geometricpredicates.cpp

利用C

/*  Sets h = e + f.  See the long version of my paper for details.           */
/*                                                                           */
/*  If round-to-even is used (as with IEEE 754), maintains the strongly      */
/*  nonoverlapping property.  (That is, if e is strongly nonoverlapping, h   */
/*  will be also.)  Does NOT maintain the nonoverlapping or nonadjacent      */
/*  properties.                                                              */
/*                                                                           */
/*****************************************************************************/

static int fast_expansion_sum_zeroelim(int elen, REAL *e, 
				       int flen, REAL *f, REAL *h)
     /* h cannot be e or f. */
{
  REAL Q;
  INEXACT REAL Qnew;
  INEXACT REAL hh;
  INEXACT REAL bvirt;
  REAL avirt, bround, around;
  int eindex, findex, hindex;
  REAL enow, fnow;

  enow = e[0];
  fnow = f[0];
  eindex = findex = 0;
  if ((fnow > enow) == (fnow > -enow)) {
    Q = enow;
    enow = e[++eindex];
  } else {
    Q = fnow;
    fnow = f[++findex];
  }
  hindex = 0;
  if ((eindex < elen) && (findex < flen)) {
    if ((fnow > enow) == (fnow > -enow)) {
      Fast_Two_Sum(enow, Q, Qnew, hh);
      enow = e[++eindex];
    } else {
      Fast_Two_Sum(fnow, Q, Qnew, hh);
      fnow = f[++findex];
    }
    Q = Qnew;
    if (hh != 0.0) {
      h[hindex++] = hh;
    }
    while ((eindex < elen) && (findex < flen)) {
      if ((fnow > enow) == (fnow > -enow)) {
        Two_Sum(Q, enow, Qnew, hh);
        enow = e[++eindex];
      } else {
        Two_Sum(Q, fnow, Qnew, hh);
        fnow = f[++findex];
      }
      Q = Qnew;
      if (hh != 0.0) {
        h[hindex++] = hh;
      }
    }
  }
  while (eindex < elen) {
    Two_Sum(Q, enow, Qnew, hh);
    enow = e[++eindex];
    Q = Qnew;
    if (hh != 0.0) {
      h[hindex++] = hh;
    }
  }
  while (findex < flen) {
    Two_Sum(Q, fnow, Qnew, hh);
    fnow = f[++findex];
    Q = Qnew;
    if (hh != 0.0) {
      h[hindex++] = hh;
    }
  }
  if ((Q != 0.0) || (hindex == 0)) {
    h[hindex++] = Q;
  }
  return hindex;
}

/*****************************************************************************/
/*                                                                           */
/*  scale_expansion_zeroelim()   Multiply an expansion by a scalar,          */
/*                               eliminating zero components from the        */
/*                               output expansion.                           */
/*                                                                           */
/*  Sets h = be.  See either version of my paper for details.                */
/*                                                                           */
/*  Maintains the nonoverlapping property.  If round-to-even is used (as     */
/*  with IEEE 754), maintains the strongly nonoverlapping and nonadjacent    */
/*  properties as well.  (That is, if e has one of these properties, so      */
/*  will h.)                                                                 */
/*                                                                           */
/*****************************************************************************/

static int scale_expansion_zeroelim(int elen, REAL *e, REAL b, REAL *h)
     /* e and h cannot be the same. */
{
  INEXACT REAL Q, sum;
  REAL hh;
  INEXACT REAL product1;
  REAL product0;
  int eindex, hindex;
  REAL enow;
  INEXACT REAL bvirt;
  REAL avirt, bround, around;
  INEXACT REAL c;
  INEXACT REAL abig;
  REAL ahi, alo, bhi, blo;
  REAL err1, err2, err3;

