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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

The axis is given by two points

p1 2 - 2 - 9 - 13 mat transpose :

p2 122 - 1013 mat transpose :

angle Ω1 1000 angle cos angle sin - 0 angle sin angle cos 33 mat :

Матрица преобразования для поворота вокруг оси y angle Ω2 angle cos 0 angle sin 010 angle sin - 0 angle cos 33 mat :

Матрица преобразования для поворота вокруг оси z angle Ω3 angle cos angle sin - 0 angle sin angle cos 000133 mat :

γ π - 3.5 / Ω1 π 4 / Ω2 * 0.85 π * Ω3 * eval :

The transformation matrix for an axis defined by two points ψ1 directcos p2 p1 - p2 p1 - (i el (2^i 13 sum sqrt / eval : (Direction cosines onto Ox,Oy Oz ≡ d directcos 2 el (2^directcos 3 el (2^+ sqrt eval : (Проектируем единичный вектор на плоскость yOz ≡ α directcos 3 el d / acos eval : (Находим углы α,β ≡ β d acos eval : directcos 1 el sign β * - Ω2 directcos 2 el sign α * Ω1 * eval 51 line :

Drawing function 3d axis L zum ax u v F 0.25 v sin * 0.25 v cos * u 31 mat : u v F1 4 u - 4 / 1.5 * v cos * 4 u - 4 / 1.5 * v sin * 1.5 u * L + 31 mat : P u v F 0 L 02 π * 112 CreateMesh : C u v F1 0402 π * 1612 CreateMesh : C P stack zum * 51 line :

3d body u v F 2.5 1.5 u cos * + (v cos * 2.5 1.5 u cos * + (v sin * 3 u * 31 mat : t M1 u v F 0 π 023 / π * 801 CreateMesh π 36 / t * Ω3 * : t M2 u v F 0 π 23 / π * 43 / π * 801 CreateMesh π 36 / t * Ω3 * : t M3 u v F 0 π 43 / π * 2 π * 801 CreateMesh π 36 / t * Ω3 * : 41 line

Axis 60 0.2 ax ψ1 * eval :

step1 071 range :

Rotate around an arbitrary axis

t M3 ψ1 * γ * 1 col p1 transpose γ * 1 col 1 el + t M3 ψ1 * γ * 2 col p1 transpose γ * 2 col 1 el + augment t M1 ψ1 * γ * 1 col p1 transpose γ * 1 col 1 el + t M1 ψ1 * γ * 2 col p1 transpose γ * 2 col 1 el + augment t M2 ψ1 * γ * 1 col p1 transpose γ * 1 col 1 el + t M2 ψ1 * γ * 2 col p1 transpose γ * 2 col 1 el + augment p1 transpose γ * 1 col 1 el p1 transpose γ * 2 col 1 el . 20 1 5 mat Axis γ * 1 col p1 transpose γ * 1 col 1 el + Axis γ * 2 col p1 transpose γ * 2 col 1 el + augment 6 1 sys