/********************************************************************

* Description: interp_arc.cc

*

*   Derived from a work by Thomas Kramer

*

* Author:

* License: GPL Version 2

* System: Linux

*

* Copyright (c) 2004 All rights reserved.

*

* Last change:

********************************************************************/

#ifndef _GNU_SOURCE

#define _GNU_SOURCE

#endif

#include <unistd.h>

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#include <string.h>

#include <ctype.h>

#include <sys/types.h>

#include <sys/stat.h>

#include <libintl.h>

#include <rtapi_math.h>

#include "rs274ngc.hh"

#include "rs274ngc_return.hh"

#include "rs274ngc_interp.hh"

#include "interp_internal.hh"

#define _(s) gettext(s)

    case CANON_PLANE_XY: return 'X';

    case CANON_PLANE_XZ: return 'Z';

    case CANON_PLANE_YZ: return 'Y';

    default: return '!';

    }

}

    case CANON_PLANE_XY: return 'Y';

    case CANON_PLANE_XZ: return 'X';

    case CANON_PLANE_YZ: return 'Z';

    default: return '!';

    }

}

/***********************************************************************/

/*! arc_data_comp_ijk

Returned Value: int

   If any of the following errors occur, this returns the error code shown.

   Otherwise, it returns INTERP_OK.

   1. The two calculable values of the radius differ by more than

      tolerance: NCE_RADIUS_TO_END_OF_ARC_DIFFERS_FROM_RADIUS_TO_START

   2. move is not G_2 or G_3: NCE_BUG_CODE_NOT_G2_OR_G3

Side effects:

   This finds and sets the values of center_x, center_y, and turn.

Called by: convert_arc_comp1

This finds the center coordinates and number of full or partial turns

counterclockwise of a helical or circular arc in ijk-format in the XY

plane. The center is computed easily from the current point and center

offsets, which are given. It is checked that the end point lies one

tool radius from the arc.

*/

                              int plane, //!<active plane

                             int side,  //!<either RIGHT or LEFT

                             double tool_radius,        //!<radius of the tool

                             double current_x,  //!<first coordinate of current point

                             double current_y,  //!<second coordinate of current point

                             double end_x,      //!<first coordinate of arc end point

                             double end_y,      //!<second coordinate of arc end point

                             int ij_absolute,   //!<how to interpret i/j numbers

                             double i_number,   //!<first coordinate of center (abs or incr)

                             double j_number,   //!<second coordinate of center (abs or incr)

                             int p_number,

                             double *center_x,  //!<pointer to first coordinate of center of arc

                             double *center_y,  //!<pointer to second coordinate of center of arc

                             int *turn, //!<pointer to number of full or partial circles CCW

                             double radius_tolerance, //!<minimum radius tolerance

                             double spiral_abs_tolerance,  //!<tolerance of start and end radius difference

                             double spiral_rel_tolerance)

{

  double arc_radius;

  double radius2;

  } else {

  }

          _("Zero-radius arc: "

       "start=(%c%.4f,%c%.4f) center=(%c%.4f,%c%.4f) end=(%c%.4f,%c%.4f) r1=%.4f r2=%.4f"),

       a, current_x, b, current_y,

       a, *center_x, b, *center_y,

       a, end_x, b, end_y, arc_radius, radius2);

          (rel_err > spiral_rel_tolerance && abs_err > spiral_abs_tolerance),

      _("Radius to end of arc differs from radius to start: "

       "start=(%c%.4f,%c%.4f) center=(%c%.4f,%c%.4f) end=(%c%.4f,%c%.4f) "

       "r1=%.4f r2=%.4f abs_err=%.4g rel_err=%.4f%%"),

       a, current_x, b, current_y,

       a, *center_x, b, *center_y,

       a, end_x, b, end_y, arc_radius, radius2,

       abs_err, rel_err*100);

                                       ((side == RIGHT) && (move == G_2)))),

      NCE_TOOL_RADIUS_NOT_LESS_THAN_ARC_RADIUS_WITH_COMP);

  /* This catches an arc too small for the tool, also */

  else

  return INTERP_OK;

}

/****************************************************************************/

/*! arc_data_comp_r

Returned Value: int

   If any of the following errors occur, this returns the error code shown.

