/// <summary>
/// Multiply the x-component of a parametric equation by a function of input.
/// </summary>
/// <param name="f">Function of input</param>
/// <param name="tp">Parametric equation</param>
/// <returns></returns>
public static ExTP MultiplyX(ExBPY f, ExTP tp)
{
var v = TExV2.Variable();
var by = ExUtils.VFloat();
return(bpi => Ex.Block(
new[] { v, by },
Ex.Assign(v, tp(bpi)),
MulAssign(v.x, f(bpi)),
v
));
}
/// <summary>
/// Add a function of input to the y-component of a parametric equation.
/// </summary>
/// <param name="f">Function of input</param>
/// <param name="tp">Parametric equation</param>
/// <returns></returns>
public static ExTP AddY(ExBPY f, ExTP tp)
{
var v = TExV2.Variable();
var by = ExUtils.VFloat();
return(bpi => Ex.Block(
new[] { v, by },
Ex.Assign(v, tp(bpi)),
ExUtils.AddAssign(v.y, f(bpi)),
v
));
}
/// <summary>
/// Multiply a unit vector at a given angle from the target function by the magnitude,
/// and add it to the target function.
/// </summary>
/// <param name="angle">Angle offset (degrees)</param>
/// <param name="magnitude">Magnitude of offset vector</param>
/// <param name="tp">Target function</param>
/// <returns></returns>
public static ExTP AddAtAngle(ExBPY angle, ExBPY magnitude, ExTP tp)
{
TExV2 v2 = TExV2.Variable();
TExV2 v2norm = TExV2.Variable();
var mag = ExUtils.VFloat();
return(bpi => Ex.Block(new[] { v2, v2norm, mag },
Ex.Assign(v2, tp(bpi)),
Ex.Assign(v2norm, Rotate(angle(bpi), Norm(v2))),
Ex.Assign(mag, magnitude(bpi)),
Ex.Assign(v2norm.x, v2.x.Add(v2norm.x.Mul(mag))),
Ex.Assign(v2norm.y, v2.y.Add(v2norm.y.Mul(mag))),
v2norm
));
}