23/06/20 21:50:23.23 OHL59uZ9.net
A(0,1,0), B(1,0,1), C(-2,2,3), P(0,-1,2)
平行移動
A'(-1,1,-1), B'(0,0,0) = O, C'(-3,2,2), P'(-1,-1,1)
x↑ := OC'↑ = (-3,2,2)
y0↑ := OA'↑ - (OC'↑・OA'↑)/|OC'↑|^2 * OC'↑ = 1/17 * (-8,11,-23)
y↑ := (-8,11,-23)
z↑ := x↑× y0↑ = (-4,-5,-1)
|x↑| = √17
|y↑| = √(42・17)
|z↑| = √42
回転＆伸縮
[x↑, y↑, z↑]^T * OC'↑ = (17,0,0) =: C''
[x↑, y↑, z↑]^T * OA'↑ = (3,42,0) =: A''
[x↑, y↑, z↑]^T * OP'↑ = (3,-26,8) =: P''
P''の△A''OC''上の最近点Q''はOC''上の(3,0,0)
Q''に対応する元の点をQとして、PQの長さ = √(26^2 / |y↑|^2 + 8^2 / |z↑|) = √(42/17)