注意一下两球的位置关系
d i s = ( o 1 , o 2 ) dis = (o_1,o_2) dis=(o1,o2)
h 1 = r 1 − ( r 1 2 + d i s 2 − r 2 2 ) / ( 2 ∗ d i s ) h1 =r_1-(r_1^2+dis^2-r_2^2)/(2*dis) h1=r1−(r12+dis2−r22)/(2∗dis)
h 2 = r 2 − ( r 2 2 + d i s 2 − r 1 2 ) / ( 2 ∗ d i s ) h2 =r_2-(r_2^2+dis^2-r_1^2)/(2*dis) h2=r2−(r22+dis2−r12)/(2∗dis)
V = π h 1 2 ( r 1 − 1 3 h 1 ) + π h 2 2 ( r 2 − 1 3 h 2 ) V = \pi{h_1^2}(r_1- \frac{1}{3}h_1)+ \pi{h_2^2}(r_2- \frac{1}{3}h_2) V=πh12(r1−31h1)+πh22(r2−31h2)
阿波罗尼斯圆的半径和圆心的求法
已知 ∣ A P ∣ = K ∣ B P ∣ |AP| = K|BP| ∣AP∣=K∣BP∣，点A的坐标为 ( x 1 , y 1 ) (x_1,y_1) (x1,y1)，点B的坐标为 ( x 2 , y 2 ) (x_2,y_2) (x2,y2)
则点P的运动轨迹为圆，且圆心：
x = x 2 + ( x 2 − x 1 ) / ( k 2 − 1 ) x=x_2+(x_2-x_1)/(k^2-1) x=x2+(x2−x1)/(k2−1)
y = y 2 + ( y 2 − y 1 ) / ( k 2 − 1 ) y=y_2+(y_2-y_1)/(k^2-1) y=y2+(y2−y1)/(k2−1)
半径 r = k / ( k 2 − 1 ) ∗ d i s ( A , B ) r =k/(k^2-1)*dis(A,B) r=k/(k2−1)∗dis(A,B)