More Web Proxy on the site http://driver.im/

Article

MathPad²: a system for the creation and exploration of mathematical sketches

Authors:

Joseph J. LaViola, Jr.,

Robert C. ZeleznikAuthors Info & Claims

SIGGRAPH '07: ACM SIGGRAPH 2007 courses

Pages 46 - es

https://doi.org/10.1145/1281500.1281557

Published: 05 August 2007 Publication History

Abstract

We present mathematical sketching, a novel, pen-based, modeless gestural interaction paradigm for mathematics problem solving. Mathematical sketching derives from the familiar pencil-and-paper process of drawing supporting diagrams to facilitate the formulation of mathematical expressions; however, with a mathematical sketch, users can also leverage their physical intuition by watching their hand-drawn diagrams animate in response to continuous or discrete parameter changes in their written formulas. Diagram animation is driven by implicit associations that are inferred, either automatically or with gestural guidance, from mathematical expressions, diagram labels, and drawing elements. The modeless nature of mathematical sketching enables users to switch freely between modifying diagrams or expressions and viewing animations. Mathematical sketching can also support computational tools for graphing, manipulating and solving equations; initial feedback from a small user group of our mathematical sketching prototype application, MathPad², suggests that it has the potential to be a powerful tool for mathematical problem solving and visualization.

References

[1]

Alvarado, C. J. 2000. A Natural Sketching Environment: Bringing the Computer into Early Stages of Mechanical Design. Master's thesis, Massachusetts Institute of Technology.

[2]

Blostein, D., and Grbavec, A. 2001. Recognition of mathematical notation. In Handbook of Character Recognition and Document Image Analysis, World Scientific, H. Bunke and P. Wang, Eds., 557--582.

[3]

Borning, A. 1979. ThingLab: A Constraint-Oriented Simulation Laboratory. PhD thesis, Stanford University.

Digital Library

[4]

Chan, K.-F., and Yeung, D.-Y. 2000. An efficient syntactic approach to structural analysis of on-line handwritten mathematical expressions. Pattern Recognition 33, 3, 375--384.

[5]

Chan, K.-F., and Yeung, D.-Y. 2000. Mathematical expression recognition: A survey. International Journal on Document Analysis and Recognition 3, 1, 3--15.

[6]

Chan, K.-F., and Yeung, D.-Y. 2001. Pencalc: A novel application of on-line mathematical expression recognition technology. In Proceedings of the Sixth International Conference on Document Analysis and Recognition, 774--778.

Digital Library

[7]

Connell, S. D., and Jain, A. K. 2000. Template-based on-line character recognition. Pattern Recognition 34, 1, 1--14.

[8]

Connell, S. D., and Jain, A. K. 2002. Writer adaptation for online handwriting recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 3, 329--346.

Digital Library

[9]

Damm, C. H., Hansen, K. M., and Thomsen, M. 2000. Tool support for cooperative object-oriented design: Gesture-based modelling on an electronic whiteboard. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, ACM Press, 518--525.

Digital Library

[10]

Forsberg, A., Dieterich, M., and Zeleznik, R. 1998. The music notepad. In Proceedings of the 11th Annual ACM Symposium on User Interface Software and Technology, ACM Press, 203--210.

Digital Library

[11]

Gross, M. D., and Do, E. Y.-L. 1996. Ambiguous intentions: A paper-like interface for creative design. In Proceedings of the 9th Annual ACM Symposium on User Interface Software and Technology, ACM Press, 183--192.

Digital Library

[12]

Hecht, E. 2000. Physics: Calculus. Brooks/Cole.

[13]

Igarashi, T., Matsuoka, S., and Tanaka, H. 1999. Teddy: A sketching interface for 3d freeform design. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques, ACM Press/Addison-Wesley Publishing Co., 409--416.

Digital Library

[14]

Kara, L. B., Gennari, L., and Strahovich, T. F. 2004. A sketch-based interface for the design and analysis of simple vibratory mechanical systems. In Proceedings of ASME International Design Engineering Technical Conferences.

[15]

Laleuf, J. R., and Spalter, A. M. 2001. A component repository for learning objects: A progress report. In Proceedings of the First ACM/IEEE-CS Joint Conference on Digital Libraries, ACM Press, 33--40.

Digital Library

[16]

Landay, J. A., and Myers, B. A. 1995. Interactive sketching for the early stages of user interface design. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, ACM Press/Addison-Wesley Publishing Co., 43--50.

