В комментариях под новостью по демке некто предположил использование геометрической алгебры.
Цитата
My bet: Conformal Geometric Algebra.
Which, simply put, is a way of representing objects in 3D space by using five dimensions.
Though this is a particular form of Geometric Algebra, it is said in various references that GA is substantially faster for computing than linear algebra for computations in up to nine dimensions.
Which, simply put, is a way of representing objects in 3D space by using five dimensions.
Though this is a particular form of Geometric Algebra, it is said in various references that GA is substantially faster for computing than linear algebra for computations in up to nine dimensions.
Геометрическая алгебра - никому не понятный раздел математики, который, как я понял, позволяет в том числе и вычислять сложные отражения аналитически.
Цитата
reflections
It can be verified that forming P g(x) P gives a new direction on the null-cone, g(x' ), where x' corresponds to a reflection in the plane of points p in R3 that satisfy g(p) . P = 0.
g(x) . A = 0 => P g(x) . A P = 0 => P g(x) P . P A P (and similarly for the wedge product), so the effect of applying P sandwich-fashion to any the quantities A in the section above is similarly to reflect the corresponding locus of points x, so the corresponding circles, spheres, lines and planes corresponding to particular types of A are reflected in exactly the same way that applying P to g(x) reflects a point x.
It can be verified that forming P g(x) P gives a new direction on the null-cone, g(x' ), where x' corresponds to a reflection in the plane of points p in R3 that satisfy g(p) . P = 0.
g(x) . A = 0 => P g(x) . A P = 0 => P g(x) P . P A P (and similarly for the wedge product), so the effect of applying P sandwich-fashion to any the quantities A in the section above is similarly to reflect the corresponding locus of points x, so the corresponding circles, spheres, lines and planes corresponding to particular types of A are reflected in exactly the same way that applying P to g(x) reflects a point x.
