parametricCurve.cxx

// Filename: parametricCurve.cxx
// Created by:  drose (04Mar01)
//
////////////////////////////////////////////////////////////////////
//
// PANDA 3D SOFTWARE
// Copyright (c) Carnegie Mellon University.  All rights reserved.
//
// All use of this software is subject to the terms of the revised BSD
// license.  You should have received a copy of this license along
// with this source code in a file named "LICENSE."
//
////////////////////////////////////////////////////////////////////

#include "parametricCurve.h"
#include "config_parametrics.h"
#include "hermiteCurve.h"
#include "nurbsCurve.h"

#include "datagram.h"
#include "datagramIterator.h"
#include "bamWriter.h"
#include "bamReader.h"
#include "omniBoundingVolume.h"

static const PN_stdfloat tolerance_divisor = 100000.0f;

TypeHandle ParametricCurve::_type_handle;


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::Constructor
//       Access: Public
//  Description: This is a virtual base class.  Don't try to construct
//               one from Scheme.
////////////////////////////////////////////////////////////////////
ParametricCurve::
ParametricCurve() : PandaNode("curve") {
  _curve_type = PCT_NONE;
  _num_dimensions = 3;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::Destructor
//       Access: Protected
//  Description:
////////////////////////////////////////////////////////////////////
ParametricCurve::
~ParametricCurve() {
  // Our drawer list must be empty by the time we destruct, since our
  // drawers all maintain reference-counting pointers to us!  If this
  // is not so, we have lost a reference count somewhere, or we have
  // gotten confused about which drawers we're registered to.
  nassertv(_drawers.empty());
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::safe_to_flatten
//       Access: Public, Virtual
//  Description: Returns true if it is generally safe to flatten out
//               this particular kind of PandaNode by duplicating
//               instances, false otherwise (for instance, a Camera
//               cannot be safely flattened, because the Camera
//               pointer itself is meaningful).
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
safe_to_flatten() const {
  return false;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::safe_to_transform
//       Access: Public, Virtual
//  Description: Returns true if it is generally safe to transform
//               this particular kind of PandaNode by calling the
//               xform() method, false otherwise.  For instance, it's
//               usually a bad idea to attempt to xform a Character.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
safe_to_transform() const {
  return false;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::is_valid
//       Access: Published, Virtual
//  Description: Returns true if the curve is defined.  This base
//               class function always returns true; derived classes
//               might override this to sometimes return false.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
is_valid() const {
  return true;
}


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::get_max_t
//       Access: Published, Virtual
//  Description: Returns the upper bound of t for the entire curve.
//               The curve is defined in the range 0.0f <= t <=
//               get_max_t().  This base class function always returns
//               1.0f; derived classes might override this to return
//               something else.
////////////////////////////////////////////////////////////////////
PN_stdfloat ParametricCurve::
get_max_t() const {
  return 1.0f;
}


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::set_curve_type
//       Access: Published
//  Description: Sets the flag indicating the use to which the curve
//               is intended to be put.  This flag is optional and
//               only serves to provide a hint to the egg reader and
//               writer code; it has no effect on the curve's
//               behavior.
//
//               Setting the curve type also sets the num_dimensions
//               to 3 or 1 according to the type.
//
//               THis flag may have one of the values PCT_XYZ,
//               PCT_HPR, or PCT_T.
////////////////////////////////////////////////////////////////////
void ParametricCurve::
set_curve_type(int type) {
  _curve_type = type;
  switch (_curve_type) {
  case PCT_XYZ:
  case PCT_HPR:
  case PCT_NONE:
    _num_dimensions = 3;
    break;

  case PCT_T:
    _num_dimensions = 1;
    break;

  default:
    assert(0);
  }
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::get_curve_type
//       Access: Published
//  Description: Returns the flag indicating the use to which the curve
//               is intended to be put.
////////////////////////////////////////////////////////////////////
int ParametricCurve::
get_curve_type() const {
  return _curve_type;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::set_num_dimensions
//       Access: Published
//  Description: Specifies the number of significant dimensions in the
//               curve's vertices.  This should be one of 1, 2, or 3.
//               Normally, XYZ and HPR curves have three dimensions;
//               time curves should always have one dimension.  This
//               only serves as a hint to the mopath editor, and also
//               controls how the curve is written out.
////////////////////////////////////////////////////////////////////
void ParametricCurve::
set_num_dimensions(int num) {
  _num_dimensions = num;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::get_num_dimensions
//       Access: Published
//  Description: Returns the number of significant dimensions in the
//               curve's vertices, as set by a previous call to
//               set_num_dimensions().  This is only a hint as to how
//               the curve is intended to be used; the actual number
//               of dimensions of any curve is always three.
////////////////////////////////////////////////////////////////////
int ParametricCurve::
get_num_dimensions() const {
  return _num_dimensions;
}


