Milagros Izquierdo (Linköping University) impartirá la conferencia "Animación en 3D vía cuaterniones"

Milagros Izquierdo (Linköping University) impartirá la conferencia:

"Animación en 3D vía cuaterniones"

Resumen:
Hamilton found the quaternions H as  very useful tools for modelling Mechanics in 3D. The quaternions are in fact the vectors in R⁴ equipped with a product, and with a complex structure (C²). More importantly S³ are the quaternions of norm 1. 
 
If we want to do animation, we are interested in expressing  isometries (movements) of the Euclidean space in 3D.  In fact, in navigation one is  interested in the isometries of S², but they are the isometries in 3D that fix the origin. If we are interested in orientation preserving isometries that fix the origin, then we have the product of two reflections in intersecting reflection planes: i.e. a rotation whose axis is the intersection line of the reflecting planes. Remember that a rotation of R³ is given by an orthogonal 3x3-matrix with determinant 1.
 
I learnt about S², S³ and the group SO(3) of rotations of R³ in this building of Maths (linear algebra and diff geometry of surfaces)
 
The goal of this talk is to convince you that the quaternions of norm 1, S³ and SO(3) are the same, pardon, they are isomorphic. This gives a fast algorithm to draw rotations in 3D: SLERP (Spherical Linear Interpolation).

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Día: Jueves, 30 de octubre de 2025
Hora: 16h
Lugar: Aula 5, edificio de Matemáticas

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