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Visual immersive haptic mathematics

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Abstract

In the modern urban society, human brain is not being sufficiently trained to deal with problems which require 3D perception. As a result, when teaching subjects richly infused with mathematics it is usually a challenge for the learners to follow the instructor and visualize how mathematical concepts reflect in 3D geometry and colors. We have proposed an approach that would allow for defining complex geometry, visual appearance and tangible physical properties of the virtual objects using language of mathematical functions. It allows the learners to get immersed within the 3D scene and explore the shapes which are being modeled visually and haptically. We illustrate this concept using our function-based extension of X3D and VRML. Besides definition of objects with mathematical functions straight in the scene file, standard X3D and VRML objects can be converted to tangible ones as well as augmented with function-defined visual appearances. Since the function-defined models are small in size, it is possible to perform their collaborative interactive modifications with concurrent synchronous visualization at each client computer with any required level of detail.

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References

  • Alias M, Black TR, Gray DR (2002) Effect of instructions on spatial visualization ability in civil engineering students. Int Educ J 3(1):1–12

    Google Scholar 

  • Guimarães LC, Barbastefano RG, Belfort E (2000) Tools for teaching mathematics: a case for Java and VRML. Comput Appl Eng Educ 8(3–4):157–161

    Article  Google Scholar 

  • Kaufmann H, Schmalstieg D (2006) Designing immersive virtual reality for geometry education. In: IEEE virtual reality conference, VR 2006. IEEE CS Press, pp 51–58

  • Kunimune S, Nagasaki E (1996) Curriculum changes on lower secondary school mathematics of Japan—focused on geometry. Eighth international congress on mathematical education. Retrieved 8 January 2008 from http://www.fi.uu.nl/en/Icme-8/WG13_6.html

  • Liu Q, Sourin A (2006a) Function-based shape modelling extension of the virtual reality modelling language. Comput Graph 30(4):629–645

    Article  Google Scholar 

  • Liu Q, Sourin A (2006b) Function-defined shape metamorphoses in visual cyberworlds. Vis Comput 22(12):977–990

    Article  Google Scholar 

  • Mathematics Syllabus Primary. Ministry of Education Singapore (2009) Retrieved from http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2007.pdf

  • Pasko A, Adzhiev V, Sourin A, Savchenko V (1995) Function representation in geometric modeling: concepts, implementations and applications. Vis Comput 11(8):429–446

    Article  Google Scholar 

  • Pasqualotti A, Dal Sasso Freitas CM (2002) MAT3D: a virtual reality modeling language environment for the teaching and learning of mathematics. CyberPsychol Behav 5(5):409–422

    Article  Google Scholar 

  • Scribner SA, Anderson AA (2005) Novice drafters’ spatial visualization development: influence of instructional methods and individual learning styles. J Ind Teach Educ 42(2):38–60

    Google Scholar 

  • Secondary Mathematics Syllabuses, Ministry of Education Singapore (2009) Retrieved from http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-secondary.pdf

  • Song KS, Lee WY (2002) A virtual reality application for geometry classes. J Comput Assist Learn 18:149–156

    Article  Google Scholar 

  • Sourin A, Wei L (2008) Visual immersive haptic rendering on the Web. Seventh ACM SIGGRAPH international conference on virtual-reality continuum and its applications in industry, VRCAI 2008, 8–9 December

  • TSG 16 (2004) Visualisation in the teaching and learning of mathematics. In: Tenth international congress of mathematical education. 4–11 July 2004, Copenhagen, Denmark, from http://www.icme-organisers.dk/tsg16

  • TSG 20 (2008) Visualization in the teaching and learning of mathematics. In: Eleventh international congress of mathematical education. 6–13 July 2008, Monterrey, Mexico, from http://tsg.icme11.org/tsg/show/21

  • Wei L, Sourin A, Sourina O (2008) Function-based visualization and haptic rendering in shared virtual spaces. Vis Comput 24(5):871–880

    Article  Google Scholar 

  • Wei L, Sourin A, Stocker H (2009) Function-based haptic collaboration in X3D. In: Proceedings of Web3D 2009, 16–17 June Darmstadt. ACM Press, Germany, pp 15–23

    Google Scholar 

  • Yeh A, Nason R (2004) VRMath: a 3D microworld for learning 3D geometry. In: Cantoni L, McLoughlin C (eds) Proceedings of world conference on educational multimedia, hypermedia and telecommunications 2004, AACE, Chesapeake, VA, pp 2183–2194

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Acknowledgments

This work was supported by the Singapore National Research Foundation Interactive Digital Media R&D Program, under research Grant NRF2008IDM-IDM004-002 “Visual and Haptic Rendering in Co-Space”.

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Authors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Alexei Sourin & Lei Wei

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  1. Alexei Sourin
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  2. Lei Wei
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Correspondence to Alexei Sourin.

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Sourin, A., Wei, L. Visual immersive haptic mathematics. Virtual Reality 13, 221–234 (2009). https://doi.org/10.1007/s10055-009-0133-2

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  • DOI: https://doi.org/10.1007/s10055-009-0133-2

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