# M. L. Sampoli: Rational rotationâ€“minimizing frames on space curves for camera motions

Source: Numerical analysis seminar

**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.