Advances in Mathematical Sketching: Moving Toward the Paradigm's Full Potential
IEEE Computer Graphics and Applications
ACM SIGGRAPH 2007 courses
ACM SIGGRAPH 2007 courses
An initial evaluation of a pen-based tool for creating dynamic mathematical illustrations
ACM SIGGRAPH 2007 courses
ACM SIGGRAPH 2007 courses
IEEE Transactions on Pattern Analysis and Machine Intelligence
Visual languages and visual thinking: sketch based interaction and modeling
Proceedings of the 6th Eurographics Symposium on Sketch-Based Interfaces and Modeling
Towards intelligent motion inferencing in mathematical sketching
Proceedings of the 15th international conference on Intelligent user interfaces
Applying mathematical sketching to sketch-based physics tutoring software
SG'10 Proceedings of the 10th international conference on Smart graphics
A pen-based tool for visualizing vector mathematics
Proceedings of the Seventh Sketch-Based Interfaces and Modeling Symposium
Technical Section: SpeedSeg: A technique for segmenting pen strokes using pen speed
Computers and Graphics
PhysicsBook: a sketch-based interface for animating physics diagrams
Proceedings of the 2012 ACM international conference on Intelligent User Interfaces
An initial evaluation of a pen-based tool for creating dynamic mathematical illustrations
SBM'06 Proceedings of the Third Eurographics conference on Sketch-Based Interfaces and Modeling
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Diagrams and illustrations are frequently used to help explain mathematical concepts. Students often create them with pencil and paper as an intuitive aid in visualizing relationships among variables, constants, and functions, and use them as a guide in writing the appropriate mathematics to solve the problem. However, such static diagrams generally assist only in the initial formulation of the required mathematics, not in “debugging” or problem analysis. This can be a severe limitation, even for simple problems with a natural mapping to the temporal dimension or problems with complex spatial relationships. To overcome these limitations we present mathematical sketching , a novel, pen-based, 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 mathematical sketching, 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. We describe the critical components of mathematical sketching as developed in the context of a prototype application called Mathpad2. We discuss the important issues of the mathematical sketching paradigm such as the development of a fluid gestural user interface, recognition of mathematical expressions, support for computational tools such as graphing, solving equations, and evaluating expressions, and the preparation and translation of mathematical sketches into animated illustrations. Additionally, we present an evaluation of MathPad2 and show that it is a powerful, easy-to-use tool for creating dynamic illustrations and mathematical visualizations.