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::calc_length
//       Access: Published
//  Description: Approximates the length of the entire curve to within
//               a few decimal places.
////////////////////////////////////////////////////////////////////
PN_stdfloat ParametricCurve::
calc_length() const {
  return calc_length(0.0f, get_max_t());
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::calc_length
//       Access: Published
//  Description: Approximates the length of the curve segment from
//               parametric time 'from' to time 'to'.
////////////////////////////////////////////////////////////////////
PN_stdfloat ParametricCurve::
calc_length(PN_stdfloat from, PN_stdfloat to) const {
  PN_stdfloat t1, t2;
  LPoint3 p1, p2;

  // Normally we expect from < to.  If they came in backwards, reverse
  // them.
  PN_stdfloat to_minus_from = to - from;

  if (to_minus_from < 0.0f) {
    PN_stdfloat temp = to;
    to = from;
    from = temp;
    to_minus_from=-to_minus_from;
  }

  // Start with a segment for each unit of t.
  int num_segs = (int)(to_minus_from) + 1;
  t2 = from;
  get_point(t2, p2);
  PN_stdfloat net = 0.0f;

  for (int i = 1; i <= num_segs; i++) {
    t1 = t2;
    p1 = p2;

    t2 = (to - from) * (PN_stdfloat)i / (PN_stdfloat)num_segs + from;
    get_point(t2, p2);

    net += r_calc_length(t1, t2, p1, p2, (p1 - p2).length());
  }
  return net;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::find_length
//       Access: Published
//  Description: Returns the parametric value corresponding to the
//               indicated distance along the curve from the starting
//               parametric value.
//
//               This is the inverse of calc_length(): rather than
//               determining the length along the curve between two
//               parametric points, it determines the position in
//               parametric time of a point n units along the curve.
//
//               The search distance must not be negative.
////////////////////////////////////////////////////////////////////
PN_stdfloat ParametricCurve::
find_length(PN_stdfloat start_t, PN_stdfloat length_offset) const {
  nassertr(length_offset >= 0.0f, start_t);
  nassertr(start_t >= 0.0f && start_t <= get_max_t(), start_t);

  PN_stdfloat t1, t2;
  LPoint3 p1, p2;

  // Start with a segment for each unit of t.
  PN_stdfloat max_t = get_max_t();
  int num_segs = (int)cfloor(max_t - start_t + 1);
  t2 = start_t;
  get_point(t2, p2);
  PN_stdfloat net = 0.0f;

  for (int i = 1; i <= num_segs; i++) {
    assert(net <= length_offset);

    t1 = t2;
    p1 = p2;

    t2 = start_t + (((max_t - start_t) * (PN_stdfloat)i) / (PN_stdfloat)num_segs);
    get_point(t2, p2);

    PN_stdfloat seglength = (p1 - p2).length();
    PN_stdfloat result;

    if (r_find_length(length_offset - net, result,
                      t1, t2, p1, p2, seglength)) {
      // Found it!
      return result;
    }

    net += seglength;
  }

  // Not on the curve?  Huh.
  return max_t;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::adjust_point
//       Access: Published, Virtual
//  Description: Recomputes the curve such that it passes through the
//               point (px, py, pz) at time t, but keeps the same
//               tangent value at that point.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
adjust_point(PN_stdfloat, PN_stdfloat, PN_stdfloat, PN_stdfloat) {
  return false;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::adjust_tangent
//       Access: Published, Virtual
//  Description: Recomputes the curve such that it has the tangent
//               (tx, ty, tz) at time t, but keeps the same position
//               at the point.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
adjust_tangent(PN_stdfloat, PN_stdfloat, PN_stdfloat, PN_stdfloat) {
  return false;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::adjust_pt
//       Access: Published, Virtual
//  Description: Recomputes the curve such that it passes through the
//               point (px, py, pz) with the tangent (tx, ty, tz).
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
adjust_pt(PN_stdfloat, PN_stdfloat, PN_stdfloat, PN_stdfloat, PN_stdfloat, PN_stdfloat, PN_stdfloat) {
  return false;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::recompute
//       Access: Published, Virtual
//  Description: Recalculates the curve, if necessary.  Returns
//               true if the resulting curve is valid, false
//               otherwise.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
recompute() {
  return is_valid();
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::stitch
//       Access: Published, Virtual
//  Description: Regenerates this curve as one long curve: the first
//               curve connected end-to-end with the second one.
//               Either a or b may be the same as 'this'.
//
//               Returns true if successful, false on failure or if
//               the curve type does not support stitching.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
stitch(const ParametricCurve *, const ParametricCurve *) {
  parametrics_cat.error()
    << get_type() << " does not support stitching.\n";
  return false;
}


