based on Geometric Constraints

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Two Parts of the Talk. Introduction to Pegasus[Igarashi, UIST 1997

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### Freehand Drawing Systembased on Geometric Constraints

### Prototype System Pegasus

OutlineOutlineOutlineOutline

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
- Any comments greatly appreciated!

Outline

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

Problem

- Diagrams
- In documents, slides, …
- By drawing editors
- Difficult to satisfy geometric relations!

Example (contd.)

- In this case, grids works well, but…

The user attempts to

draw a perpendicular line,

GRID

but grid prevents desired placements.

ROTATE

rotates it, but fails to get precise angle.

Outline

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

Interactive Beautification

Beautify.

Ambiguity Handling

But free strokes are ambiguous.

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

Live Demo

Outline

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

Beautification Systems

[Pavlidis 1985] ...

Free Stroke Vectorization

[Apple Newton] [SmartSketch] ...

Free Stroke Vectorization (contd.)

Local context

Drawing Systems based on Geometric Constraints

[Sutherland 1963] [Nelson 1985] ...

Drawing Systems based on Geometric Constraints (contd.)

- 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

Segment coordinates

Constraint Inference

Multiple constraints

Constraint Solver

Multiple candidates

Candidate Evaluation

Primary candidate

Beautification AlgorithmInput

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 InferencePerpendicular

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

Edge Connection

x0 = const, y0 = const

etc.

(x1, y1)

(x0, y0)

Constraint Inference (contd.)

- How?
- Supported constraints

if (distance(point1, point2) < 30)

infer constraint(point1 == point2);

Input

Possible constraints

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

Output

Beautification candidates

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

Constraint SolverPerpendicular

Same Length

Edge Connection

Horizontal

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

Purpose

To confirm the intuition !

“It’s difficult for novice users

to use commands”

“Interactive beautification is good”

Experimental Settings

- 18 subjects
- 3 diagrams, 3 editors (9 sessions / person)

Systems

- CAD ... AutoSketch(AutoDesk), CAD Software.
- Draw ... SmartSketch(Future Wave), Drawing Editor.
- Pegasus…Our Prototype system.

On AMiTY (a pen computer)

Diagrams and Constraints

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)

Evaluation: Conclusion

- Pegasus cannot do everything
- But: certainly useful in its target domain

CAD

Paint

Geometric diagrams,

rapidly & precisely!

1. Problem

2. Our Idea & Demonstration

3. Related Work

4. Algorithm

5. Evaluation

6. Ongoing Study

7. Summary

Ongoing Work

- Address limitations of Pegasus
- Only lines
- Too many candidates
- Forgets constraints

Limitation: Only Lines (contd.)

- 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

Limitation: Too Many Candidates

Overlapping…

Constraint switching interface

- Visualize conflicting constraints
- Enable manual switching
- Challenges
- How to detect conflicting constraints efficiently?

Limitation: Forgets Constraints

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

Summary

- Pegasus: freehand drawing system
- User study showed promising results
- Geometric constraints play an important role in sketch beautification
- Further improvements to be made

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