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M. L. Sampoli: Rational rotation–minimizing frames on space curves for camera motions

Date: 22. 10. 2012
Source: Numerical analysis seminar
Sreda 24. 10. 2012 od 10h do 11h, soba 3.06 na Jadranski 21

Predavanje od 10h do 11h

M. L. Sampoli: Rational rotation–minimizing frames on space curves for camera motions

The study of frames associated with a spatial curve and having specific
properties, is a very active research field. In particular, the attention has
been so far mainly focused on adapted frames, those where one of the vectors
of the orthonormal triple coincides with the unit tangent at every point
on a curve. Recently, directed frames have been introduced, that is frames
having one vector of the basis coincident with the unit polar vector, defining
the direction from the origin of the reference system to each point on a
curve. Directed frames are particularly suitable for describing the motion
of a camera moving along a spatial path while imaging a stationary object.
Among directed frames, rotation–minimizing frames, are particularly useful
for motion planning and therefore they have received quite a lot of attention.
In this talk, after having reviewed the the main definitions and properties
of adapted and directed frames, an interpolation method for constructing
rational curves on the unit sphere with rational directed rotation-minimizing
frames is discussed. Both the curve and the rotation–minimizing directed
frame produced by the scheme are C^1 continuous and are rational of degree 8.