Spline approximation of offset curves
Computer Aided Geometric Design
Loop detection in surface patch intersections
Computer Aided Geometric Design
Offset approximation of uniform B-splines
Computer-Aided Design
Intersection of offsets of parametric surfaces
Computer Aided Geometric Design
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
Curve offsetting based on Legendre series
Computer Aided Geometric Design
Contour machining of free-form surfaces with real-time PH curve CNC interpolators
Computer Aided Geometric Design
Fast computation of generalized Voronoi diagrams using graphics hardware
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Approximation of circular arcs and offset curves by Bézier curves of high degree
Journal of Computational and Applied Mathematics
Offsets of Two-Dimensional Profiles
IEEE Computer Graphics and Applications
Medial axis computation for planar free-form shapes
Computer-Aided Design
Computation of singularities and intersections of offsets of planar curves
Computer Aided Geometric Design
A second order algorithm for orthogonal projection onto curves and surfaces
Computer Aided Geometric Design
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
Precise Hausdorff distance computation for planar freeform curves using biarcs and depth buffer
The Visual Computer: International Journal of Computer Graphics
Coons BVH for freeform geometric models
Proceedings of the 2011 SIGGRAPH Asia Conference
Efficient point-projection to freeform curves and surfaces
Computer Aided Geometric Design
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We present an efficient algorithm for trimming both local and global self-intersections in planar offset curves. The algorithm is based on a G^1-continuous biarc approximation of the given planar curves. We first consider an implementation that employs a distance map which can be stored in the graphics hardware depth buffer. The depth-buffer approach is easier to implement than a different approach that is based on a biarc-tree, a hierarchical data structure for the biarc approximation of the given planar curves. Though more involved technically, the biarc-tree algorithm is more efficient both in computing time and in memory space needed for storing the data structure. We demonstrate the real-time performance of our algorithm using several experimental results.