double VectorType::angleBetweenVectors(VectorType secondVector)
{
//cos(theta) = (u . v) / (|u|*|v|
double theta = acos(dotProduct(secondVector)
/
(vectorLength() * secondVector.vectorLength())
);
return theta;
}
double Common::intersectFace(RayType inputRay, FaceType inputFace)
{
//cout <<"Attempting a face intersection" << endl;
//find the location of the intersection between a ray and a triangle face.
//return the distance to the intersection.
//return -1 if there is no intersection.
//determine plane equation.
//Let the vector e1 be defined along the edge from p0 to p1
//Let the vector e2 be defined along the edge from p0 to p2
//Let the vector n be defined by the cross product of e1 and e2
//That's annoying, now these vector names are 1 based, and points are 0 based.
//WTF? Consistency? Nah.
double denominator = (inputFace.A * inputRay.direction.x) + (inputFace.B * inputRay.direction.y) + (inputFace.C * inputRay.direction.z);
//cout << "den:" << denominator << endl;
double numerator = 0 - ((inputFace.A * inputRay.origin.x) + (inputFace.B * inputRay.origin.y) + (inputFace.C * inputRay.origin.z) + inputFace.D);
if(thresholdEquals(denominator,0))
{
//if the denominator is zero, the ray grazes the plane, never intersects.
//cout << "Demonimator is 0." << endl;
return -1;
}
else
{
double t = numerator / denominator;
if(thresholdEquals(t,0))
{
//cout << "Intersect at t=0" << endl;
//if t is 0, the ray intersects at the ray's origin. That doesn't count.
return -1;
}
else if (t < 0)
{
//cout << "Negative T" << endl;
//object is behind the eye. No intersection.
return -1;
}
else
{
//cout << "Plane intersection found. Will determine if it is a triangle intersection." << endl;
//We have to check if the intersection point is actually inside the triangle.
//Calculate barycentric coordinates.
// The area of an arbitrary triangle can also be
//computed as half of the length of the cross
//product of the vectors describing any two of
//its sides:
//wait, N is a normal vector. Already have that.
PointType intersectionPoint;
//px = (x0 + t⋅xd)
//py = (y0 + t⋅yd)
//pz = (z0 + t⋅zd)
intersectionPoint.x = inputRay.origin.x + t * inputRay.direction.x;
intersectionPoint.y = inputRay.origin.y + t * inputRay.direction.y;
intersectionPoint.z = inputRay.origin.z + t * inputRay.direction.z;
VectorType n = inputFace.e1.crossProduct(inputFace.e2);//.normalize();
double totalArea = n.vectorLength() / 2;
VectorType centerV1 = vectorFromHereToPoint(intersectionPoint, inputFace.v1);
VectorType centerV2 = vectorFromHereToPoint(intersectionPoint, inputFace.v2);
VectorType centerV3 = vectorFromHereToPoint(intersectionPoint, inputFace.v3);
double areaA = centerV1
.crossProduct(centerV2).vectorLength()/2;
double areaB = centerV1
.crossProduct(centerV3).vectorLength()/2;
double areaC = centerV2
.crossProduct(centerV3).vectorLength()/2;
double alpha = areaA / totalArea;
double beta = areaB / totalArea;
double gamma = areaC / totalArea;
//cout <<"sumArea:" << (areaA + areaB + areaC) << endl;
//cout <<"sumGreek:" << (alpha + beta + gamma) << endl;
//cout <<"totalArea:" << totalArea << endl;
//I know that the point is outside the traingle if any of alpha,beta, or gamma
//is < 0 or > 1
if(alpha > 1 || beta > 1 || gamma > 1 || alpha < 0 || beta < 0 || gamma < 0)
{
//cout << "outside triangle" << endl;
return -1;
}
//if (alpha + beta + gamma == 1) {
// point is in triangle
if(thresholdEquals((alpha+ beta + gamma),1))
{
//cout <<"Triangle intersection found." << endl;
return t;
}
}
}
//I don't think we should get here. But if there's a problem, assume no intersect.
return -1;
}
