/// <summary>
/// Wrap a position equation around a cylinder.
/// </summary>
/// <param name="radius">Radius of the cylinder</param>
/// <param name="ang0">Starting angle offset (radians) on the cylinder. 0 = z-axis</param>
/// <param name="maxWrap">Maximum angle value (radians) of the wrap. After this, the function will continue along the tangent. Starting offset not included. Absolute value tested.</param>
/// <param name="axisOff">Offset angle (radians) of the axis of the cylinder from the y-axis</param>
/// <param name="position">Position equation</param>
/// <returns></returns>
public static tv3 CylinderWrap(efloat radius, efloat ang0, efloat maxWrap, efloat axisOff, ev2 position) =>
EEx.Resolve(radius, ang0, axisOff, position, (r, a0, axis, _v2) => {
var cs = new TExV2();
var xyd = new TExV2();
var v2 = new TExV2(_v2);
var v3 = new TExV3();
var a = ExUtils.VFloat();
var aRem = ExUtils.VFloat();
var aMax = ExUtils.VFloat();
var a_cs = new TExV2();
var a0_cs = new TExV2();
return(Ex.Block(new[] { v3, cs, xyd, a, aRem, aMax, a_cs, a0_cs },
aMax.Is(maxWrap),
cs.Is(CosSin(axis)),
xyd.Is(ConvertBasis(v2, cs)),
a.Is(xyd.x.Div(r)),
aRem.Is(E0),
Ex.IfThen(Abs(a).GT(aMax), Ex.Block(
Ex.IfThen(a.LT0(), MulAssign(aMax, EN1)),
aRem.Is(a.Sub(aMax)),
a.Is(aMax)
)),
a0_cs.Is(CosSin(a0)),
a_cs.Is(CosSin(a.Add(a0))),
xyd.x.Is(r.Mul(a_cs.y.Sub(a0_cs.y).Add(aRem.Mul(a_cs.x)))),
v3.Is(TP3(DeconvertBasis(xyd, cs))),
v3.z.Is(r.Mul(a_cs.x.Sub(a0_cs.x).Sub(aRem.Mul(a_cs.y)))),
v3
));
});
/// <summary>
/// Derive a Vector2 from a Vector3 by dropping the Z-component.
/// </summary>
public static ExTP TP(ExTP3 xyz)
{
var v3 = TExV3.Variable();
return(bpi => Ex.Block(new ParameterExpression[] { v3 },
Ex.Assign(v3, xyz(bpi)),
ExUtils.V2(v3.x, v3.y)
));
}
/// <summary>
/// Note: requires that normalVec and planeVec are perpendicular.
/// </summary>
public static tv3 RotateInPlane(tfloat rot, tv3 normalVec, ev3 planeVec) => EEx.Resolve(planeVec, p => {
var cs = new TExV2();
var cross = new TExV3();
return(Ex.Block(new ParameterExpression[] { cs, cross },
cs.Is(CosSinDeg(rot)),
cross.Is(CrossProduct(normalVec, p)),
cs.x.Mul(p).Add(cs.y.Mul(v3Mag(p).Div(v3Mag(cross)).Mul(cross)))
));
});
/// <summary>
/// Derive a V2RV2 from a nonrotational vector and a rotational vector3.
/// </summary>
/// <param name="nrot">Nonrotational component</param>
/// <param name="rot">Rotational component (x,y,angle)</param>
/// <returns></returns>
public static trv2 V2V3(ev2 nrot, ev3 rot) => EEx.Resolve(nrot, rot, (_nr, _r) => {
var nr = new TExV2(_nr);
var r = new TExV3(_r);
return(VRV2(nr.x, nr.y, r.x, r.y, r.z));
});
