public static ExpVector NormalAtInPlane(this IEntity self, Exp t, IPlane plane)
{
if (self.plane != null)
{
var tang = self.TangentAt(t);
if (tang == null)
{
return(null);
}
var n = ExpVector.Cross(tang, Vector3.forward);
if (plane == self.plane)
{
return(n);
}
return(plane.DirToFrom(n, self.plane));
}
Param p = new Param("pOn");
var pt = self.PointOn(p);
var result = new ExpVector(pt.x.Deriv(p).Deriv(p), pt.y.Deriv(p).Deriv(p), pt.z.Deriv(p).Deriv(p));
result.x.Substitute(p, t);
result.y.Substitute(p, t);
result.z.Substitute(p, t);
if (plane == null)
{
return(result);
}
return(plane.DirToPlane(result));
}
public static Exp pointLineDistance(ExpVector p, ExpVector p0, ExpVector p1, bool is3d)
{
if (is3d)
{
var d = p0 - p1;
return(ExpVector.Cross(d, p0 - p).Magnitude() / d.Magnitude());
}
return(((p0.y - p1.y) * p.x + (p1.x - p0.x) * p.y + p0.x * p1.y - p1.x * p0.y) / Exp.Sqrt(Exp.Sqr(p1.x - p0.x) + Exp.Sqr(p1.y - p0.y)));
}
public void GenerateEquations(EquationSystem sys)
{
sys.AddParameters(parameters);
sys.AddEquation(u.Magnitude() - 1.0);
sys.AddEquation(v.Magnitude() - 1.0);
var cross = ExpVector.Cross(u, v);
var dot = ExpVector.Dot(u, v);
sys.AddEquation(Exp.Atan2(cross.Magnitude(), dot) - Math.PI / 2);
sys.AddEquation(n - ExpVector.Cross(u, v));
}
public static Exp angle3d(ExpVector d0, ExpVector d1)
{
return(Exp.Atan2(ExpVector.Cross(d0, d1).Magnitude(), ExpVector.Dot(d0, d1)));
}