private Mogre.Vector3 getOrbitalPosition(Mogre.Vector3 focalPoint, Quaternion direction, float distanceToFocalPoint)
{
Mogre.Vector3 eyePos, xAxis, yAxis, zAxis;
Quaternion m_Orientation = direction;
Mogre.Matrix3 m_ViewMatrix;
// Get the rotation matrix from the quaternion
m_ViewMatrix = m_Orientation.ToRotationMatrix();
// Get the axis we need them for the camera position calculation (the axes span a new coord frame)
xAxis = new Mogre.Vector3(m_ViewMatrix[0, 0], m_ViewMatrix[0, 1], m_ViewMatrix[0, 2]);
yAxis = new Mogre.Vector3(m_ViewMatrix[1, 0], m_ViewMatrix[1, 1], m_ViewMatrix[1, 2]);
zAxis = new Mogre.Vector3(m_ViewMatrix[2, 0], m_ViewMatrix[2, 1], m_ViewMatrix[2, 2]);
eyePos = focalPoint + zAxis * distanceToFocalPoint;
// Transform our vector in the orbital space. Here we rotate and flip it.
m_ViewMatrix[0, 3] = -xAxis.DotProduct(eyePos);
m_ViewMatrix[1, 3] = -yAxis.DotProduct(eyePos);
m_ViewMatrix[2, 3] = -zAxis.DotProduct(eyePos);
Mogre.Vector3 m_CamPos = new Mogre.Vector3();
// So extract the cam position for the sake of completeness
m_CamPos.x = m_ViewMatrix[0, 3];
m_CamPos.y = m_ViewMatrix[1, 3];
m_CamPos.z = m_ViewMatrix[2, 3];
return(m_CamPos);
}
public static Tuple <bool, float> Intersects(Ray ray, Sphere sphere, bool discardInside)
{
Vector3 raydir = ray.Direction;
// Adjust ray origin relative to sphere center
Vector3 rayorig = ray.Origin - sphere.Center;
float radius = sphere.Radius;
// Check origin inside first
if (rayorig.SquaredLength <= radius * radius && discardInside)
{
return(Tuple.Create(true, 0.0f));
}
// Mmm, quadratics
// Build coeffs which can be used with std quadratic solver
// ie t = (-b +/- sqrt(b*b + 4ac)) / 2a
float a = raydir.DotProduct(raydir);
float b = 2 * rayorig.DotProduct(raydir);
float c = rayorig.DotProduct(rayorig) - radius * radius;
// Calc determinant
float d = (b * b) - (4 * a * c);
if (d < 0)
{
// No intersection
return(Tuple.Create(false, 0.0f));
}
// BTW, if d=0 there is one intersection, if d > 0 there are 2
// But we only want the closest one, so that's ok, just use the
// '-' version of the solver
float t = (-b - Math.Sqrt(d)) / (2 * a);
if (t < 0)
{
t = (-b + Math.Sqrt(d)) / (2 * a);
}
return(Tuple.Create(true, t));
}
public static Vector3 CalculateTangentSpaceVector(
Vector3 position1, Vector3 position2, Vector3 position3,
float u1, float v1, float u2, float v2, float u3, float v3)
{
//side0 is the vector along one side of the triangle of vertices passed in,
//and side1 is the vector along another side. Taking the cross product of these returns the normal.
Vector3 side0 = position1 - position2;
Vector3 side1 = position3 - position1;
//Calculate face normal
Vector3 normal = side1.CrossProduct(side0);
normal.Normalise();
//Now we use a formula to calculate the tangent.
float deltaV0 = v1 - v2;
float deltaV1 = v3 - v1;
Vector3 tangent = deltaV1 * side0 - deltaV0 * side1;
tangent.Normalise();
//Calculate binormal
float deltaU0 = u1 - u2;
float deltaU1 = u3 - u1;
Vector3 binormal = deltaU1 * side0 - deltaU0 * side1;
binormal.Normalise();
//Now, we take the cross product of the tangents to get a vector which
//should point in the same direction as our normal calculated above.
//If it points in the opposite direction (the dot product between the normals is less than zero),
//then we need to reverse the s and t tangents.
//This is because the triangle has been mirrored when going from tangent space to object space.
