A simple method for computing general position in displaying three-dimensional objects
Computer Vision, Graphics, and Image Processing
OBBTree: a hierarchical structure for rapid interference detection
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
An interface for sketching 3D curves
I3D '99 Proceedings of the 1999 symposium on Interactive 3D graphics
DAB: interactive haptic painting with 3D virtual brushes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Viewpoint entropy: a new tool for obtaining good views of molecules
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Automatic Selection of Reference Views for Image-Based Scene Representations
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Viewpoint Selection using Viewpoint Entropy
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
VIS '95 Proceedings of the 6th conference on Visualization '95
Interactive topological drawing
Interactive topological drawing
Haptic exploration of unknown objects
Haptic exploration of unknown objects
Proceedings of the 5th international conference on Multimodal interfaces
Real-time knot-tying simulation
The Visual Computer: International Journal of Computer Graphics
A Haptic-Rendering Technique Based on Hybrid Surface Representation
IEEE Computer Graphics and Applications
Dynamic Thread for Real-Time Knot-Tying
WHC '05 Proceedings of the First Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems
Haptic rendering with predictive representation of local geometry
HAPTICS'04 Proceedings of the 12th international conference on Haptic interfaces for virtual environment and teleoperator systems
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We present a novel multi-modal haptic interface for sketching and exploring the structure and properties of mathematical knots. Our interface derives from the familiar pencil-and-paper process of drawing 2D knot diagrams to facilitate the creation and exploration of mathematical knots; however, with a touch-based interface, users can also leverage their physical intuition by seeing, touching, and feeling the knots. The pure haptic component provides an intuitive interaction model for exploring knots, focusing on resolving the apparent conflict between the continuous structure of the actual knot and the visual discontinuities at occlusion boundaries. The auditory component adds redundant cues that emphasize the traditional knot crossings, where the haptic proxy crosses a visual disruption in the graphics image. Our paradigm enhances and extends traditional 2D sketching methods by exploiting both touch and sound to assist in building clearer mental models of geometry such as knot structures.