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::write_egg
//       Access: Published
//  Description: Writes an egg description of the nurbs curve to the
//               specified output file.  Returns true if the file is
//               successfully written.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
write_egg(Filename filename, CoordinateSystem cs) {
  pofstream out;
  filename.set_text();

  if (!filename.open_write(out)) {
    parametrics_cat.error()
      << "Unable to write to " << filename << "\n";
    return false;
  }
  return write_egg(out, filename, cs);
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::write_egg
//       Access: Published
//  Description: Writes an egg description of the nurbs curve to the
//               specified output stream.  Returns true if the file is
//               successfully written.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
write_egg(ostream &out, const Filename &filename, CoordinateSystem cs) {
  string curve_type;
  switch (get_curve_type()) {
  case PCT_XYZ:
    curve_type = "xyz";
    break;

  case PCT_HPR:
    curve_type = "hpr";
    break;

  case PCT_T:
    curve_type = "t";
    break;
  }

  if (!has_name()) {
    // If we don't have a name, come up with one.
    string name = filename.get_basename_wo_extension();

    if (!curve_type.empty()) {
      name += "_";
      name += curve_type;
    }

    set_name(name);
  }

  if (cs == CS_default) {
    cs = get_default_coordinate_system();
  }

  if (cs != CS_invalid) {
    out << "<CoordinateSystem> { ";
    switch (cs) {
    case CS_zup_right:
      out << "Z-Up";
      break;

    case CS_yup_right:
      out << "Y-Up";
      break;

    case CS_zup_left:
      out << "Z-Up-Left";
      break;

    case CS_yup_left:
      out << "Y-Up-Left";
      break;

    default:
      break;
    }
    out << " }\n\n";
  }


  if (!format_egg(out, get_name(), curve_type, 0)) {
    return false;
  }

  if (out) {
    return true;
  } else {
    return false;
  }
}



////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::get_bezier_segs
//       Access: Public, Virtual
//  Description: Fills up the indicated vector with a list of
//               BezierSeg structs that describe the curve.  This
//               assumes the curve is a PiecewiseCurve of
//               CubicCurvesegs.  Returns true if successful, false
//               otherwise.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
get_bezier_segs(ParametricCurve::BezierSegs &) const {
  return false;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::get_bezier_seg
//       Access: Public, Virtual
//  Description: Fills the BezierSeg structure with a description of
//               the curve segment as a Bezier, if possible, but does
//               not change the _t member of the structure.  Returns
//               true if successful, false otherwise.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
get_bezier_seg(ParametricCurve::BezierSeg &) const {
  return false;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::get_nurbs_interface
//       Access: Public, Virtual
//  Description: Returns a pointer to the object as a
//               NurbsCurveInterface object if it happens to be a
//               NURBS-style curve; otherwise, returns NULL.
////////////////////////////////////////////////////////////////////
NurbsCurveInterface *ParametricCurve::
get_nurbs_interface() {
  return (NurbsCurveInterface *)NULL;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::convert_to_hermite
//       Access: Public, Virtual
//  Description: Stores an equivalent curve representation in the
//               indicated Hermite curve, if possible.  Returns true
//               if successful, false otherwise.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
convert_to_hermite(HermiteCurve *hc) const {
  BezierSegs bz_segs;
  if (!get_bezier_segs(bz_segs)) {
    return false;
  }

  hc->set_curve_type(_curve_type);

