public static Exp angle2d(ExpVector d0, ExpVector d1, bool angle360 = false)
{
Exp nu = d1.x * d0.x + d1.y * d0.y;
Exp nv = d0.x * d1.y - d0.y * d1.x;
if (angle360)
{
return(Math.PI - Exp.Atan2(nv, -nu));
}
return(Exp.Atan2(nv, nu));
}
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 ExpVector PointOn(Exp a, ExpVector point)
{
/*
* var ax = GetAxis();
* var axn = ax.Normalized();
* var o = GetOrigin();
* var prj = ExpVector.ProjectPointToLine(point, o, o + ax);
* var ra = Exp.Atan2(new Exp(step) / 4.0, (point - prj).Magnitude());
*/
var ax = GetAxis().Eval();
var axn = ax.normalized;
var o = GetOrigin().Eval();
var prj = ExpVector.ProjectPointToLine(point.Eval(), o, o + ax);
var t = a / (2.0 * Mathf.PI);
var ra = Exp.Atan2(new Exp(step) / 4.0, (point.Eval() - prj).magnitude);
var res = ExpVector.RotateAround(point, point - prj, o, ra);
res = ExpVector.RotateAround(res, ax, o, a);
return(res + (ExpVector)axn * t * step);
}
public static Exp angle3d(ExpVector d0, ExpVector d1)
{
return(Exp.Atan2(ExpVector.Cross(d0, d1).Magnitude(), ExpVector.Dot(d0, d1)));
}