Function-based single and dual point haptic interaction in Cyberworlds

Polygon and point based models dominate virtual reality. These models also affect haptic rendering algorithms, which are often based on collision with polygons. With application to dual point haptic devices for operations like grasping, complex polygon and point based models will make the collision detection procedure slow. This results in the system not able to achieve interactivity for force rendering. To solve this issue, we use mathematical functions to define and implement geometry (curves, surfaces and solid objects), visual appearance (3D colours and geometric textures) and various tangible physical properties (elasticity, friction, viscosity, and force fields). The function definitions are given as analytical formulas (explicit, implicit and parametric), function scripts and procedures. We proposed an algorithm for haptic rendering of virtual scenes including mutually penetrating objects with different sizes and arbitrary location of the observer without a prior knowledge of the scene to be rendered. The algorithm is based on casting multiple haptic rendering rays from the Haptic Interaction Point (HIP), and it builds a stack to keep track on all colliding objects with the HIP. The algorithm uses collision detection based on implicit function representation of the object surfaces. The proposed approach allows us to be flexible when choosing the actual rendering platform, while it can also be easily adopted for dual point haptic collision detection as well as force and torque rendering. The function-defined objects and parts constituting them can be used together with other common definitions of virtual objects such as polygon meshes, point sets, voxel volumes, etc. We implemented an extension of X3D and VRML as well as several standalone application examples to validate the proposed methodology. Experiments show that our concern about fast, accurate rendering as well as compact representation could be fulfilled in various application scenarios and on both single and dual point haptic devices.