Collision detection problem (intersection with plane) - algorithm

Question

I'm doing a scene using openGL (a house). I want to do some collision detection, mainly with the walls in the house.
I have tried the following code:
// a plane is represented with a normal and a position in space
Vector planeNor(0,0,1);
Vector position(0,0,-10);
Plane p(planeNor,position);
Vector vel(0,0,-1);
double lamda; // this is the intersection point
Vector pNormal; // the normal of the intersection
// this method is from Nehe's Lesson 30
coll= p.TestIntersionPlane(vel,Z,lamda,pNormal);
glPushMatrix();
glBegin(GL_QUADS);
if(coll)
glColor3f(1,0,0);
else
glColor3f(1,1,1);
glVertex3d(0,0,-10);
glVertex3d(3,0,-10);
glVertex3d(3,3,-10);
glVertex3d(0,3,-10);
glEnd();
glPopMatrix();
Nehe's method:
#define EPSILON 1.0e-8
#define ZERO EPSILON
bool Plane::TestIntersionPlane(const Vector3 & position,const Vector3 & direction, double& lamda, Vector3 & pNormal)
{
double DotProduct=direction.scalarProduct(normal); // Dot Product Between Plane Normal And Ray Direction
double l2;
// Determine If Ray Parallel To Plane
if ((DotProduct<ZERO)&&(DotProduct>-ZERO))
return false;
l2=(normal.scalarProduct(position))/DotProduct; // Find Distance To Collision Point
if (l2<-ZERO) // Test If Collision Behind Start
return false;
pNormal= normal;
lamda=l2;
return true;
}
Z is initially (0,0,0) and every time I move the camera towards the plane, I reduce its z component by 0.1 (i.e. Z.z-=0.1 ).
I know that the problem is with the vel vector, but I can't figure out what the right value should be. Can anyone please help me?

Answer 1

You're passing "vel" (which I suppose is velocity of the moving thing) as "Position", and Z (which I suppose is position) as "Direction".
Your calculation of "Distance to Collision Point" makes no sense. It doesn't take position of the plane into account at all (or maybe it does, if the variables are misnamed).
You define pNormal, but I can't see any use for it. Is it supposed to mean something else?
It's almost impossible to get something like this working without understanding the math. Try a simpler version of the test, maybe assuming a z=0 plane and +z-axis movement, get that working and then take another look at the general case.

Answer 2

Thank you for your help.
I looked into the code again and I changed the collision detection method into the following:
//startPoint: the ray's starting point.
//EndPoint: the ray's ending point.
//lamda: the intersection point.
bool Plane::TestIntersionPlane(const Vector3& startPoint,const Vector3& Endpoint, double& lamda)
{
double cosAlpha=Endpoint.scalarProduct(normal); // calculates the angle between the plane's normal and the ray vector.
// Determine If Ray Parallel To Plane
if ((cosAlpha<ZERO)&&(cosAlpha>-ZERO))
return false;
// delta D is the plane's distance from the origin minus the ray's distance from the origin.
double deltaD = distance - startPoint.scalarProduct(normal); //distance is a double representing the plane's distance from the origin.
lamda= deltaD/cosAlpha;// distance between the plane and the vector
// if the distance between the ray and the plane is greater than zero then they haven't intersected.
if(lamda > ZERO)
return false;
return true;
}
This seems to work with all planes except when the ray is too far from the plane. For example if the plane is at z=-10 and the ray's starting point is: 0,0,3 and it's ending point is 0,0,2 then this is detected as a collision but when I move the ray to start(0,0,2) and end(0,0,1) it's not detected as a collision.
The math seems correct to me, so I'm not sure how to handle this.