#!/usr/bin/python
# coding: utf8
# ベクトルの外積から求める方法
 
# ２点からベクトルを求める
# 引数 p1, p2 : (x, y, z)のタプル
def get_vector(p1, p2):
    x = p2[0] - p1[0]
    y = p2[1] - p1[1]
    z = p2[2] - p1[2]
    return (x, y, z)
 
# ２つのベクトルから外積を求める
# 引数 v1, v2 : (x, y, z)のタプル
def get_cross_product(v1, v2):
    x = (v1[1] * v2[2]) - (v1[2] * v2[1])
    y = (v1[2] * v2[0]) - (v1[0] * v2[2])
    z = (v1[0] * v2[1]) - (v1[1] * v2[0])
    return (x, y, z)
 
# メイン
def main():
    pa = (50, 600, 900)   
    pb = (385, 630, 905)    
    pc = (260, 30, 915)
 
    #ベクトルをつくる
    vab = get_vector(pa, pb)    # a から b へ向かうベクトル
    vac = get_vector(pa, pc)    # a から c へ向かうベクトル
    print('vab=' + str(vab))
    print('vac=' + str(vac))
 
    # 求める平面の法線ベクトル(=vabとvacの外積)を求める
    vn = get_cross_product(vab, vac)
    '''
    法線ベクトル vn = (p, q, r), 平面上の任意の点 P0=(x0, y0, z0) とすれば
    p(x-x0) + q(y-y0) + r(z-z0) = 0 が求める平面の方程式
    ax + by + cz = d の形へ直すと a,b,c,d の各値は
    a = p, b = q, c = r
    d = p*x0 + q*y0 + r*z0
    '''
    d = vn[0]*pa[0] + vn[1]*pa[1] + vn[2]*pa[2]    # paの値を使ってdを計算(pb,pcでも一緒)
 
    # 結果の表示
    print('a= ', str(vn[0]))
    print('b= ', str(vn[1]))
    print('c= ', str(vn[2]))
    print('d= ', str(d))
 
# プログラム開始
if __name__ == '__main__':
    main()

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