Strip trees: a hierarchical representation for curves
Communications of the ACM
The Performance of Curve Representation Schemes
IEEE Computer Graphics and Applications
Point inversion and projection for NURBS curve and surface: control polygon approach
Computer Aided Geometric Design
A Robotic Teacher of Chinese Handwriting
HAPTICS '02 Proceedings of the 10th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Passive and Active Assistance for Human Performance of a Simulated Underactuated Dynamic Task
HAPTICS '03 Proceedings of the 11th Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems (HAPTICS'03)
A Study on Design and Analysis of Virtual Fixtures for Cutting in Training Environments
WHC '05 Proceedings of the First Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Telemaque, a New Visuo-Haptic Interface for Remediation of Dysgraphic Children
WHC '05 Proceedings of the First Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Haptic Attributes and Human Motor Skills
HAPTICS '06 Proceedings of the Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Comparative Study: Virtual Fixtures and Shared Control for Rehabilitation of Fine Motor Skills
WHC '07 Proceedings of the Second Joint EuroHaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Assembling virtual fixtures for guidance in training environments
HAPTICS'04 Proceedings of the 12th international conference on Haptic interfaces for virtual environment and teleoperator systems
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Virtual fixture is widely used for motor skill assistance and training. For motor skills involving long and self-intersecting trajectories with variational curvatures, existing methods based on analytic representation of curves can not meet real time and stability requirements of haptic rendering. In this paper, a simple and efficient hierarchical structure is proposed to represent the time ordered geometry of the desired trajectory. The minimum distance from the position of the tool to the desired trajectory is calculated by filtering impossible segments while traversing the hierarchy. To avoid the force discontinuity caused by the singularity of the absolute minimum distance, a constraint conversion method is proposed. The experiments verified that the proposed method satisfied real time and stability requirements of haptic rendering. It enables applications of virtual fixture for assistance and training in handwriting, surgery operation and other skills involving complex trajectories.