public override Polynom GetImplicitPolynomial()
{
if (implicitPolynomial == null)
{
PolynomVector w = zAxis ^ (location.ToVector() - PolynomVector.xyz); // the distance of a point to the axis
Polynom l = zAxis * PolynomVector.xyz - zAxis * location.ToVector(); // the distance from location along the axis
//(w*w)/(l*l)==(xAxis*xAxis)/(zAxis*zAxis) == tan(half opening angle)
implicitPolynomial = (w * w) - ((xAxis * xAxis) / (zAxis * zAxis)) * (l * l);
double d1 = implicitPolynomial.Eval(PointAt(new GeoPoint2D(0.5, 0.5)));
double d2 = implicitPolynomial.Eval(PointAt(new GeoPoint2D(10, -10)));
GeoPoint p = PointAt(new GeoPoint2D(1, 0)) + GetNormal(new GeoPoint2D(1, 0)).Normalized; // a point with distance 1 from the cone
double d = implicitPolynomial.Eval(p); // this should be 1
implicitPolynomial = (1 / d) * implicitPolynomial; // OK, this makes a good scaling (but it is not the distance)
}
return(implicitPolynomial);
}
public override Polynom GetImplicitPolynomial()
{
if (implicitPolynomial == null)
{
PolynomVector x = (new GeoVector(center.x, center.y, center.z) - PolynomVector.xyz);
implicitPolynomial = (x * x) - xAxis * xAxis;
// we need to scale the implicit polynomial so that it yields the true distance to the surface
GeoPoint p = center + xAxis + xAxis.Normalized; // a point outside the sphere with distance 1
double d = implicitPolynomial.Eval(p); // this should be 1 when the polynomial is normalized
if ((xAxis ^ yAxis) * zAxis < 0)
{
d = -d; // inverse oriented sphere
}
implicitPolynomial = (1 / d) * implicitPolynomial; // normalize the polynomial
}
return(implicitPolynomial);
}
public override Polynom GetImplicitPolynomial()
{
if (implicitPolynomial == null)
{
GeoVector zNormed = zAxis.Normalized;
PolynomVector x = zNormed ^ (new GeoVector(location.x, location.y, location.z) - PolynomVector.xyz);
implicitPolynomial = (x * x) - xAxis * xAxis;
// we need to scale the implicit polynomial so that it yields the true distance to the surface
GeoPoint p = location + xAxis + xAxis.Normalized; // a point outside the cylinder with distance 1
double d = implicitPolynomial.Eval(p); // this should be 1 when the polynomial is normalized
if ((xAxis ^ yAxis) * zAxis < 0)
{
d = -d; // inverse oriented cylinder
}
implicitPolynomial = (1 / d) * implicitPolynomial; // normalize the polynomial
}
return(implicitPolynomial);
}
