Function ORIENTATION

• Defined in theory: Simple-geometry
• Source code: simple-geometry.lisp

Slots on this function:

Documentation:

Function relating frames in space. Returns a direction cosine matrix. An important property of orientation is the ability to 'chain' orientations through multiplication, (orientation ?f1 ?f3) = (orientation ?f1 ?f2) * (orientation ?f2 ?f3).

Instance-Of: Function

Arity: 3

Axioms:

(Nth-Domain Orientation 3 3d-Direction-Cosine)

(Nth-Domain Orientation 2 3d-Frame)

(Nth-Domain Orientation 1 3d-Frame)

(= (Orientation ?F1 ?F3)
   (* (Orientation ?F1 ?F2) (Orientation ?F2 ?F3)))

Other Related Axioms:

(=> (= (Orientation ?F1 ?F2) ?Dircos)
    (Forall (?Dyad)
            (=> (3d-Dyad ?Dyad)
                (= (Tensor-To-Matrix ?Dyad ?F1)
                   (* (Inverse ?Dircos)
                      (* (Tensor-To-Matrix ?Dyad ?F2) ?Dircos))))))

(=> (= (Orientation ?F1 ?F2) ?Dircos)
    (Forall (?V)
            (=> (3d-Vector-Quantity ?V)
                (= (Tensor-To-Matrix ?V ?F1)
                   (* ?Dircos (Tensor-To-Matrix ?V ?F2))))))