A geometry education haptic VR application based on a new virtual hand representation

The present paper describes an enhanced haptic virtual reality application for geometry education. The proposed application allows the user to create and edit a scene that consists of three-dimensional geometrical objects in order to form and solve complex geometrical problems. The core of the proposed scheme is based on a novel interference detection algorithm, which utilizes implicit surfaces, such as superquadrics, and their analytical description to speed up collision detection between the virtual hand and the virtual environment. Intersection tests are executed utilizing the implicit analytical formulae of the superquadrics. Experimental results demonstrate the high applicability of the proposed application and the huge gain in speed of the proposed collision detection approach when compared to state of the art methods.