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Freehand Drawing System based on Geometric Constraints Kaisuke Nakajima Joint work with Takeo Igarashi User Interface Research Group The University of Tokyo

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Two Parts of the Talk Introduction to Pegasus [Igarashi, UIST 1997 & CHI 1998] Improvement attempts My current study Any comments greatly appreciated!

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Outline 1. Problem 2. Our Idea & Demonstration 3. Related Work 4. Algorithm 5. Evaluation 6. Ongoing Study 7. Summary

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

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Example

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CopyFlipMove

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Example (contd.) In this case, grids works well, but…

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Geometric constraints Another Example

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The user attempts to draw a perpendicular line,

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but grid prevents desired placements. GRID

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He draws a box separately, and...

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rotates it, but fails to get precise angle. ROTATE

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Better strategy: copy the slope rotate 90 degrees COPY ROTATE

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The user must plan detailed strategy. Copy Flip Move Rotat e Grid Planning overhead Why Difficult?

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Outline 1. Problem 2. Our Idea & Demonstration 3. Related Work 4. Algorithm 5. Evaluation 6. Ongoing Study 7. Summary

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Our Idea Sketching is easy! Sketch Beautify Interactive Beautification [Igarashi, UIST 1997] Sketch + Beautify

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Draw and... Interactive Beautification

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Beautify. Satisfied Constraints Draw and... Interactive Beautification

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Beautify. Draw and... Interactive Beautification

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Beautify. Interactive Beautification

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But free strokes are ambiguous. Ambiguity Handling

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Generate multiple candidates Let the user select Ambiguity Handling

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In this way, the user can construct precise geometric diagrams without any editing commands!!

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Prototype System Pegasus Live Demo

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Diagrams Drawn

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Outline 1. Problem 2. Our Idea & Demonstration 3. Related Work 4. Algorithm 5. Evaluation 6. Ongoing Study 7. Summary

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[Pavlidis 1985]... Beautification Systems

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Batch-based too many errors! More Interaction (+ multiple candidates) Beautification Systems (contd.)

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[Apple Newton] [SmartSketch]... Free Stroke Vectorization

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Local context Free Stroke Vectorization (contd.)

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Global contextLocal context Free Stroke Vectorization (contd.)

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Drawing Systems based on Geometric Constraints [Sutherland 1963] [Nelson 1985]...

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Drawing Systems based on Geometric Constraints (contd.) Previous work Explicitly specify constraints Our approach Infer constraints

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Outline 1. Problem 2. Our Idea & Demonstration 3. Related Work 4. Algorithm 5. Evaluation 6. Ongoing Study 7. Summary

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Beautification Algorithm Constraint Inference Segment coordinates Multiple constraints Constraint Solver Multiple candidates Candidate Evaluation Primary candidate

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Constraint Inference Input Reference segments (array of (X 0, Y 0, X 1, Y 1 )) New stroke (x 0, y 0, x 1, y 1 ) Output Possible constraints (linear equations of (x 0, y 0, x 1, y 1 )) Perpendicular const * (x 1 – x 0 ) + const * (y 1 – y 0 ) = 0 Edge Connection x 0 = const, y 0 = const etc. (x 0, y 0 ) (x 1, y 1 )

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Constraint Inference (contd.) How? Supported constraints if (distance(point1, point2) < 30) infer constraint(point1 == point2);

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Constraint Solver Input Possible constraints (linear equations of (x 0, y 0, x 1, y 1 )) Output Beautification candidates (array of (x 0, y 0, x 1, y 1 )) Perpendicular Edge Connection Same Length Horizontal

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Constraint Solver (contd.)

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Candidate Evaluation Candidate nearest to the original stroke Primary candidate

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Outline 1. Problem 2. Our Idea & Demonstration 3. Related Work 4. Algorithm 5. Evaluation 6. Ongoing Study 7. Summary

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To confirm the intuition ! “It’s difficult for novice users to use commands” “Interactive beautification is good” Purpose

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Rapidness How fast? Precision Beautiful? Two Measures

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

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Systems CAD... AutoSketch (AutoDesk), CAD Software. Draw... SmartSketch (Future Wave), Drawing Editor. Pegasus…Our Prototype system. On AMiTY (a pen computer)

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Diagrams and Constraints A) B) C) Parallel-1 Parallel-2 Perpendicular Vertical and Horizontal Connected (all Vertices) Symmetric-1 Symmetric-2 Connected (all Vertices) Parallel-1 Parallel-2 Equal Interval Connected (all Vertices)

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Results Rapidness Precision Averaged drawing time for three diagrams 0 100 200 300 400 500 600 CAD Draw Pegasus 0 20 40 60 80 100 CADDrawPegasus The ratio of sessions where all constraints are satisfied Pegasus outperformed CAD and Draw, in both rapidness and precision.

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Evaluation: Conclusion Pegasus cannot do everything But: certainly useful in its target domain CAD Paint Geometric diagrams, rapidly & precisely!

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Outline 1. Problem 2. Our Idea & Demonstration 3. Related Work 4. Algorithm 5. Evaluation 6. Ongoing Study 7. Summary

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Ongoing Work Address limitations of Pegasus Only lines Too many candidates Forgets constraints

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Limitation: Only Lines Support curves Circles, ellipses, arcs, Bézier curves (Experimental demo)

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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

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Limitation: Too Many Candidates Overlapping… Constraint switching interface Visualize conflicting constraints Enable manual switching Challenges How to detect conflicting constraints efficiently?

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Limitation: Forgets Constraints Remember constraints Maintain them during manipulation Chorus [Hosobe 2001] Stretch! Skewed

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Outline 1. Problem 2. Our Idea & Demonstration 3. Related Work 4. Algorithm 5. Evaluation 6. Ongoing Study 7. Summary

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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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Thank you Papers & demos available at http://www-ui.is.s.u-tokyo.ac.jp/

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