Digital Library

[17]

Lee, H.-J., and Wang, J.-S. 1995. Design of a mathematical expression recognition system. In Proceedings of the Third International Conference on Document Analysis and Recognition, IEEE Press, 1084--1087.

Digital Library

[18]

Li, X., and Yeung, D.-Y. 1997. On-line handwritten alphanumeric character recognition using dominant points in strokes. Pattern Recognition 30, 1, 31--44.

Digital Library

[19]

Matsakis, N. E. 1999. Recognition of Handwritten Mathematical Expressions. Master's thesis, Massachusetts Institute of Technology.

[20]

Miller, E. G., and Viola, P. A. 1998. Ambiguity and constraint in mathematical expression recognition. In Proceedings of the Fifteenth National Conference on Artificial Intelligence, 784--791.

Digital Library

[21]

Moran, T. P., Chiu, P., and van Melle, W. 1997. Pen-based interaction techniques for organizing material on an electronic whiteboard. In Proceedings of the 10th Annual ACM Symposium on User Interface Software and Technology, ACM Press, 45--54.

Digital Library

[22]

Mynatt, E. D., Igarashi, T., Edwards, W. K., and LaMarca, A. 1999. Flatland: New dimensions in office white-boards. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, ACM Press, 346--353.

Digital Library

[23]

Smithies, S., Novins, K., and Arvo, J. 1999. A handwriting-based equation editor. In Proceedings of Graphics Interface'99, 84--91.

Digital Library

[24]

Spalter, A. M., and Simpson, R. M. 2000. Integrating interactive computer-based learning experiences into established curricula: A case study. In Proceedings of the 5th Annual SIGCSE/SIGCUE ITiCSE Conference on Innovation and Technology in Computer Science Education, ACM Press, 116--119.

Digital Library

[25]

Varberg, D., and Purcell, E. J. 1992. Calculus with Analytic Geometry. Prentice Hall.

[26]

Young, H. D. 1992. University Physics. Addison-Wesley Publishing Company.

[27]

Zanibbi, R., Novins, K., Arvo, J., and Zanibbi, K. 2001. Aiding manipulation of handwritten mathematical expressions through style-preserving morphs. In Proceedings of Graphics Interface 2001, 127--134.

Digital Library

[28]

Zanibbi, R., Blostein, D., and Cordy, J. 2002. Recognizing mathematical expressions using tree transformation. IEEE Transactions on Pattern Analysis and Machine Intelligence 24, 11, 1--13.

Digital Library

[29]

Zeleznik, R. C., Herndon, K. P., and Hughes, J. F. 1996. Sketch: An interface for sketching 3d scenes. In Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, ACM Press, 163--170.

Digital Library

Cited By

Gunturu AWen YZhang NThundathil JKazi RSuzuki R(2024)Augmented Physics: Creating Interactive and Embedded Physics Simulations from Static Textbook DiagramsProceedings of the 37th Annual ACM Symposium on User Interface Software and Technology10.1145/3654777.3676392(1-12)Online publication date: 13-Oct-2024
https://dl.acm.org/doi/10.1145/3654777.3676392
Chulpongsatorn NLunding MSoni NSuzuki R(2023)Augmented Math: Authoring AR-Based Explorable Explanations by Augmenting Static Math TextbooksProceedings of the 36th Annual ACM Symposium on User Interface Software and Technology10.1145/3586183.3606827(1-16)Online publication date: 29-Oct-2023
https://dl.acm.org/doi/10.1145/3586183.3606827
Seddati ODupont SMahmoudi S(2017)DeepSketch 3Multimedia Tools and Applications10.1007/s11042-017-4799-276:21(22333-22359)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1007/s11042-017-4799-2
Show More Cited By

Index Terms

MathPad²: a system for the creation and exploration of mathematical sketches
1. Human-centered computing
  1. Human computer interaction (HCI)
    1. Interaction paradigms
2. Mathematics of computing
  1. Mathematical software

Recommendations

MathPad²: a system for the creation and exploration of mathematical sketches
SIGGRAPH '06: ACM SIGGRAPH 2006 Courses

We present mathematical sketching, a novel, pen-based, modeless gestural interaction paradigm for mathematics problem solving. Mathematical sketching derives from the familiar pencil-and-paper process of drawing supporting diagrams to facilitate the ...
MathPad²: a system for the creation and exploration of mathematical sketches
SIGGRAPH '04: ACM SIGGRAPH 2004 Papers

We present mathematical sketching, a novel, pen-based, modeless gestural interaction paradigm for mathematics problem solving. Mathematical sketching derives from the familiar pencil-and-paper process of drawing supporting diagrams to facilitate the ...
MathPad²: a system for the creation and exploration of mathematical sketches

