Finding point on a 3D line in C - c

Question

I have two 3D points: (x1, y1, z1) and (x3, y3, z3) and want to find a point (x2, y2, z2) on that line given z2, which is between z1 and z3.
Here is what I have currently:
#include<math.h>
#include<stdlib.h>
#include<stdio.h>
double *findPoint (double x1, double y1, double z1, double x3, double y3, double z3, double z2)
{
double *ret = malloc(3 * sizeof(double));
double dot = (x1 * x3) + (y1 * y3) + (z1 * z3);
printf("dot %e\n", dot);
double magprd = ((x1 * x1) + (y1 * y1) + (z1 * z1)) * ((x3 * x3) + (y3 * y3) + (z3 * z3));
printf("magprd %e\n", magprd);
double angle = acos(dot / magprd);
printf("angle %e\n", angle);
double distance = z2 / asin(angle);
printf("distance %e\n", distance);
double x2 = x1 - ((distance * x1) / 3);
double y2 = y1 - ((distance * y1) / 3);
ret[0] = x2;
ret[1] = y2;
ret[2] = z2;
return ret;
}
int main() {
// return pointer to array containing x2, y2, z2 corresponding to
// z=4 on line between point at x1, y1, z1 and x3, y3, z3
double *p = findPoint(1, 2, 3, 11, 12, 13, 4);
if(p) {
printf("point on line at z=4 is %e, %e, %e\n", p[0], p[1], p[2]);
free(p);
}
return 0;
}
This doesn't work properly, though:
$ clang -lm test.c -o test
$ ./test
dot 7.400000e+01
magprd 6.076000e+03
angle 1.558617e+00
distance nan
point on line at z=4 is nan, nan, 4.000000e+00
How can I fix findPoint so that it solves this problem? Thanks!

Answer 1

You math looks very complicated. I would suggest this code:
typedef struct { double x,y,z; } Point;
Point findPoint(Point a, Point b, double z) {
double dx = b.x - a.x;
double dy = b.y - a.y;
double dz = b.z - a.z;
if(dz == 0.0) {
// ERROR
return (Point){ 0,0,0 };
}
double p = (z - a.z) / dz;
return (Point){ a.x + p*dx, a.y + p*dy, a.z + p*dz };
}
If you do not want to use by value I suggest this:
int findPoint(const Point* a, const Point* b, double z, Point* c) {
double dx = b->x - a->x;
double dy = b->y - a->y;
double dz = b->z - a->z;
if(dz == 0.0) {
// ERROR
return 0;
}
double p = (z - a.z) / dz;
c->x = a.x + p*dx;
c->y = a.y + p*dy;
c->z = a.z + p*dz };
return 1;
}
Point* a = malloc(sizeof(Point));
a->x = 1;
a->y = 2;
a->z = 3;
Point* b = malloc(sizeof(Point));
b->x = 11;
b->y = 12;
b->z = 13;
Point* c = malloc(sizeof(Point));
if(findPoint(a,b,4,c)) {
printf("Result: %e %e %e\n", c->x, c->y, c->z);
}
else {
printf("Error!\n");
}

Answer 2

You can simplify your function to
double *findPoint (double x1, double y1, double z1, double x3, double y3, double z3, double z2)
{
double *ret = malloc(3 * sizeof(double));
double tmp = (z2 - z1)/(z3 - z1); // Assuming that z1 != z3
double x2 = x1 + tmp * (x3 - x1);
double y2 = y1 + tmp * (y3 - y1);
ret[0] = x2;
ret[1] = y2;
ret[2] = z2;
return ret;
}
That gives the result
point on line at z=4 is 2.000000e+00, 3.000000e+00, 4.000000e+00