I am trying to create a plane from 3 points in the form of Ax + By + Cz + D = 0. I think I am doing this right by computing 2 vectors through a common point as:

V1 = P3 - P1

V2 = P2 - P1

and then computing a cross product

V1 X V2

then I should be able to take point 1 and use it with the formula to determine the distance from the plane to the point. I think I should get 0, but I am not.

Has anyone done this before? Are these numbers correct? Someone told me that a matrix calculation would be better something about a determinant. How do I compute a determinant of a 3 X 3 matrix to make the formula Ax + By + Cz + D = 0

Here's my sample program I need to incorporate this function into the rest of my program after I know it is working right.

Code:

#include <iostream>
#include <math.h>
using namespace std;
void calc_plane(double[], double[], double[], double[]);
void calc_plane2(double[], double[], double[]);
int main ()
{
double pt1[3];
pt1[0] = 1200;
pt1[1] = 2400;
pt1[2] = -35.89;
double pt2[3];
pt2[0] = 1200;
pt2[1] = 1800;
pt2[2] = -35.89;
double pt3[3];
pt3[0] = 1845;
pt3[1] = 2400;
pt3[2] = -35.89;
double plane[5];
calc_plane(pt1, pt2, pt3, plane);
calc_plane2(pt1, pt2, pt3);
return 0;
}
void calc_plane2(double pt1[3], double pt2[3], double pt3[3])
{
double a, b, c, d;
a = ((pt2[1] - pt1[1]) * (pt3[2] - pt1[2])) - ((pt3[1] - pt1[1]) * (pt2[2] - pt1[2]));
b = ((pt3[0] - pt1[0]) * (pt2[2] - pt1[2])) - ((pt2[0] - pt1[0]) * (pt3[2] - pt1[2]));
c = ((pt2[0] - pt1[0]) * (pt2[1] - pt1[1])) - ((pt3[0] - pt1[0]) * (pt2[1] - pt1[1]));
d = 0 - (pt1[0] * a) + (pt1[1] * b) + (pt1[2] * c);
cout << a << "x + " << b << "y + " << c << "z + " << d << endl;
double distPoint2;
double denom;
denom = sqrt( (a * a) + (b * b) + (c * c));
distPoint2 = (pt2[0] * a) + (pt2[1] * b) + (pt2[2] * c) + d;
distPoint2 = distPoint2 / denom;
cout << "Distance to Point 2: " << distPoint2 << endl;
distPoint2 = (1400 * a) + (2000 * b) + (60.58 * c) + d;
distPoint2 = distPoint2 / denom;
cout << "Distance to Point 2: " << distPoint2 << endl;
}
void calc_plane(double pt1[3], double pt2[3], double pt3[3], double plane[5])
{
cout << "Point 1: " << pt1[0] << ", " << pt1[1] << ", " << pt1[2] << endl;
cout << "Point 2: " << pt2[0] << ", " << pt2[1] << ", " << pt2[2] << endl;
cout << "Point 3: " << pt3[0] << ", " << pt3[1] << ", " << pt3[2] << endl;
double v1[3] = { pt2[0]-pt1[0], pt2[1]-pt1[1], pt2[2]-pt1[2] };
double v2[3] = { pt3[0]-pt1[0], pt3[1]-pt1[1], pt3[2]-pt1[2] };
// 0, -600, 0
// 645, 0, 0
plane[0] = ( v1[1]*v2[2] ) - ( v1[2]*v2[1] );
// 0, 0
plane[1] = ( v1[2]*v2[0] ) - ( v1[0]*v2[2] );
// 0, 0
plane[2] = ( v1[0]*v2[1] ) - ( v1[1]*v2[0] ); // cross product
// 387000
plane[3] = ( pt1[0]*plane[0] ) + ( pt1[1]*plane[1] ) + (pt1[2]*plane[2]);
plane[4] = 0 - plane[3]; // dist
cout << "Vector 1" << v1[0] << ", " << v1[1] << ", " << v1[2] << endl;
cout << "Vector 2" << v2[0] << ", " << v2[1] << ", " << v2[2] << endl;
cout << plane[0] << "x + " << plane[1] << "y + " << plane[2] << "z + " << plane[3] << endl;
cout << "Distance: " << plane[4] << endl;
}