signed distance between plane and point

Question

I cannot find a consistent method for finding the signed distance between a point and a plane. How can I calculate this given a plane defined as a point and a normal?

struct Plane
{
    Vec3 point;
    Vec3 normal;
} 

Answer 1

You're making things much too complicated. If your normal is normalized, you can just do this:

float dist = dotProduct(p.normal, (vectorSubtract(point, p.point)));

Answer 2

dont worry i understand exactly how you feel. I am assuming you want some code snippets. so you can implement it in your own. you need to do a lot more work than just finding out the dot product.

It is up to you to understand this algorithm and to implement it into your own program what i will do is give you an implementation of this algorithm

signed distance between point and plane

Here are some sample "C++" implementations of these algorithms.

// Assume that classes are already given for the objects:
//    Point and Vector with
//        coordinates {float x, y, z;}
//        operators for:
//            Point  = Point ± Vector
//            Vector = Point - Point
//            Vector = Scalar * Vector    (scalar product)
//    Plane with a point and a normal {Point V0; Vector n;}
//===================================================================

// dot product (3D) which allows vector operations in arguments
#define dot(u,v)   ((u).x * (v).x + (u).y * (v).y + (u).z * (v).z)
#define norm(v)    sqrt(dot(v,v))  // norm = length of vector
#define d(u,v)     norm(u-v)       // distance = norm of difference

// pbase_Plane(): get base of perpendicular from point to a plane
//    Input:  P = a 3D point
//            PL = a plane with point V0 and normal n
//    Output: *B = base point on PL of perpendicular from P
//    Return: the distance from P to the plane PL
float
pbase_Plane( Point P, Plane PL, Point* B)
{
    float    sb, sn, sd;

    sn = -dot( PL.n, (P - PL.V0));
    sd = dot(PL.n, PL.n);
    sb = sn / sd;

    *B = P + sb * PL.n;
    return d(P, *B);
}

Taken from here: http://www.softsurfer.com/Archive/algorithm_0104/algorithm_0104.htm

PK