   Otherwise, it returns INTERP_OK.

   1. The arc radius is too small to reach the end point:

      NCE_RADIUS_TOO_SMALL_TO_REACH_END_POINT

   2. The arc radius is not greater than the tool_radius, but should be:

      NCE_TOOL_RADIUS_NOT_LESS_THAN_ARC_RADIUS_WITH_COMP

   3. An imaginary value for offset would be found, which should never

      happen if the theory is correct: NCE_BUG_IN_TOOL_RADIUS_COMP

Side effects:

   This finds and sets the values of center_x, center_y, and turn.

Called by: convert_arc_comp1

This finds the center coordinates and number of full or partial turns

counterclockwise of a helical or circular arc (call it arc1) in

r-format in the XY plane.  Arc2 is constructed so that it is tangent

to a circle whose radius is tool_radius and whose center is at the

point (current_x, current_y) and passes through the point (end_x,

end_y). Arc1 has the same center as arc2. The radius of arc1 is one

tool radius larger or smaller than the radius of arc2.

If the value of the big_radius argument is negative, that means [NCMS,

page 21] that an arc larger than a semicircle is to be made.

Otherwise, an arc of a semicircle or less is made.

The algorithm implemented here is to construct a line L from the

current point to the end point, and a perpendicular to it from the

center of the arc which intersects L at point P. Since the distance

from the end point to the center and the distance from the current

point to the center are known, two equations for the length of the

perpendicular can be written. The right sides of the equations can be

set equal to one another and the resulting equation solved for the

length of the line from the current point to P. Then the location of

P, the length of the perpendicular, the angle of the perpendicular,

and the location of the center, can be found in turn.

This needs to be better documented, with figures. There are eight

possible arcs, since there are three binary possibilities: (1) tool

inside or outside arc, (2) clockwise or counterclockwise (3) two

positions for each arc (of the given radius) tangent to the tool

outline and through the end point. All eight are calculated below,

since theta, radius2, and turn may each have two values.

To see two positions for each arc, imagine the arc is a hoop, the

tool is a cylindrical pin, and the arc may rotate around the end point.

The rotation covers all possible positions of the arc. It is easy to

see the hoop is constrained by the pin at two different angles, whether

the pin is inside or outside the hoop.

*/

                            int plane,

                           int side,    //!< either RIGHT or LEFT

                           double tool_radius,  //!< radius of the tool

                           double current_x,    //!< first coordinate of current point

                           double current_y,    //!< second coordinate of current point

                           double end_x,        //!< first coordinate of arc end point

                           double end_y,        //!< second coordinate of arc end point

                           double big_radius,   //!< radius of arc

                           int p_number,

                           double *center_x,    //!< pointer to first coordinate of center of arc

                           double *center_y,    //!< pointer to second coordinate of center of arc

                           int *turn,           //!< pointer to number of full or partial circles CCW

                           double tolerance)    //!< tolerance of differing radii

{

  double abs_radius;            // absolute value of big_radius

                                       ((side == RIGHT) && (move == G_2)))),

      NCE_TOOL_RADIUS_NOT_LESS_THAN_ARC_RADIUS_WITH_COMP);

  return arc_data_r(move, plane, current_x, current_y, end_x, end_y, big_radius, p_number,

}

/****************************************************************************/

/*! arc_data_ijk

Returned Value: int

   If any of the following errors occur, this returns the error code shown.

   Otherwise, it returns INTERP_OK.

   1. The two calculable values of the radius differ by more than

      tolerance: NCE_RADIUS_TO_END_OF_ARC_DIFFERS_FROM_RADIUS_TO_START

   2. The move code is not G_2 or G_3: NCE_BUG_CODE_NOT_G2_OR_G3

   3. Either of the two calculable values of the radius is zero:

      NCE_ZERO_RADIUS_ARC

Side effects:

   This finds and sets the values of center_x, center_y, and turn.

Called by:

   convert_arc2

   convert_arc_comp2

This finds the center coordinates and number of full or partial turns

counterclockwise of a helical or circular arc in ijk-format. This

function is used by convert_arc2 for all three planes, so "x" and

"y" really mean "first_coordinate" and "second_coordinate" wherever

they are used here as suffixes of variable names. The i and j prefixes

are handled similarly.

