Class 3D-DIRECTION-COSINE

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

Slots on this class:

Documentation:

A direction cosine matrix is an orthogonal three-dimensional matrix.

Instance-Of: Class

Subclass-Of: Orthogonal-matrix

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Slots on instances of this class:

Row-Dimension: 3

Equivalence Axioms:

(<=> (3d-Direction-Cosine ?Dircos)
     (And (Orthogonal-Matrix ?Dircos) (Row-Dimension ?Dircos 3)))

Axioms:

(Orthogonal-Matrix ?Dircos)

Other Related Axioms:

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

(<= (Row-Dimension $X 3) (3d-Direction-Cosine $X))

(<=> (3d-Direction-Cosine ?Dircos)
     (And (Orthogonal-Matrix ?Dircos) (Row-Dimension ?Dircos 3)))

(Nth-Domain Simple-Rotation 3 3d-Direction-Cosine)

(=> (= (Simple-Rotation ?Axis ?Angle) ?Dircos)
    (3d-Direction-Cosine ?Dircos))