一、问题求解
空间直线同球体交点问题求解，为求解二元二次方程问题，下面是求解过程
二、代码实现
1、代码实现
1 void cal_q ( double par_x, double par_y, double par_z, double par_r, double bpx, double bpy, double bpz, double spx, double spy, double spz ) { 2 double x_1, x_2, y_1, y_2, z_1, z_2; 3 4 if ( bpx != spx ) { 5 double k_xy = ( spy - bpy ) / ( spx - bpx ); 6 double b_xy = bpy - k_xy * bpx; 7 8 double k_zx = ( spz - bpz ) / ( spx - bpx ); 9 double b_zx = bpz - k_zx * bpx; 10 11 double A = 1 + k_xy * k_xy + k_zx * k_zx; 12 double B = 2 * k_xy * ( b_xy - par_y ) + 2 * k_zx * ( b_zx - par_z ) - 2 * par_x; 13 double C = par_x * par_x + ( b_xy - par_y ) * ( b_xy - par_y ) + ( b_zx - par_z ) * ( b_zx - par_z ) - par_r * par_r; 14 15 x_1 = ( -B + sqrt ( B * B - 4 * A * C ) ) / ( 2 * A ); 16 y_1 = k_xy * x_1 + b_xy; 17 z_1 = k_zx * x_1 + b_zx; 18 19 x_2 = ( -B - sqrt ( B * B - 4 * A * C ) ) / ( 2 * A ); 20 y_2 = k_xy * x_2 + b_xy; 21 z_2 = k_zx * x_2 + b_zx; 22 23 printf ( "x_1: %10.5f y_1: %10.5f z_1: %10.5f ", x_1, y_1, z_1 ); 24 printf ( "x_2: %10.5f y_2: %10.5f z_2: %10.5f ", x_2, y_2, z_2 ); 25 26 printf ( "bpx != spx " ); 27 } else { 28 if ( bpy != spy ) { 29 double k_zy = ( spz - bpz ) / ( spy - bpy ); 30 double b_zy = spz - k_zy * spy; 31 32 double A = 1 + k_zy * k_zy; 33 double B = 2 * k_zy * ( b_zy - par_z ) - 2 * par_y; 34 double C = par_y * par_y + ( b_zy - par_z ) * ( b_zy - par_z ) + ( bpx - par_x ) * ( bpx - par_x ) - par_r * par_r; 35 36 x_1 = bpx; 37 y_1 = ( -B + sqrt ( B * B - 4 * A * C ) ) / ( 2 * A ); 38 z_1 = k_zy * y_1 + b_zy; 39 40 x_2 = bpx; 41 y_2 = ( -B - sqrt ( B * B - 4 * A * C ) ) / ( 2 * A ); 42 z_2 = k_zy * y_2 + b_zy; 43 44 printf ( "x_1: %10.5f y_1: %10.5f z_1: %10.5f ", x_1, y_1, z_1 ); 45 printf ( "x_2: %10.5f y_2: %10.5f z_2: %10.5f ", x_2, y_2, z_2 ); 46 47 printf ( "bpx == spx && bpy != spy " ); 48 } else { 49 if ( bpz != spz ) { 50 x_1 = bpx; 51 y_1 = bpy; 52 z_1 = par_z + sqrt ( par_r * par_r - ( bpx - par_x ) * ( bpx - par_x ) - ( bpy - par_y ) * ( bpy - par_y ) ); 53 54 x_2 = bpx; 55 y_2 = bpy; 56 z_2 = par_z - sqrt ( par_r * par_r - ( bpx - par_x ) * ( bpx - par_x ) - ( bpy - par_y ) * ( bpy - par_y ) ); 57 58 printf ( "x_1: %10.5f y_1: %10.5f z_1: %10.5f ", x_1, y_1, z_1 ); 59 printf ( "x_2: %10.5f y_2: %10.5f z_2: %10.5f ", x_2, y_2, z_2 ); 60 61 printf ( "bpx == spx && bpy == spy " ); 62 } else { 63 printf ( "Warning: two points overlap !!!! " );64 } 65 } 66 } 67 }
2、测试
1 #include <cstdio> 2 #include <cmath> 3 4 void cal_q ( double, double, double, double, double, double, double, double, double, double ); 5 6 int main() { 7 double par_x = 20; 8 double par_y = 20; 9 double par_z = 20; 10 double par_r = 15; 11 12 double bpx = 20; 13 double bpy = 30; 14 double bpz = 40; 15 16 double spx = 20; 17 double spy = 20; 18 double spz = 20; 19 20 printf ( "bpx: %10.5f bpy: %10.5f bpz: %10.5f ", bpx, bpy, bpz ); 21 printf ( "spx: %10.5f spy: %10.5f spz: %10.5f ", spx, spy, spz ); 22 23 cal_q ( par_x, par_y, par_z, par_r, bpx, bpy, bpz, spx, spy, spz ); 24 25 return 0; 26 }
3、图形显示测试结果