  // Now convert the Bezier segments to a Hermite.  Normally, the
  // Beziers will match up head-to-tail, but if they don't, that's a
  // cut.
  hc->remove_all_cvs();

  int i, n;
  if (!bz_segs.empty()) {
    PN_stdfloat scale_in = 0.0f;
    PN_stdfloat scale_out = bz_segs[0]._t;
    n = hc->append_cv(HC_SMOOTH, bz_segs[0]._v[0]);
    hc->set_cv_out(n, 3.0f * (bz_segs[0]._v[1] - bz_segs[0]._v[0]) / scale_out);

    for (i = 0; i < (int)bz_segs.size()-1; i++) {
      scale_in = scale_out;
      scale_out = bz_segs[i+1]._t - bz_segs[i]._t;

      if (!bz_segs[i]._v[3].almost_equal(bz_segs[i+1]._v[0], 0.0001f)) {
        // Oops, we have a cut.
        hc->set_cv_type(n, HC_CUT);
      }

      n = hc->append_cv(HC_FREE, bz_segs[i+1]._v[0]);
      hc->set_cv_in(n, 3.0f * (bz_segs[i]._v[3] - bz_segs[i]._v[2]) / scale_in);
      hc->set_cv_tstart(n, bz_segs[i]._t);

      hc->set_cv_out(n, 3.0f * (bz_segs[i+1]._v[1] - bz_segs[i+1]._v[0]) / scale_out);
    }

    // Now the last CV.
    scale_in = scale_out;
    i = bz_segs.size()-1;
    n = hc->append_cv(HC_SMOOTH, bz_segs[i]._v[3]);
    hc->set_cv_in(n, 3.0f * (bz_segs[i]._v[3] - bz_segs[i]._v[2]) / scale_in);
    hc->set_cv_tstart(n, bz_segs[i]._t);
  }

  // Finally, go through and figure out which CV's are smooth or G1.
  int num_cvs = hc->get_num_cvs();
  for (n = 1; n < num_cvs-1; n++) {
    if (hc->get_cv_type(n)!=HC_CUT) {
      LVector3 in = hc->get_cv_in(n);
      LVector3 out = hc->get_cv_out(n);

      if (in.almost_equal(out, 0.0001f)) {
        hc->set_cv_type(n, HC_SMOOTH);
      } else {
        in.normalize();
        out.normalize();
        if (in.almost_equal(out, 0.0001f)) {
          hc->set_cv_type(n, HC_G1);
        }
      }
    }
  }
  return true;
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::convert_to_nurbs
//       Access: Public, Virtual
//  Description: Stores in the indicated NurbsCurve a NURBS
//               representation of an equivalent curve.  Returns true
//               if successful, false otherwise.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
convert_to_nurbs(ParametricCurve *nc) const {
  NurbsCurveInterface *nurbs = nc->get_nurbs_interface();
  nassertr(nurbs != (NurbsCurveInterface *)NULL, false);

  BezierSegs bz_segs;
  if (!get_bezier_segs(bz_segs)) {
    return false;
  }

  nc->set_curve_type(_curve_type);

  nurbs->remove_all_cvs();
  nurbs->set_order(4);
  if (!bz_segs.empty()) {
    int i;
    for (i = 0; i < (int)bz_segs.size(); i++) {
      nurbs->append_cv(bz_segs[i]._v[0]);
      nurbs->append_cv(bz_segs[i]._v[1]);
      nurbs->append_cv(bz_segs[i]._v[2]);
      if (i == (int)bz_segs.size()-1 ||
          !bz_segs[i]._v[3].almost_equal(bz_segs[i+1]._v[0], 0.0001f)) {
        nurbs->append_cv(bz_segs[i]._v[3]);
      }
    }

    PN_stdfloat t;
    int ki = 4;
    nurbs->set_knot(0, 0.0f);
    nurbs->set_knot(1, 0.0f);
    nurbs->set_knot(2, 0.0f);
    nurbs->set_knot(3, 0.0f);

    for (i = 0; i < (int)bz_segs.size(); i++) {
      t = bz_segs[i]._t;

      nurbs->set_knot(ki, t);
      nurbs->set_knot(ki+1, t);
      nurbs->set_knot(ki+2, t);
      ki += 3;
      if (i == ((int)bz_segs.size())-1 ||
          !bz_segs[i]._v[3].almost_equal(bz_segs[i+1]._v[0], 0.0001f)) {
        nurbs->set_knot(ki, t);
        ki++;
      }
    }
  }

  return nc->recompute();
}


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::register_drawer
//       Access: Public
//  Description: Registers a Drawer with this curve that will
//               automatically be updated whenever the curve is
//               modified, so that the visible representation of the
//               curve is kept up to date.  This is called
//               automatically by the ParametricCurveDrawer.
//
//               Any number of Drawers may be registered with a
//               particular curve.
////////////////////////////////////////////////////////////////////
void ParametricCurve::
register_drawer(ParametricCurveDrawer *drawer) {
  _drawers.push_back(drawer);
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::unregister_drawer
//       Access: Public
//  Description: Removes a previously registered drawer from the list
//               of automatically-refreshed drawers.  This is called
//               automatically by the ParametricCurveDrawer.
////////////////////////////////////////////////////////////////////
void ParametricCurve::
unregister_drawer(ParametricCurveDrawer *drawer) {
  _drawers.remove(drawer);
}




