CoordinateSystem wrong matrix transformation for pitch angle==90 degrees

[ebortoluzzi]

when the pitch angle is == 90 degrees the cos(pitch)=0.0 and the the elements of the rotation matrix [0,0] and [1,0] shall be 0.0,
[0,0] = cos(pitch)*cos(yaw)
[1,0) = cos(pitch)*sin(yaw)

which is a special case see
Euler Angle Formulas
David Eberly, Geometric Tools, Redmond WA 98052
https://www.geometrictools.com/
2.6 Factor as RzRyRx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pag 9
case

however I tried your formula with bad results
pt1 = new double[3] { 3, 1, 2 };
.....
// Define your angles
Angle yaw = Angle.FromDegrees(30); // Around Z
Angle pitch = Angle.FromDegrees(90); // Around Y
Angle roll = Angle.FromDegrees(60); // Around X

  // Create the rotated coordinate system ZYX
  coordSys = new CoordinateSystem().RotateNoReset(yaw,pitch,roll);
  coordSys = coordSys.SetTranslation(new Vector3D(pt1[0], pt1[1], pt1[2]));

  var coordSys2 = new CoordinateSystem();
  coordSys2 = coordSys2.RotateCoordSysAroundVector(coordSys.ZAxis.Normalize(), yaw);
  coordSys2 = coordSys2.RotateCoordSysAroundVector(coordSys.YAxis.Normalize(), pitch);
  coordSys2 = coordSys2.RotateCoordSysAroundVector(coordSys.XAxis.Normalize(), roll);
  coordSys2 = coordSys2.SetTranslation(new Vector3D(pt1[0], pt1[1], pt1[2]));

both return a rotation matrix with [1,0]<>0.0
5.30288E-17 0 1
1 2.22045E-16 -5.30288E-17
-2.22045E-16 1 0

while the correct one shall be
5.30288E-17 0.5 0.866025
3.06162E-17 0.866025 -0.5
-1 5.30288E-17 3.06162E-17

[ebortoluzzi]

I found this work correctly

  var coordSys = new CoordinateSystem();
  coordSys.Multiply(CoordinateSystem.Yaw(yaw), coordSys);
  coordSys.Multiply(CoordinateSystem.Pitch(pitch), coordSys);
  coordSys.Multiply(CoordinateSystem.Roll(roll), coordSys);
  coordSys = coordSys.SetTranslation(new Vector3D(frmCoords[0],
                                     frmCoords[1], frmCoords[2]));