//reverse tangents if necessary
Vector3 tangentCross = tangent.CrossProduct(binormal);
if (tangentCross.DotProduct(normal) < 0.0f)
{
tangent = -tangent;
binormal = -binormal;
}
return(tangent);
}
private Mogre.Vector3 getOrbitalPosition(Mogre.Vector3 focalPoint, Quaternion direction, float distanceToFocalPoint)
{
Mogre.Vector3 eyePos, xAxis, yAxis, zAxis;
Quaternion m_Orientation = direction;
Mogre.Matrix3 m_ViewMatrix;
// Get the rotation matrix from the quaternion
m_ViewMatrix = m_Orientation.ToRotationMatrix();
// Get the axis we need them for the camera position calculation (the axes span a new coord frame)
xAxis = new Mogre.Vector3(m_ViewMatrix[0, 0], m_ViewMatrix[0, 1], m_ViewMatrix[0, 2]);
yAxis = new Mogre.Vector3(m_ViewMatrix[1, 0], m_ViewMatrix[1, 1], m_ViewMatrix[1, 2]);
zAxis = new Mogre.Vector3(m_ViewMatrix[2, 0], m_ViewMatrix[2, 1], m_ViewMatrix[2, 2]);
eyePos = focalPoint + zAxis * distanceToFocalPoint;
// Transform our vector in the orbital space. Here we rotate and flip it.
m_ViewMatrix[0, 3] = -xAxis.DotProduct(eyePos);
m_ViewMatrix[1, 3] = -yAxis.DotProduct(eyePos);
m_ViewMatrix[2, 3] = -zAxis.DotProduct(eyePos);
Mogre.Vector3 m_CamPos = new Mogre.Vector3();
// So extract the cam position for the sake of completeness
m_CamPos.x = m_ViewMatrix[0, 3];
m_CamPos.y = m_ViewMatrix[1, 3];
m_CamPos.z = m_ViewMatrix[2, 3];
return m_CamPos;
}
public static Tuple <bool, float> Intersects(Ray ray, Vector3 a, Vector3 b, Vector3 c, Vector3 normal, bool positiveSide, bool negativeSide)
{
//
// Calculate intersection with plane.
//
float t;
{
float denom = normal.DotProduct(ray.Direction);
// Check intersect side
if (denom > +float.Epsilon)
{
if (!negativeSide)
{
return(Tuple.Create(false, 0.0f));
}
}
else if (denom < -float.Epsilon)
{
if (!positiveSide)
{
return(Tuple.Create(false, 0.0f));
}
}
else
{
// Parallel or triangle area is close to zero when
// the plane normal not normalised.
return(Tuple.Create(false, 0.0f));
}
t = normal.DotProduct(a - ray.Origin) / denom;
if (t < 0)
{
// Intersection is behind origin
return(Tuple.Create(false, 0.0f));
}
}
//
// Calculate the largest area projection plane in X, Y or Z.
//
int i0, i1;
{
float n0 = Abs(normal[0]);
float n1 = Abs(normal[1]);
float n2 = Abs(normal[2]);
i0 = 1; i1 = 2;
if (n1 > n2)
{
if (n1 > n0)
{
i0 = 0;
}
}
else
{
if (n2 > n0)
{
i1 = 0;
}
}
}
//
// Check the intersection point is inside the triangle.
//
{
float u1 = b[i0] - a[i0];
float v1 = b[i1] - a[i1];
float u2 = c[i0] - a[i0];
float v2 = c[i1] - a[i1];
float u0 = t * ray.Direction[i0] + ray.Origin[i0] - a[i0];
float v0 = t * ray.Direction[i1] + ray.Origin[i1] - a[i1];
float alpha = u0 * v2 - u2 * v0;
float beta = u1 * v0 - u0 * v1;
float area = u1 * v2 - u2 * v1;
// epsilon to avoid float precision error
const float EPSILON = 1e-3f;
float tolerance = -EPSILON * area;
if (area > 0)
{
if (alpha < tolerance || beta < tolerance || alpha + beta > area - tolerance)
{
return(Tuple.Create(false, 0.0f));
}
}
else
{
if (alpha > tolerance || beta > tolerance || alpha + beta < area - tolerance)
{
return(Tuple.Create(false, 0.0f));
}
}
}
return(Tuple.Create(true, t));
}
/// <summary>Calculate a face normal without normalize, including the w component which is the offset from the origin. </summary>
public static Vector4 CalculateFaceNormalWithoutNormalize(Vector3 v1, Vector3 v2, Vector3 v3)
{
Vector3 vector = Math.CalculateBasicFaceNormalWithoutNormalize(v1, v2, v3);
return(new Vector4(vector.x, vector.y, vector.z, -vector.DotProduct(v1)));
}