public void TestVectorCrossProducts()
{
Scientrace.Vector x = Scientrace.Vector.x1vector();
Scientrace.Vector y = Scientrace.Vector.y1vector();
Scientrace.Vector z = Scientrace.Vector.z1vector();
Assert.AreEqual(x.crossProduct(y), z);
Assert.AreEqual(y.crossProduct(x), z * -1);
Assert.AreEqual(y.crossProduct(z), x);
}
public string getX3DRotationTag(Scientrace.NonzeroVector fromVector, Scientrace.NonzeroVector toVector)
{
Scientrace.Vector r = fromVector.crossProduct(toVector);
double angle =
Math.Acos(toVector.normalized().dotProduct(fromVector.normalized())) // the angle to be rotated
* Math.Sign(r.crossProduct(fromVector).dotProduct(toVector));
try {
return("<Transform rotation='" + r.tryToUnitVector().trico() + " " + angle + "' >");
} catch { // if fromVector has the same direction as toVector, the crossProduct is a zerovector which cannot be normalized.
return("<Transform>"); //no transformation, just open so it can be closed afterwards
}
}
private Scientrace.NonzeroVector calcTriangleHeightVector(ShadowObject3d sho3d)
{
Scientrace.Vector length = sho3d.getVector("length");
Scientrace.Vector width = sho3d.getVector("width");
Scientrace.Vector heightdir = sho3d.getVector("heightdir");
double angle = sho3d.getDouble("angle");
//create a vector orthogonal to length en width in the same binary direction as heightdir.
Scientrace.UnitVector owl = (width.crossProduct(length) *
Math.Sign(width.crossProduct(length).dotProduct(heightdir))).tryToUnitVector();
Scientrace.NonzeroVector bdir = ( //calculate the direction of the short side of the prism
owl * Math.Sin(angle) +
width.tryToUnitVector() * Math.Cos(angle)
).tryToNonzeroVector();
if ((bdir.length < 0.99999) || (bdir.length > 1.00001))
{
throw new ArgumentOutOfRangeException("bdir.length", bdir.length, "!= 1");
}
Scientrace.VectorTransform trf = new Scientrace.VectorTransform(
width.tryToNonzeroVector(), owl.tryToNonzeroVector(), length.tryToNonzeroVector());
Scientrace.NonzeroVector hdirtrf = trf.transform(heightdir).tryToNonzeroVector();
Scientrace.Vector hprimetrf = new Scientrace.Vector(hdirtrf.x, hdirtrf.y, 0); //eliminate "length" component of heightdir in hprime
//Console.WriteLine("HPRIMTRF:"+hprimetrf.trico());
Scientrace.NonzeroVector hprimedir = trf.transformback(hprimetrf).tryToNonzeroVector().normalized();
/* ^
* /C\
* / \
* h'/ \ b
* / \
* /B_______A\
* width
* angle = A; beta = B; gamma = C.
*/
//sine rule: hprimelen / sin A = width.length() / sin C = blen / sin B
double beta, gamma;
beta = Math.Acos(hprimedir.normalized().dotProduct(width.tryToNonzeroVector().normalized()));
gamma = Math.PI - (angle + beta);
double hprimelen;
double sinruleconstant = width.length / Math.Sin(gamma);
hprimelen = sinruleconstant * Math.Sin(angle);
Scientrace.NonzeroVector hprime = hprimedir * hprimelen;
// check: (trf.transform(hprime).x / hdirtrf.x) == (trf.transform(hprime).y / hdirtrf.y)
double xycoeff = ((trf.transform(hprime).x / hdirtrf.x) / (trf.transform(hprime).y / hdirtrf.y));
if (Math.Abs(1 - xycoeff) > 0.00001) //doesn't do anything if .x/.x = NaN, but that's OK for now.
{
throw new ArgumentOutOfRangeException("xycoeff", xycoeff, "!=1");
}
try {
Scientrace.NonzeroVector h = ((Math.Abs(hdirtrf.x) > Math.Abs(hdirtrf.y)) ? // Preventing .x or .y denominator == 0 errors.
trf.transformback(hdirtrf * (trf.transform(hprime).x / hdirtrf.x)) :
trf.transformback(hdirtrf * (trf.transform(hprime).y / hdirtrf.y))
).tryToNonzeroVector();
return(h);
} catch (Scientrace.ZeroNonzeroVectorException zne) {
Console.WriteLine("ERROR: calculated height for triangularprism has length zero!");
throw (zne);
}
} //end calcTriangleHeightVector