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Visual immersive haptic mathematics.

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Title: Visual immersive haptic mathematics.
Authors: Sourin, Alexei1 assourin@ntu.edu.sg, Lei Wei1 weil0004@ntu.edu.sg
Source: Virtual Reality. Dec2009, Vol. 13 Issue 4, p221-234. 14p. 2 Color Photographs, 1 Illustration, 9 Diagrams.
Subjects: Geometry problems & exercises, VRML (Computer program language), Visual perception, Mathematical analysis, Mathematical functions
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. [ABSTRACT FROM AUTHOR]
Copyright of Virtual Reality is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Virtual Reality is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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