We present mathematical sketching, a novel, pen-based, modeless gestural interaction paradigm for mathematics problem solving. Mathematical sketching derives from the familiar pencil-and-paper process of drawing supporting diagrams to facilitate the ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Conferences

SIGGRAPH '07: ACM SIGGRAPH 2007 courses

August 2007

6166 pages

ISBN:9781450318235

DOI:10.1145/1281500

Conference Chairs:
Sara McMains
University of California, Berkeley
,
Peter-Pike Sloan
Microsoft Corporation

Copyright © 2007 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 August 2007

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Conference

SIGGRAPH07

Sponsor:

SIGGRAPH

SIGGRAPH07: Special Interest Group on Computer Graphics and Interactive Techniques Conference

August 5 - 9, 2007

California, San Diego

Acceptance Rates

Overall Acceptance Rate 1,822 of 8,601 submissions, 21%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

13
Total Citations
View Citations
20
Total Downloads

Downloads (Last 12 months)3
Downloads (Last 6 weeks)1

Reflects downloads up to 09 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Gunturu AWen YZhang NThundathil JKazi RSuzuki R(2024)Augmented Physics: Creating Interactive and Embedded Physics Simulations from Static Textbook DiagramsProceedings of the 37th Annual ACM Symposium on User Interface Software and Technology10.1145/3654777.3676392(1-12)Online publication date: 13-Oct-2024
https://dl.acm.org/doi/10.1145/3654777.3676392
Chulpongsatorn NLunding MSoni NSuzuki R(2023)Augmented Math: Authoring AR-Based Explorable Explanations by Augmenting Static Math TextbooksProceedings of the 36th Annual ACM Symposium on User Interface Software and Technology10.1145/3586183.3606827(1-16)Online publication date: 29-Oct-2023
https://dl.acm.org/doi/10.1145/3586183.3606827
Seddati ODupont SMahmoudi S(2017)DeepSketch 3Multimedia Tools and Applications10.1007/s11042-017-4799-276:21(22333-22359)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1007/s11042-017-4799-2
Vargas González ATaranta ELaViola J(2017)Sketch Based Interaction Techniques for Chart Creation and ManipulationFrontiers in Pen and Touch10.1007/978-3-319-64239-0_5(65-82)Online publication date: 2-Dec-2017
https://doi.org/10.1007/978-3-319-64239-0_5
Bhat AKasiviswanathan GMathew CPolsley SProut EGoldberg DHammond T(2017)An Intelligent Sketching Interface for Education Using Geographic Information SystemsFrontiers in Pen and Touch10.1007/978-3-319-64239-0_11(147-163)Online publication date: 2-Dec-2017
https://doi.org/10.1007/978-3-319-64239-0_11
Agarwal SAgrawal MChaudhury S(2017)Recognizing Electronic Circuits to Enrich Web Documents for Electronic SimulationGraphic Recognition. Current Trends and Challenges10.1007/978-3-319-52159-6_5(60-74)Online publication date: 8-Jan-2017
https://doi.org/10.1007/978-3-319-52159-6_5
Weitnauer ELandy DOttmar E(2016)Graspable math: Towards dynamic algebra notations that support learners better than paper2016 Future Technologies Conference (FTC)10.1109/FTC.2016.7821641(406-414)Online publication date: Dec-2016
https://doi.org/10.1109/FTC.2016.7821641
Seddati ODupont SMahmoudi S(2016)DeepSketch 2: Deep convolutional neural networks for partial sketch recognition2016 14th International Workshop on Content-Based Multimedia Indexing (CBMI)10.1109/CBMI.2016.7500261(1-6)Online publication date: Jun-2016
https://doi.org/10.1109/CBMI.2016.7500261
Lee BSmith GRiche NKarlson ACarpendale S(2015)SketchInsight: Natural data exploration on interactive whiteboards leveraging pen and touch interaction2015 IEEE Pacific Visualization Symposium (PacificVis)10.1109/PACIFICVIS.2015.7156378(199-206)Online publication date: Apr-2015
https://doi.org/10.1109/PACIFICVIS.2015.7156378
Cummins SDavies IRice ABeresford A(2015)EqualityProceedings of the 2015 IEEE 15th International Conference on Advanced Learning Technologies10.1109/ICALT.2015.34(270-274)Online publication date: 6-Jul-2015
https://dl.acm.org/doi/10.1109/ICALT.2015.34
Show More Cited By

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents