public static void GetCircleParams(MultiVector obj, out MultiVector n, out MultiVector c, out double r)
{
if (!obj.ContainsOnly(2))
throw new InvalidEntityException();
// c cross n
MultiVector ccd = MultiVector.Vector(
-obj[Basis.E23],
obj[Basis.E13],
-obj[Basis.E12]);
// c dot n
double d = obj[Basis.EPLANE];
n = MultiVector.Vector(
obj[Basis.E1 ^ Basis.E0],
obj[Basis.E2 ^ Basis.E0],
obj[Basis.E3 ^ Basis.E0]);
c = MultiVector.CrossProduct(n, ccd) + n * d;
c /= (double)MultiVector.ScalarProduct(n, n);
double x;
if (n.E1 != 0) x = (obj[Basis.E1 ^ Basis.E8] + (double)d * c.E1) / n.E1;
else if (n.E2 != 0) x = (obj[Basis.E2 ^ Basis.E8] + (double)d * c.E2) / n.E2;
else if (n.E3 != 0) x = (obj[Basis.E3 ^ Basis.E8] + (double)d * c.E3) / n.E3;
else throw new InvalidEntityException();
r = Math.Sqrt((double)MultiVector.ScalarProduct(c, c) - 2 * x);
n /= n.Length;
}
public static void GetLineParams(MultiVector obj, out MultiVector t, out MultiVector d)
{
if (!obj.ContainsOnly(2))
{
throw new InvalidEntityException();
}
d = MultiVector.Vector(
-obj[Basis.E23],
obj[Basis.E13],
-obj[Basis.E12]);
double norm = d.Length;
if (norm == 0.0)
{
throw new InvalidEntityException();
}
d /= norm;
// d cross t
MultiVector dct = MultiVector.Vector(
obj[Basis.E1 ^ Basis.E8],
obj[Basis.E2 ^ Basis.E8],
obj[Basis.E3 ^ Basis.E8]) / norm;
t = MultiVector.CrossProduct(dct, d);
}
public static void GetPlaneParams(MultiVector obj, out MultiVector n, out double d)
{
if (!obj.ContainsOnly(1) || obj.E0 != 0.0)
{
throw new InvalidEntityException();
}
n = MultiVector.Vector(obj.E1, obj.E2, obj.E3);
double norm = n.Length;
n /= norm;
d = obj.E8 / norm;
}
public static void GetSphereParams(MultiVector obj, out MultiVector c, out double r)
{
if (!obj.ContainsOnly(1) || obj.E0 == 0.0)
{
throw new InvalidEntityException();
}
obj /= obj.E0;
c = MultiVector.Vector(obj.E1, obj.E2, obj.E3);
r = Math.Sqrt(Math.Abs(2 * obj.E8 - (double)MultiVector.ScalarProduct(c, c)));
// HACK
if (Math.Abs(r) < 1E-3)
{
r = 0.0;
}
}
public static void GetCircleParams(MultiVector obj, out MultiVector n, out MultiVector c, out double r)
{
if (!obj.ContainsOnly(2))
{
throw new InvalidEntityException();
}
// c cross n
MultiVector ccd = MultiVector.Vector(
-obj[Basis.E23],
obj[Basis.E13],
-obj[Basis.E12]);
// c dot n
double d = obj[Basis.EPLANE];
n = MultiVector.Vector(
obj[Basis.E1 ^ Basis.E0],
obj[Basis.E2 ^ Basis.E0],
obj[Basis.E3 ^ Basis.E0]);
c = MultiVector.CrossProduct(n, ccd) + n * d;
c /= (double)MultiVector.ScalarProduct(n, n);
double x;
if (n.E1 != 0)
{
x = (obj[Basis.E1 ^ Basis.E8] + (double)d * c.E1) / n.E1;
}
else if (n.E2 != 0)
{
x = (obj[Basis.E2 ^ Basis.E8] + (double)d * c.E2) / n.E2;
}
else if (n.E3 != 0)
{
x = (obj[Basis.E3 ^ Basis.E8] + (double)d * c.E3) / n.E3;
}
else
{
throw new InvalidEntityException();
}
r = Math.Sqrt((double)MultiVector.ScalarProduct(c, c) - 2 * x);
n /= n.Length;
}
public static void GetPointPairParams(MultiVector obj, out MultiVector p1, out MultiVector p2)
{
if (!obj.ContainsOnly(3))
{
throw new InvalidEntityException();
}
obj = obj.Dual;
double delta = Math.Sqrt(Math.Abs((double)MultiVector.InnerProduct(obj, obj)));
try
{
MultiVector temp = MultiVector.InnerProduct(Basis.E8, obj);
p1 = (+delta + obj) / temp;
p2 = (-delta + obj) / temp;
}
catch (InvalidOperationException)
{
throw new InvalidEntityException();
}
}
public static void GetSphereParams(MultiVector obj, out MultiVector c, out double r)
