private double[] GetIntersectionsFromBook(Tuple4 origin, Tuple4 dir)
{
if (!Constants.EpsilonCompare(1.0, dir.Length()))
{
throw new ArgumentException("Direction should be normalized", nameof(dir));
}
var sphereToRay = Tuple4.Subtract(origin, Tuple4.ZeroPoint);
var a = Tuple4.DotProduct(dir, dir);
var b = 2 * Tuple4.DotProduct(dir, sphereToRay);
var c = Tuple4.DotProduct(sphereToRay, sphereToRay) - 1.0;
var discriminant = b * b - 4 * a * c;
if (discriminant < 0.0)
{
return(null);
}
var discriminantSqrt = Math.Sqrt(discriminant);
var t0 = (-b - discriminantSqrt) / (2 * a);
var t1 = (-b + discriminantSqrt) / (2 * a);
// Ray originates inside sphere
// When t > 0 that is intersection in the direction of the ray
// other intersection is in the opposite direction
return(new double[] { t0, t1 });
}
public static IMatrix LookAtTransform(Tuple4 from, Tuple4 to, Tuple4 up)
{
var forward = Tuple4.Normalize(Tuple4.Subtract(to, from));
var upNormalized = Tuple4.Normalize(up);
var left = Tuple4.CrossProduct(forward, upNormalized);
var trueUp = Tuple4.CrossProduct(left, forward);
var viewMatrix = new Matrix(new double[, ]
{
{ left.X, left.Y, left.Z, -Tuple4.DotProduct(left, from) },
{ trueUp.X, trueUp.Y, trueUp.Z, -Tuple4.DotProduct(trueUp, from) },
{ -forward.X, -forward.Y, -forward.Z, Tuple4.DotProduct(forward, from) },
{ 0.0, 0.0, 0.0, 1.0 }
});
return(viewMatrix);
/*
* // Create a 4x4 orientation matrix from the left, up, and forward vectors
* // This is transposed which is equivalent to performing an inverse
* // if the matrix is orthonormalized (in this case, it is).
* var orientation = new Matrix(new double[,]
* {
* { left.X, left.Y, left.Z, 0.0 },
* { trueUp.X, trueUp.Y, trueUp.Z, 0.0 },
* { -forward.X, -forward.Y, -forward.Z, 0.0 },
* { 0.0, 0.0, 0.0, 1.0 }
* }, false);
*
* // Create a 4x4 translation matrix.
* // The eye position is negated which is equivalent
* // to the inverse of the translation matrix.
* var translation = Translation(-from.X, -from.Y, -from.Z);
*
* // Combine the orientation and translation to compute
* // the final view matrix. Note that the order of
* // multiplication is reversed because the matrices
* // are already inverted.
* return Multiply(orientation, translation);
*/
}
public static IMatrix EulerAnglesTransformDirectConstruction(Tuple4 from, double pitch, double yaw)
{
double cosPitch = Math.Cos(pitch);
double sinPitch = Math.Sin(pitch);
double cosYaw = Math.Cos(yaw);
double sinYaw = Math.Sin(yaw);
Tuple4 xaxis = new Tuple4(cosYaw, 0, -sinYaw, TupleFlavour.Vector);
Tuple4 yaxis = new Tuple4(sinYaw * sinPitch, cosPitch, cosYaw * sinPitch, TupleFlavour.Vector);
Tuple4 zaxis = new Tuple4(sinYaw * cosPitch, -sinPitch, cosPitch * cosYaw, TupleFlavour.Vector);
var viewMatrix = new Matrix(new double[, ]
{
{ xaxis.X, xaxis.Y, xaxis.Z, -Tuple4.DotProduct(xaxis, from) },
{ yaxis.X, yaxis.Y, yaxis.Z, -Tuple4.DotProduct(yaxis, from) },
{ zaxis.X, zaxis.Y, zaxis.Z, -Tuple4.DotProduct(zaxis, from) },
{ 0, 0, 0, 1 }
});
return(viewMatrix);
}
private double[] GetIntersections(Tuple4 origin, Tuple4 dir)
{
if (!Constants.EpsilonCompare(1.0, dir.Length()))
{
throw new ArgumentException("Direction should be normalized", nameof(dir));
}
var l = Tuple4.Subtract(Center, origin);
var tca = Tuple4.DotProduct(l, dir);
var d2 = Tuple4.DotProduct(l, l) - tca * tca;
if (d2 > radius2)
{
return(null);
}
var thc = Math.Sqrt(radius2 - d2);
var t0 = tca - thc;
var t1 = tca + thc;
// Ray originates inside sphere
// When t > 0 that is intersection in the direction of the ray
// other intersection is in the opposite direction
return(new double[] { t0, t1 });
}