*/

                         int plane,

                        double current_x,       //!< first coordinate of current point

                        double current_y,       //!< second coordinate of current point

                        double end_x,   //!< first coordinate of arc end point

                        double end_y,   //!< second coordinate of arc end point

                        int ij_absolute,        //!<how to interpret i/j numbers

                        double i_number,        //!<first coordinate of center (abs or incr)

                        double j_number,        //!<second coordinate of center (abs or incr)

                        int p_number,

                        double *center_x,       //!< pointer to first coordinate of center of arc

                        double *center_y,       //!< pointer to second coordinate of center of arc

                        int *turn,      //!< pointer to no. of full or partial circles CCW

                        double radius_tolerance, //!<minimum radius tolerance

                        double spiral_abs_tolerance,  //!<tolerance of start and end radius difference

                        double spiral_rel_tolerance)

{

  double radius;                /* radius to current point */

  double radius2;               /* radius to end point     */

  } else {

  }

       "start=(%c%.4f,%c%.4f) center=(%c%.4f,%c%.4f) end=(%c%.4f,%c%.4f) r1=%.4f r2=%.4f"),

       a, current_x, b, current_y,

       a, *center_x, b, *center_y,

       a, end_x, b, end_y, radius, radius2);

          (rel_err > spiral_rel_tolerance && abs_err > spiral_abs_tolerance),

      _("Radius to end of arc differs from radius to start: "

       "start=(%c%.4f,%c%.4f) center=(%c%.4f,%c%.4f) end=(%c%.4f,%c%.4f) "

       "r1=%.4f r2=%.4f abs_err=%.4g rel_err=%.4f%%"),

       a, current_x, b, current_y,

       a, *center_x, b, *center_y,

       a, end_x, b, end_y, radius, radius2,

       abs_err, rel_err*100);

  else

  return INTERP_OK;

}

/****************************************************************************/

/*! arc_data_r

Returned Value: int

   If any of the following errors occur, this returns the error shown.

   Otherwise, it returns INTERP_OK.

   1. The radius is too small to reach the end point:

      NCE_ARC_RADIUS_TOO_SMALL_TO_REACH_END_POINT

   2. The current point is the same as the end point of the arc

      (so that it is not possible to locate the center of the circle):

      NCE_CURRENT_POINT_SAME_AS_END_POINT_OF_ARC

Side effects:

   This finds and sets the values of center_x, center_y, and turn.

Called by:

   convert_arc2

   convert_arc_comp2

This finds the center coordinates and number of full or partial turns

counterclockwise of a helical or circular arc in the r format. This

function is used by convert_arc2 for all three planes, so "x" and

"y" really mean "first_coordinate" and "second_coordinate" wherever

they are used here as suffixes of variable names.

If the value of the radius argument is negative, that means [NCMS,

page 21] that an arc larger than a semicircle is to be made.

Otherwise, an arc of a semicircle or less is made.

The algorithm used here is based on finding the midpoint M of the line

L between the current point and the end point of the arc. The center

of the arc lies on a line through M perpendicular to L.

*/

                       int plane,

                      double current_x, //!< first coordinate of current point

                      double current_y, //!< second coordinate of current point

                      double end_x,     //!< first coordinate of arc end point

                      double end_y,     //!< second coordinate of arc end point

                      double radius,    //!< radius of arc

                      int p_number,

                      double *center_x, //!< pointer to first coordinate of center of arc

                      double *center_y, //!< pointer to second coordinate of center of arc

                      int *turn,        //!< pointer to number of full or partial circles CCW

                      double tolerance) //!< tolerance of differing radii

{

  double abs_radius;            /* absolute value of given radius */

  double half_length;           /* distance from M to end point   */

  double mid_x;                 /* first coordinate of M          */

  double mid_y;                 /* second coordinate of M         */

  double offset;                /* distance from M to center      */

  double theta;                 /* angle of line from M to center */

  double turn2;                 /* absolute value of half of turn */

      NCE_CURRENT_POINT_SAME_AS_END_POINT_OF_ARC);

      NCE_ARC_RADIUS_TOO_SMALL_TO_REACH_END_POINT);

  /* check needed before calling asin   */

  else

}