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circutil.c

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/*
  circutil.c

  Generalized circle utilities

  Modification history:

  18-Jun-1997  FMP created
  */

#include <math.h>               /* acos() */
#include "posemath.h"           /* these decls, PM_CARTESIAN */

/*
  pmCircleInit() takes the defining parameters of a generalized circle
  and sticks them in the structure. It also computes the radius and vectors
  in the plane that are useful for other functions and that don't need
  to be recomputed every time.
  */
int pmCircleInit(PM_CIRCLE * circle,
                 PM_CARTESIAN start, PM_CARTESIAN end,
                 PM_CARTESIAN center, PM_CARTESIAN normal,
                 int turn)
{
  double dot;
  PM_CARTESIAN rEnd;

  if (0 == circle)
    {
      return -1;
    }

  /* load and normalize required descriptions */
  circle->start = start;
  circle->end = end;
  circle->center = center;
  pmCartNorm(normal, &circle->normal);
  circle->turn = turn;          /* 0 = 0..360, 1 = 360..720,
                                   -1 = 0..-360, -2 = -360..-720, etc. */

  /* radius */
  pmCartCartDisp(start, center, &circle->radius);

  /* vector in plane of circle from center to start, magnitude radius */
  pmCartCartSub(start, center, &circle->rTan);

  /* vector in plane of circle perpendicular to uTan, magnitude radius */
  pmCartCartCross(circle->normal, circle->rTan, &circle->rPerp);

  /* do rHelix, rEnd */
  pmCartCartSub(end, center, &circle->rHelix);
  pmCartPlaneProj(circle->rHelix, circle->normal, &rEnd);
  pmCartMag(rEnd, &circle->spiral);
  circle->spiral -= circle->radius;
  pmCartCartSub(circle->rHelix, rEnd, &circle->rHelix);
  pmCartNorm(rEnd, &rEnd);
  pmCartScalMult(rEnd, circle->radius, &rEnd);

  /* angle */
  pmCartCartDot(start, rEnd, &dot);
  dot = dot / (circle->radius * circle->radius);
  circle->angle = acos(dot);
  if (turn > 0)
    {
      circle->angle += turn * 2.0 * PM_PI;
    }
  else if (turn < 0)
    {
      circle->angle = - circle->angle - (turn + 1) * 2.0 * PM_PI;
    }

  return pmErrno = 0;
}

/*
  pmCirclePoint() returns the vector to the point at the given angle along
  the circle. If the circle is a helix or spiral or combination, the
  point will include interpolation off the actual circle.
  */
int pmCirclePoint(PM_CIRCLE * circle, double angle, PM_CARTESIAN * point)
{
  PM_CARTESIAN par, perp;
  double scale;

  /* compute components rel to center */
  pmCartScalMult(circle->rTan, cos(angle), &par);
  pmCartScalMult(circle->rPerp, sin(angle), &perp);

  /* add to get radius vector rel to center */
  pmCartCartAdd(par, perp, point);

  /* get scale for spiral, helix interpolation */
  scale = angle / circle->angle;

  /* add scaled vector in radial dir for spiral */
  pmCartNorm(*point, &par);
  pmCartScalMult(par, scale * circle->spiral, &par);
  pmCartCartAdd(*point, par, point);

  /* add scaled vector in helix dir */
  pmCartScalMult(circle->rHelix, scale, &perp);
  pmCartCartAdd(*point, perp, point);

  return pmErrno = 0;
}

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