{
if (!obj.ContainsOnly(1) || obj.E0 == 0.0)
throw new InvalidEntityException();
obj /= obj.E0;
c = MultiVector.Vector(obj.E1, obj.E2, obj.E3);
r = Math.Sqrt(Math.Abs(2 * obj.E8 - (double)MultiVector.ScalarProduct(c, c)));
// HACK
if (Math.Abs(r) < 1E-3)
r = 0.0;
}
public static void GetPointPairParams(MultiVector obj, out MultiVector p1, out MultiVector p2)
{
if (!obj.ContainsOnly(3))
throw new InvalidEntityException();
obj = obj.Dual;
double delta = Math.Sqrt(Math.Abs((double)MultiVector.InnerProduct(obj, obj)));
try
{
MultiVector temp = MultiVector.InnerProduct(Basis.E8, obj);
p1 = (+delta + obj) / temp;
p2 = (-delta + obj) / temp;
}
catch (InvalidOperationException)
{
throw new InvalidEntityException();
}
}
public static void GetPlaneParams(MultiVector obj, out MultiVector n, out double d)
{
if (!obj.ContainsOnly(1) || obj.E0 != 0.0)
throw new InvalidEntityException();
n = MultiVector.Vector(obj.E1, obj.E2, obj.E3);
double norm = n.Length;
n /= norm;
d = obj.E8 / norm;
}
public static void GetLineParams(MultiVector obj, out MultiVector t, out MultiVector d)
{
if (!obj.ContainsOnly(2))
throw new InvalidEntityException();
d = MultiVector.Vector(
-obj[Basis.E23],
obj[Basis.E13],
-obj[Basis.E12]);
double norm = d.Length;
if (norm == 0.0)
throw new InvalidEntityException();
d /= norm;
// d cross t
MultiVector dct = MultiVector.Vector(
obj[Basis.E1 ^ Basis.E8],
obj[Basis.E2 ^ Basis.E8],
obj[Basis.E3 ^ Basis.E8]) / norm;
t = MultiVector.CrossProduct(dct, d);
}
public static GeometricEntity GetGeometricEntity(MultiVector obj)
{
if (obj.ContainsOnly(0))
{
return GeometricEntity.Scalar;
}
if (obj.ContainsOnly(1))
{
if (obj.E0 == 0 && obj.E8 == 0)
return GeometricEntity.Vector;
if (obj.E0 == 0)
return GeometricEntity.Plane;
MultiVector center; double radius;
GetSphereParams(obj, out center, out radius);
if (radius == 0)
return GeometricEntity.Point;
return GeometricEntity.Sphere;
}
if (obj.ContainsOnly(2))
{
if (obj.ContainsOnly(Basis.E12, Basis.E13, Basis.E23))
return GeometricEntity.Bivector;
if (MultiVector.InnerProduct(Basis.E8, obj) == 0.0)
return GeometricEntity.Line;
return GeometricEntity.Circle;
}
if (obj.ContainsOnly(3))
{
if (obj.ContainsOnly(Basis.E123))
return GeometricEntity.Trivector;
try
{
MultiVector p1, p2;
GetPointPairParams(obj, out p1, out p2);
return GeometricEntity.PointPair;
}
catch (InvalidEntityException)
{
return GeometricEntity.Unknown;
}
}
return GeometricEntity.Unknown;
}
public static GeometricEntity GetGeometricEntity(MultiVector obj)
{
if (obj.ContainsOnly(0))
{
return(GeometricEntity.Scalar);
}
if (obj.ContainsOnly(1))
{
if (obj.E0 == 0 && obj.E8 == 0)
{
return(GeometricEntity.Vector);
}
if (obj.E0 == 0)
{
return(GeometricEntity.Plane);
}
MultiVector center; double radius;
GetSphereParams(obj, out center, out radius);
if (radius == 0)
{
return(GeometricEntity.Point);
}
return(GeometricEntity.Sphere);
}
if (obj.ContainsOnly(2))
{
if (obj.ContainsOnly(Basis.E12, Basis.E13, Basis.E23))
{
return(GeometricEntity.Bivector);
}
if (MultiVector.InnerProduct(Basis.E8, obj) == 0.0)
{
return(GeometricEntity.Line);
}
return(GeometricEntity.Circle);
}
if (obj.ContainsOnly(3))
{
if (obj.ContainsOnly(Basis.E123))
{
return(GeometricEntity.Trivector);
}
try
{
MultiVector p1, p2;
GetPointPairParams(obj, out p1, out p2);
return(GeometricEntity.PointPair);
}
catch (InvalidEntityException)
{
return(GeometricEntity.Unknown);
}
}
return(GeometricEntity.Unknown);
}
