Visual immersive haptic mathematics
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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.
KeywordsShape and surface modeling Virtual reality Physically based modeling Shape modeling Haptic collaboration Shared virtual spaces Electronic education
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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