There is probably a really simple solution I am just not seeing it. If I have a 3D box whose dimensions are from 1>x>-1, 1>y>-1, 1>z>-1 And I have two arbitrary points that are connected by a line how I can find the point or points, if any where that line intersects the sides of the box. This is for a clipping algorithm I am righting and needs to be done many times per frame so speed & efficiency are an issue. Ideally I am looking for a formula that I can just plug my numbers in to and get an answer, pretty much in the same way you would do with a sphere and a ray.

If you just need a boolean result, there are very fast algorithms based on the separating axis test.

If you need the actual points of intersection, I think you''ll have to carry out the ray/plane intersection tests. However, due to the unit box and axis-aligned planes, I imagine this could be optimized quite a bit.

I''m not positive about this though - there may be a faster algorithm I''m not aware of.

Here is what I came up with but its not working.
I think the problem, is when i solve for the ClipedPoints.

int ClipProject(Point3d A,Point3d B ,Point3d& C ,Point3d& D){	double n = 1.0;	double f = 5000.0;	double a =(n+f)/(f-n) ;	double b =(2.0*n*f)/(n-f);	double Mx,My,Mz,bx,by,bz;	Point3d ClipedPoint[6];	if(A.z == 0.0) A.z=0.00000000001;	if(B.z == 0.0) B.z=0.00000000001;	int i;	A.y /= A.z;	A.x /= A.z;	A.z = -(a+b/A.z);	B.y /= B.z;	B.x /= B.z;	B.z = -(a+b/B.z);	if(A.y == B.y) My = 9999999999999999.9;	else My = (A.x-B.x)/(A.y-B.y);	if(A.z == B.z) Mz = 9999999999999999.9;	else Mz = (A.x-B.x)/(A.z-B.z);	by = A.y -(My*A.x);	bz = A.z -(Mz*A.x);	ClipedPoint[0].x = 1; ClipedPoint[0].y = My + by; ClipedPoint[0].z = Mz + bz; // X = 1	ClipedPoint[1].x =-1; ClipedPoint[1].y =-My + by; ClipedPoint[1].z =-Mz + bz; // X = -1	if(A.x == B.x) My = 9999999999999999.9;	else Mx = (A.y-B.y)/(A.x-B.x);	if(A.z == B.z) My = 9999999999999999.9;	else Mz = (A.y-B.y)/(A.z-B.z);	bx = A.x -(Mx*A.y);	bz = A.z -(Mz*A.y);	ClipedPoint[2].x = Mx + bx; ClipedPoint[2].y = 1; ClipedPoint[2].z = Mz + bz; // Y = 1	ClipedPoint[3].x =-Mx + bx; ClipedPoint[3].y =-1; ClipedPoint[3].z =-Mz + bz; // Y = -1	if(A.y == B.y) My = 9999999999999999.9;	else My = (A.z-B.z)/(A.y-B.y);	if(A.x == B.x) My = 9999999999999999.9;	else Mx = (A.z-B.z)/(A.x-B.x);	by = A.y -(My*A.z);	bx = A.x -(Mx*A.z);	ClipedPoint[4].x = Mx + bx; ClipedPoint[4].y = My + by; ClipedPoint[4].z = 1; // Z = 1	ClipedPoint[5].x =-Mx + bx; ClipedPoint[5].y =-My + by; ClipedPoint[5].z =-1; // Z = -1		if(B.z<1 && B.z > -1 && B.y <1 && B.y > -1 && B.x <1 && B.x > -1)	{		D = B;		D.y -=    0.75;		D.x +=    1.0;		D.y *= -640.0/2;		D.x *=  640.0/2;		if(A.z<1 && A.z > -1 && A.y <1 && A.y > -1 && A.x <1 && A.x > -1)		{			C = A;			C.y -=    0.75;			C.x +=    1.0;			C.y *= -640.0/2;			C.x *=  640.0/2;			return 1;		}		else		{			for(i=0;i<6;i++)			{					C = ClipedPoint[i];				if(	(	(A.x <= C.x && C.x <= B.x && A.y <= C.y && C.y <= B.y && A.z <= C.z && C.z <= B.z)||						(A.x >= C.x && C.x >= B.x && A.y >= C.y && C.y >= B.y && A.z >= C.z && C.z >= B.z)					)&& (C.z<=1 && C.z >= -1 && C.y <=1 && C.y >= -1 && C.x <=1 && C.x >= -1)				  ){					C.y -=    0.75;					C.x +=    1.0;					C.y *= -640.0/2;					C.x *=  640.0/2;					return 1;				  }			}		}	}	else	{		//D = clip B		if(A.z<1 && A.z > -1 && A.y <1 && A.y > -1 && A.x <1 && A.x > -1)		{			C = A;			C.y -=    0.75;			C.x +=    1.0;			C.y *= -640.0/2;			C.x *=  640.0/2;			for(i=0;i<6;i++)			{					D = ClipedPoint[i];				if(	(	(A.x <= D.x && D.x <= B.x && A.y <= D.y && D.y <= B.y && A.z <= D.z && D.z <= B.z)||						(A.x >= D.x && D.x >= B.x && A.y >= D.y && D.y >= B.y && A.z >= D.z && D.z >= B.z)					)&& (D.z<=1 && D.z >= -1 && D.y <=1 && D.y >= -1 && D.x <=1 && D.x >= -1)				  ){					D.y -=    0.75;					D.x +=    1.0;					D.y *= -640.0/2;					D.x *=  640.0/2;					return 1;				  }			}		}		else		{			//clip both, not done yet.			//D = cliped B			//C = cliped A			if(C.z<=1 && C.z >= -1 && C.y <=1 && C.y >= -1 && C.x <=1 && C.x >= -1 && 				D.z<=1 && D.z >= -1 && D.y <=1 && D.y >= -1 && D.x <=1 && D.x >= -1)			{								return 1;			}			else return 0;		}	}	return 0;}