     suivant: Matrix factorizations monter: Isometries précédent: Recognize an isometry :   Table des matières   Index

## Find the matrix of an isometry : mkisom

mkisom takes as argument :
• In dimension 3, the list of characteristic elements (axis direction, angle for a rotation or normal to the plane for a symmetry) and +1 for a direct isometry or -1 an indirect isometry.
• In dimension 2, a characteristic element (an angle or a vector) and +1 for a direct isometry (rotation) or -1 for an indirect isometry (symmetry).
mkisom returns the matrix of the corresponding isometry.
Input :
mkisom([[-1,2,-1],pi],1)
Output the matrix of the rotation of axis [- 1, 2, - 1] and angle :
[[-2/3,-2/3,1/3],[-2/3,1/3,-2/3],[1/3,-2/3,-2/3]]
Input :
mkisom([pi],-1)
Output the matrix of the symmetry with respect to O :
[[-1,0,0],[0,-1,0],[0,0,-1]]
Input :
mkisom([1,1,1],-1)
Output the matrix of the symmetry with respect to the plane x + y + z = 0 :
[[1/3,-2/3,-2/3],[-2/3,1/3,-2/3],[-2/3,-2/3,1/3]]
Input :
mkisom([[1,1,1],pi/3],-1)
Output the matrix of the product of a rotation of axis [1, 1, 1] and angle and of a symmetry with respect to the plane x + y + z = 0:
[[0,-1,0],[0,0,-1],[-1,0,0]]
Input :
mkisom(pi/2,1)
Output the matrix of the plane rotation of angle :
[[0,-1],[1,0]]
Input :
mkisom([1,2],-1)
Output matrix of the plane symmetry with respect to the line of equation x + 2y = 0:
[[3/5,-4/5],[-4/5,-3/5]]     suivant: Matrix factorizations monter: Isometries précédent: Recognize an isometry :   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse