86531fbe-44e5-47f1-97d1-d98e6d1b0359 96 10 10 false true 1 decimal

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Rotate around an arbitrary axis in space

The algorithm is taken from the book:D. F. Rogers and J. A. Adams. Mathematical Elements for Computer Graphics,second edition. McGraw-Hill Publishing Company, 1990,pages 121-127

B 233 2.5 222233 2.5 2 2.5 33333333222211 1.5 2212222222 1.5 1122 1.5 111211222222211 1.5 2222211 1.5 2211112325 mat transpose :

The axis is given by two points

p1 11 0. 0.25 - 13 mat transpose :

p2 31613 mat transpose :

p3 12 0.3 - 13 mat transpose :

p4 12413 mat transpose :

p1 p2 δ Bδ Rotations and translations matrices in 3D T 100001000010 p1 - 1 el p1 - 2 el p1 - 3 el 144 mat : Rx 10000 α cos α sin 00 α sin - α cos 0000144 mat : 12 mat Ry β - cos 0 β - sin - 00100 β - sin 0 β - cos 0000144 mat : Rδ δ cos δ sin 00 δ sin - δ cos 000010000144 mat : 12 mat ecos p2 p1 - p2 p1 - norme / eval : (Direction cosines onto Ox,Oy Oz ≡ d ecos 2 el (2^ecos 3 el (2^+ sqrt eval : α ecos 3 el d / acos eval : β d acos eval : 13 mat X B 1 augment : M T Rx * Ry * eval : M1 X M * Rδ * M 1 -^* eval : 13 mat M1 1 col M1 2 col M1 3 col augment 71 line :

τ 071 range :

γ 0.8232 - 0.4194 - 0.3827 0.5677 0.6187 - 0.543 0.009 0.6643 0.7474 33 mat :

p3 p4 π 36 / t * Bδ γ * 10 * B γ * 10 * p3 transpose p4 transpose stack γ * 10 * 3 1 sys p1 p2 π 36 / - ( t * Bδ γ * 10 * B γ * 10 * p1 transpose p2 transpose stack γ * 10 * 3 1 sys