Solid shape
Curve intersection using Be´zier clipping
Computer-Aided Design - Special Issue: Be´zier Techniques
Free form surface analysis using a hybrid of symbolic and numeric computation
Free form surface analysis using a hybrid of symbolic and numeric computation
Six degree-of-freedom haptic rendering using voxel sampling
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Voronoi Diagrams for Planar Shapes
IEEE Computer Graphics and Applications
A Framework for Fast and Accurate Collision Detection for Haptic Interaction
VR '99 Proceedings of the IEEE Virtual Reality
Efficient collision detection for animation and robotics
Efficient collision detection for animation and robotics
Realistic Ray Tracing
Degree Reduction for NURBS Symbolic Computation on Curves
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Computation of the solutions of nonlinear polynomial systems
Computer Aided Geometric Design
Comparison of three curve intersection algorithms
Computer-Aided Design
A new class of algorithms for the processing of parametric curves
Computer-Aided Design
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
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This paper presents a novel approach to continuously and robustly tracking critical (geometrically, perpendicular and/or extremal) distances from a moving plane point $p \in \mathbb R^2$ to a static parametrized piecewise rational curve γ(s) ($s \in \mathbb R$). The approach is a combination of local marching, and the detection and computation of global topological change, both based on the differential properties of a constructed implicit surface. Unlike many techniques, it does not use any global search strategy except at initialization. Implementing the mathematical idea from singularity community, we encode the critical distance surface as an implicit surface $\mathcal{I}$ in the augmented parameter space. A point ps = (p,s) is in the augmented parametric space $\mathbb R^3 = \mathbb R^2 \times \mathbb R$, where p varies over $\mathbb R^2$. In most situations, when p is perturbed, its corresponding critical distances can be evolved without structural change by marching along a sectional curve on $\mathcal{I}$. However, occasionally, when the perturbation crosses the evolute of γ, there is a transition event at which a pair of p's current critical distances is annihilated, or a new pair is created and added to the set of p's critical distances. To safely eliminate any global search for critical distances, we develop robust and efficient algorithm to perform the detection and computation of transition events. Additional transition events caused by various curve discontinuities are also investigated. Our implementation assumes a B-spline representation for the curve and has interactive speed even on a lower end laptop computer.