  Split(b, bhi, blo);
  Two_Product_Presplit(e[0], b, bhi, blo, Q, hh);
  hindex = 0;
  if (hh != 0) {
    h[hindex++] = hh;
  }
  for (eindex = 1; eindex < elen; eindex++) {
    enow = e[eindex];
    Two_Product_Presplit(enow, b, bhi, blo, product1, product0);
    Two_Sum(Q, product0, sum, hh);
    if (hh != 0) {
      h[hindex++] = hh;
    }
    Fast_Two_Sum(product1, sum, Q, hh);
    if (hh != 0) {
      h[hindex++] = hh;
    }
  }
  if ((Q != 0.0) || (hindex == 0)) {
    h[hindex++] = Q;
  }
  return hindex;
}

/*****************************************************************************/
/*                                                                           */
/*  estimate()   Produce a one-word estimate of an expansion's value.        */
/*                                                                           */
/*  See either version of my paper for details.                              */
/*                                                                           */
/*****************************************************************************/

static REAL estimate(int elen, REAL *e)
{
  REAL Q;
  int eindex;

  Q = e[0];
  for (eindex = 1; eindex < elen; eindex++) {
    Q += e[eindex];
  }
  return Q;
}

/*****************************************************************************/
/*                                                                           */
/*  orient2dfast()   Approximate 2D orientation test.  Nonrobust.            */
/*  orient2dexact()   Exact 2D orientation test.  Robust.                    */
/*  orient2dslow()   Another exact 2D orientation test.  Robust.             */
/*  orient2d()   Adaptive exact 2D orientation test.  Robust.                */
/*                                                                           */
/*               Return a positive value if the points pa, pb, and pc occur  */
/*               in counterclockwise order; a negative value if they occur   */
/*               in clockwise order; and zero if they are collinear.  The    */
/*               result is also a rough approximation of twice the signed    */
/*               area of the triangle defined by the three points.           */
/*                                                                           */
/*  Only the first and last routine should be used; the middle two are for   */
/*  timings.                                                                 */
/*                                                                           */
/*  The last three use exact arithmetic to ensure a correct answer.  The     */
/*  result returned is the determinant of a matrix.  In orient2d() only,     */
/*  this determinant is computed adaptively, in the sense that exact         */
/*  arithmetic is used only to the degree it is needed to ensure that the    */
/*  returned value has the correct sign.  Hence, orient2d() is usually quite */
/*  fast, but will run more slowly when the input points are collinear or    */
/*  nearly so.                                                               */
/*                                                                           */
/*****************************************************************************/

static REAL orient2dadapt(REAL *pa, REAL *pb, REAL *pc, REAL detsum)
{
  INEXACT REAL acx, acy, bcx, bcy;
  REAL acxtail, acytail, bcxtail, bcytail;
  INEXACT REAL detleft, detright;
  REAL detlefttail, detrighttail;
  REAL det, errbound;
  REAL B[4], C1[8], C2[12], D[16];
  INEXACT REAL B3;
  int C1length, C2length, Dlength;
  REAL u[4];
  INEXACT REAL u3;
  INEXACT REAL s1, t1;
  REAL s0, t0;

  INEXACT REAL bvirt;
  REAL avirt, bround, around;
  INEXACT REAL c;
  INEXACT REAL abig;
  REAL ahi, alo, bhi, blo;
  REAL err1, err2, err3;
  INEXACT REAL _i, _j;
  REAL _0;

  acx = (REAL) (pa[0] - pc[0]);
  bcx = (REAL) (pb[0] - pc[0]);
  acy = (REAL) (pa[1] - pc[1]);
  bcy = (REAL) (pb[1] - pc[1]);

  Two_Product(acx, bcy, detleft, detlefttail);
  Two_Product(acy, bcx, detright, detrighttail);

