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Nonexistence of rational rotation-minimizing frames on cubic curves
  • C. Han
  • Mathematics, Computer Science
  • Comput. Aided Geom. Des.
  • 1 May 2008
TLDR
There is no rational rotation-minimizing frame (RMF) along any non-planar regular cubic polynomial curve and it is proved its nonexistence in the case of cubic curves. Expand
Characterization and construction of helical polynomial space curves
Helical space curves are characterized by the property that their unit tangents maintain a constant inclination with respect to a fixed line, the axis of the helix. Equivalently, a helix exhibits aExpand
Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves
TLDR
Using the new spline, called the Minkowski Pythagorean hodograph curve which was recently introduced, the algorithm is based on the domain decomposition scheme which reduces a complicated domain into a union of simple subdomains each of which is very easy to handle. Expand
Euler-Rodrigues frames on spatial Pythagorean-hodograph curves
  • H. Choi, C. Han
  • Mathematics, Computer Science
  • Comput. Aided Geom. Des.
  • 1 October 2002
TLDR
It is proved that the minimum degree of non-planar PH curves whose ERF is an rotation-minimizing frame is seven, and the Euler–Rodrigues frame is equivalent to the Frenet frame on cubic PH curves. Expand
Two-dimensional offsets and medial axis transform
TLDR
The concept of monotonic fundamental domain is introduced as a device for detecting the correct topology of offsets as well as for stable numerical computation. Expand
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
  • R. Farouki, C. Han
  • Mathematics, Computer Science
  • Comput. Aided Geom. Des.
  • 1 October 2003
TLDR
The function that describes the angular deviation between the RMF and ERF is derived in closed form, and is approximated by Pade (rational Hermite) interpolation, which furnish compact approximations of excellent accuracy, amenable to use in a variety of applications. Expand
The Medial Axis Transform
  • H. Choi, C. Han
  • Mathematics, Computer Science
  • Handbook of Computer Aided Geometric Design
  • 2002
TLDR
The chapter presents various algorithms for computing the medial axis, a one-dimensional graph extracted from a planar shape, and briefly describes the data structure. Expand
Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme
Abstract We describe a method that serves to simultaneously determine the topological configuration of the intersection curve of two parametric surfaces and generate compatible decompositions ofExpand
Topologically consistent trimmed surface approximations based on triangular patches
A scheme to approximate the trimmed surfaces defined by two tensor-product surface patches, intersecting in a smooth curve segment that extends between diametrically opposite patch corners, isExpand
Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants
TLDR
A novel construction of rational rotation-minimizing motions may prove useful in applications such as computer animation, geometric sweep operations, and robot trajectory planning. Expand
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