article

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

Authors:

Joseph J. LaViola, Jr.,

Robert C. ZeleznikAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 23, Issue 3

Pages 432 - 440

https://doi.org/10.1145/1015706.1015741

Published: 01 August 2004 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.

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Cited By

Sharma SSharma CAsenso ESharma K(2023)Research Constituents and Trends in Smart Farming: An Analytical Retrospection from the Lens of Text MiningJournal of Sensors10.1155/2023/69162132023:1Online publication date: 11-Aug-2023
https://doi.org/10.1155/2023/6916213
Xia ZMonteiro KVan KSuzuki R(2023)RealityCanvas: Augmented Reality Sketching for Embedded and Responsive Scribble Animation EffectsProceedings of the 36th Annual ACM Symposium on User Interface Software and Technology10.1145/3586183.3606716(1-14)Online publication date: 29-Oct-2023
https://dl.acm.org/doi/10.1145/3586183.3606716
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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

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 23, Issue 3

August 2004

684 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1015706

Editor:
John C. Hart

Issue’s Table of Contents

Copyright © 2004 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]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 August 2004

Published in TOG Volume 23, Issue 3

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Cited By

Sharma SSharma CAsenso ESharma K(2023)Research Constituents and Trends in Smart Farming: An Analytical Retrospection from the Lens of Text MiningJournal of Sensors10.1155/2023/69162132023:1Online publication date: 11-Aug-2023
https://doi.org/10.1155/2023/6916213
Xia ZMonteiro KVan KSuzuki R(2023)RealityCanvas: Augmented Reality Sketching for Embedded and Responsive Scribble Animation EffectsProceedings of the 36th Annual ACM Symposium on User Interface Software and Technology10.1145/3586183.3606716(1-14)Online publication date: 29-Oct-2023
https://dl.acm.org/doi/10.1145/3586183.3606716
Höhn MWunderlich MBallweg KKohlhammer JLandesberger T(2023)Interactive Input and Visualization for Planning with Temporal UncertaintySN Computer Science10.1007/s42979-023-01705-44:3Online publication date: 23-Feb-2023
https://dl.acm.org/doi/10.1007/s42979-023-01705-4
Saquib NHuq FHaque S(2022)graphiti: Sketch-based Graph Analytics for Images and VideosProceedings of the 2022 CHI Conference on Human Factors in Computing Systems10.1145/3491102.3501923(1-15)Online publication date: 29-Apr-2022
https://dl.acm.org/doi/10.1145/3491102.3501923
Jain GChopra SChopra SParihar A(2022)Attention-Net: An Ensemble Sketch Recognition Approach Using Vector ImagesIEEE Transactions on Cognitive and Developmental Systems10.1109/TCDS.2020.302305514:1(136-145)Online publication date: Mar-2022
https://doi.org/10.1109/TCDS.2020.3023055
Saquib NKazi RWei LMark GRoy DKitamura YQuigley AIsbister KIgarashi TBjørn PDrucker S(2021)Constructing Embodied Algebra by SketchingProceedings of the 2021 CHI Conference on Human Factors in Computing Systems10.1145/3411764.3445460(1-16)Online publication date: 6-May-2021
https://dl.acm.org/doi/10.1145/3411764.3445460
Li LZou CZheng YSu QFu HTai C(2021) Sketch-R2CNN : An RNN-Rasterization-CNN Architecture for Vector Sketch Recognition IEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2020.298762627:9(3745-3754)Online publication date: 1-Sep-2021
https://doi.org/10.1109/TVCG.2020.2987626
Zhelezniakov DZaytsev VRadyvonenko O(2021)Online Handwritten Mathematical Expression Recognition and Applications: A SurveyIEEE Access10.1109/ACCESS.2021.30634139(38352-38373)Online publication date: 2021
https://doi.org/10.1109/ACCESS.2021.3063413
Ung HNguyen CPhan KKhuong VNakagawa M(2021)Clustering online handwritten mathematical expressionsPattern Recognition Letters10.1016/j.patrec.2021.03.027146(267-275)Online publication date: Jun-2021
https://doi.org/10.1016/j.patrec.2021.03.027
Parihar AJain GChopra SChopra S(2021)SketchFormer: transformer-based approach for sketch recognition using vector imagesMultimedia Tools and Applications10.1007/s11042-020-09837-y80:6(9075-9091)Online publication date: 1-Mar-2021
https://dl.acm.org/doi/10.1007/s11042-020-09837-y
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