  Two_Two_Diff(detleft, detlefttail, detright, detrighttail,
               B3, B[2], B[1], B[0]);
  B[3] = B3;

  det = estimate(4, B);
  errbound = ccwerrboundB * detsum;
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  Two_Diff_Tail(pa[0], pc[0], acx, acxtail);
  Two_Diff_Tail(pb[0], pc[0], bcx, bcxtail);
  Two_Diff_Tail(pa[1], pc[1], acy, acytail);
  Two_Diff_Tail(pb[1], pc[1], bcy, bcytail);

  if ((acxtail == 0.0) && (acytail == 0.0)
      && (bcxtail == 0.0) && (bcytail == 0.0)) {
    return det;
  }

  errbound = ccwerrboundC * detsum + resulterrbound * Absolute(det);
  det += (acx * bcytail + bcy * acxtail)
       - (acy * bcxtail + bcx * acytail);
  if ((det >= errbound) || (-det >= errbound)) {
    return det;
  }

  Two_Product(acxtail, bcy, s1, s0);
  Two_Product(acytail, bcx, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  C1length = fast_expansion_sum_zeroelim(4, B, 4, u, C1);

  Two_Product(acx, bcytail, s1, s0);
  Two_Product(acy, bcxtail, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  C2length = fast_expansion_sum_zeroelim(C1length, C1, 4, u, C2);

  Two_Product(acxtail, bcytail, s1, s0);
  Two_Product(acytail, bcxtail, t1, t0);
  Two_Two_Diff(s1, s0, t1, t0, u3, u[2], u[1], u[0]);
  u[3] = u3;
  Dlength = fast_expansion_sum_zeroelim(C2length, C2, 4, u, D);

  return(D[Dlength - 1]);
}

REAL orient2d(REAL *pa, REAL *pb, REAL *pc)
{
  REAL detleft, detright, det;
  REAL detsum, errbound;
  REAL orient;

  FPU_ROUND_DOUBLE;

  detleft = (pa[0] - pc[0]) * (pb[1] - pc[1]);
  detright = (pa[1] - pc[1]) * (pb[0] - pc[0]);
  det = detleft - detright;

  if (detleft > 0.0) {
    if (detright <= 0.0) {
      FPU_RESTORE;
      return det;
    } else {
      detsum = detleft + detright;
    }
  } else if (detleft < 0.0) {
    if (detright >= 0.0) {
      FPU_RESTORE;
      return det;
    } else {
      detsum = -detleft - detright;
    }
  } else {
    FPU_RESTORE;
    return det;
  }

  errbound = ccwerrboundA * detsum;
  if ((det >= errbound) || (-det >= errbound)) {
    FPU_RESTORE;
    return det;
  }

  orient = orient2dadapt(pa, pb, pc, detsum);
  FPU_RESTORE;
  return orient;
}

/*****************************************************************************/
/*                                                                           */
/*  orient3dfast()   Approximate 3D orientation test.  Nonrobust.            */
/*  orient3dexact()   Exact 3D orientation test.  Robust.                    */
/*  orient3dslow()   Another exact 3D orientation test.  Robust.             */
/*  orient3d()   Adaptive exact 3D orientation test.  Robust.                */
/*                                                                           */
/*               Return a positive value if the point pd lies below the      */
/*               plane passing through pa, pb, and pc; "below" is defined so */
/*               that pa, pb, and pc appear in counterclockwise order when   */
/*               viewed from above the plane.  Returns a negative value if   */
/*               pd lies above the plane.  Returns zero if the points are    */
/*               coplanar.  The result is also a rough approximation of six  */
/*               times the signed volume of the tetrahedron defined by the   */
/*               four points.                                                */
/*                                                                           */
/*  Only the first and last routine should be used; the middle two are for   */
/*  timings.                                                                 */
/*                                                                           */
/*  The last three use exact arithmetic to ensure a correct answer.  The     */
/*  result returned is the determinant of a matrix.  In orient3d() only,     */
/*  this determinant is computed adaptively, in the sense that exact         */
/*  arithmetic is used only to the degree it is needed to ensure that the    */
/*  returned value has the correct sign.  Hence, orient3d() is usually quite */
/*  fast, but will run more slowly when the input points are coplanar or     */
/*  nearly so.                                                               */
/*                                                                           */
/*****************************************************************************/

static REAL orient3dadapt(REAL *pa, REAL *pb, REAL *pc, REAL *pd, 
			  REAL permanent)