FUNCTION convert_spatial_to_ypr_rotation

(* SCHEMA kinematic_structure_schema; *)

FUNCTION convert_spatial_to_ypr_rotation (pair     : kinematic_pair;
                                          rotation : spatial_rotation)
                                                   : ypr_rotation;
  LOCAL
    axis       : direction;
    angle      : plane_angle_measure;   -- rotation angle in application
                                        -- specific units
    conv_angle : plane_angle_measure;   -- rotation angle in radians
    ya, pa, ra : plane_angle_measure;   -- yaw, pitch, and roll angle
    ucf        : REAL;                  -- unit conversion factor
    dx, dy, dz : REAL;                  -- components of direction vector
    s_a, c_a   : REAL;                  -- sine and cosine of rotation angle
    rotmat     : ARRAY [1 : 3] OF
                 ARRAY [1 : 3] OF REAL; -- rotation matrix
    cm1        : REAL;
    s_y, c_y   : REAL;
    s_r, c_r   : REAL;
  END_LOCAL;

  -- If rotation is already a ypr_rotation, return it immediately
  IF 'KINEMATIC_STRUCTURE_SCHEMA.YPR_ROTATION' IN TYPEOF (rotation) THEN
    RETURN (rotation);
  END_IF;

  -- rotation is a rotation_about_direction

  axis  := normalise (rotation\rotation_about_direction.direction_of_axis);
  angle := rotation\rotation_about_direction.rotation_angle;

  -- a zero rotation is converted trivially
  IF (angle = 0.0) THEN
    RETURN ([0.0, 0.0, 0.0]);
  END_IF;

  dx := axis.direction_ratios[1];
  dy := axis.direction_ratios[2];
  dz := axis.direction_ratios[3];

  -- provide angle measured in radian

  conv_angle := plane_angle_for_pair_in_radian (pair, angle);

  IF (conv_angle = ?) THEN
    RETURN (?);
  END_IF;

  ucf := angle / conv_angle;
  s_a := SIN (conv_angle);
  c_a := COS (conv_angle);

  -- axis parallel either to x-axis or to z-axis?
  IF (dy = 0.0) AND (dx * dz = 0.0) THEN
    REPEAT WHILE (conv_angle <= - PI);
      conv_angle := conv_angle + 2.0 * PI;
    END_REPEAT;
    REPEAT WHILE (conv_angle > PI);
      conv_angle := conv_angle - 2.0 * PI;
    END_REPEAT;

    ya := ucf * conv_angle;
    IF (conv_angle <> PI) THEN
      ra := - ya;
    ELSE
      ra := ya;
    END_IF;

    IF (dx <> 0.0) THEN
      -- axis parallel to x-axis - use x-axis as roll axis
      IF (dx > 0.0) THEN
        RETURN ([0.0, 0.0, ya]);
      ELSE
        RETURN ([0.0, 0.0, ra]);
      END_IF;
    ELSE
      -- axis parallel to z-axis - use z-axis as yaw axis
      IF (dz > 0.0) THEN
        RETURN ([ya, 0.0, 0.0]);
      ELSE
        RETURN ([ra, 0.0, 0.0]);
      END_IF;
    END_IF;
  END_IF;

  -- axis parallel to y-axis - use y-axis as pitch axis
  IF ((dy <> 0.0) AND (dx = 0.0) AND (dz = 0.0)) THEN
    IF (c_a >= 0.0) THEN
      ya := 0.0;
      ra := 0.0;
    ELSE
      ya := ucf * PI;
      ra := ya;
    END_IF;

    pa := ucf * ATAN (s_a, ABS (c_a));
    IF (dy < 0.0) THEN
      pa := - pa;
    END_IF;

    RETURN ([ya, pa, ra]);
  END_IF;

  -- axis not parallel to any axis of coordinate system
  -- compute rotation matrix

  cm1 := 1.0 - c_a;

  rotmat := [ [ dx * dx * cm1 + c_a,
                dx * dy * cm1 - dz * s_a,
                dx * dz * cm1 + dy * s_a ],
              [ dx * dy * cm1 + dz * s_a,
                dy * dy * cm1 + c_a,
                dy * dz * cm1 - dx * s_a ],
              [ dx * dz * cm1 - dy * s_a,
                dy * dz * cm1 + dx * s_a,
                dz * dz * cm1 + c_a ] ];

  -- rotmat[1][3] equals SIN (pitch_angle)
  IF (ABS (rotmat[1][3]) = 1.0) THEN
    -- |pa| = PI/2
    BEGIN
      IF (rotmat[1][3] = 1.0) THEN
        pa := 0.5 * PI;
      ELSE
        pa := -0.5 * PI;
      END_IF;

      -- In this case, only the sum or difference of roll and yaw angles
      -- is relevant and can be evaluated from the matrix.
      -- According to IP `rectangular pitch angle' for ypr_rotation,
      -- the roll angle is set to zero.

      ra := 0.0;
      ya := ATAN (rotmat[2][1], rotmat[2][2]);

      -- result of ATAN is in the range [-PI/2, PI/2].
      -- Here all four quadrants are needed.

      IF (rotmat[2][2] < 0.0) THEN
        IF ya <= 0.0 THEN
          ya := ya + PI;
        ELSE
          ya := ya - PI;
        END_IF;
      END_IF;
    END;
  ELSE
    -- COS (pitch_angle) not equal to zero
    BEGIN
      ya := ATAN (- rotmat[1][2], rotmat[1][1]);

      IF (rotmat[1][1] < 0.0) THEN
        IF (ya <= 0.0) THEN
          ya := ya + PI;
        ELSE
          ya := ya - PI;
        END_IF;
      END_IF;

      ra := ATAN (-rotmat[2][3], rotmat[3][3]);

      IF (rotmat[3][3] < 0.0) THEN
        IF (ra <= 0.0) THEN
          ra := ra + PI;
        ELSE
          ra := ra - PI;
        END_IF;
      END_IF;

      s_y := SIN (ya);
      c_y := COS (ya);
      s_r := SIN (ra);
      c_r := COS (ra);

      IF ((ABS (s_y) > ABS (c_y)) AND
          (ABS (s_y) > ABS (s_r)) AND
          (ABS (s_y) > ABS (c_r))) THEN
        cm1 := - rotmat[1][2] / s_y;
      ELSE
        IF ((ABS (c_y) > ABS (s_r)) AND (ABS (c_y) > ABS (c_r))) THEN
          cm1 := rotmat[1][1] / c_y;
        ELSE
          IF (ABS (s_r) > ABS (c_r)) THEN
            cm1 := - rotmat[2][3] / s_r;
          ELSE
            cm1 := rotmat[3][3] / c_r;
          END_IF;
        END_IF;
      END_IF;

      pa := ATAN (rotmat[1][3], cm1);

    END;
  END_IF;

  ya := ya * ucf;
  pa := pa * ucf;
  ra := ra * ucf;

  RETURN ([ya, pa, ra]);

END_FUNCTION;

Referenced By

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2012-03-27T17:14:00-04:00