////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::invalidate
//       Access: Protected
//  Description: Called from a base class to mark a section of the
//               curve that has been modified and must be redrawn or
//               recomputed in some way.
////////////////////////////////////////////////////////////////////
void ParametricCurve::
invalidate(PN_stdfloat, PN_stdfloat) {
  invalidate_all();
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::invalidate_all
//       Access: Protected
//  Description: Called from a base class to indicate that the curve
//               has changed in some substantial way and must be
//               entirely redrawn.
////////////////////////////////////////////////////////////////////
void ParametricCurve::
invalidate_all() {
  /*
  DrawerList::iterator n;
  for (n = _drawers.begin();
       n != _drawers.end();
       ++n) {
    (*n)->redraw();
  }
  */
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::format_egg
//       Access: Protected, Virtual
//  Description: Formats the curve as an egg structure to write to the
//               indicated stream.  Returns true on success, false on
//               failure.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
format_egg(ostream &, const string &, const string &, int) const {
  return false;
}


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::r_calc_length
//       Access: Private
//  Description: The recursive implementation of calc_length.  This
//               function calculates the length of a segment of the
//               curve between points t1 and t2, which presumably
//               evaluate to the endpoints p1 and p2, and the segment
//               has the length seglength.
////////////////////////////////////////////////////////////////////
PN_stdfloat ParametricCurve::
r_calc_length(PN_stdfloat t1, PN_stdfloat t2, const LPoint3 &p1, const LPoint3 &p2,
              PN_stdfloat seglength) const {
  static const PN_stdfloat length_tolerance = 0.0000001f;
  static const PN_stdfloat t_tolerance = 0.000001f;

  if (t2 - t1 < t_tolerance) {
    // Stop recursing--we've just walked off the limit for
    // representing smaller values of t.
    return 0.0f;
  }

  PN_stdfloat tmid;
  LPoint3 pmid;
  PN_stdfloat left, right;

  // Calculate the point on the curve midway between the two
  // endpoints.
  tmid = (t1+t2)*0.5f;
  get_point(tmid, pmid);

  // Did we increase the length of the segment measurably?
  left = (p1 - pmid).length();
  right = (pmid - p2).length();

  if ((left + right) - seglength < length_tolerance) {
    // No.  We're done.
    return seglength;
  } else {
    // Yes.  Keep going.
    return r_calc_length(t1, tmid, p1, pmid, left) +
      r_calc_length(tmid, t2, pmid, p2, right);
  }
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::r_find_length
//       Access: Private
//  Description: The recursive implementation of find_length.  This is
//               similar to r_calc_length, above.  target_length is
//               the length along the curve past t1 that we hope to
//               find.  If the indicated target_length falls within
//               this segment, returns true and sets found_t to the
//               point along the segment.  Otherwise, updates
//               seglength with the accurate calculated length of the
//               segment and returns false.
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
r_find_length(PN_stdfloat target_length, PN_stdfloat &found_t,
              PN_stdfloat t1, PN_stdfloat t2,
              const LPoint3 &p1, const LPoint3 &p2,
              PN_stdfloat &seglength) const {
  static const PN_stdfloat length_tolerance = 0.0000001f;
  static const PN_stdfloat t_tolerance = 0.000001f;

  if (target_length < t_tolerance) {
    // Stop recursing--we've just walked off the limit for
    // representing smaller values of t.
    found_t = t1;
    return true;

  }

  PN_stdfloat tmid;
  LPoint3 pmid;
  PN_stdfloat left, right;

  // Calculate the point on the curve midway between the two
  // endpoints.
  tmid = (t1+t2)*0.5f;
  get_point(tmid, pmid);

  // Did we increase the length of the segment measurably?
  left = (p1 - pmid).length();
  right = (pmid - p2).length();

  if ((left + right) - seglength < length_tolerance) {
    // No.  Curve is relatively straight over this interval.
    return find_t_linear(target_length, found_t, t1, t2, p1, p2);
    /*
    if (target_length <= seglength) {
      // Compute t value that corresponds to target_length
      // Maybe the point is in the left half of the segment?
      if (r_find_t(target_length, found_t, t1, tmid, p1, pmid)) {
        return true;
      }
      // Maybe it's on the right half?
      if (r_find_t(target_length - left, found_t, tmid, t2, pmid, p2)) {
        return true;
      }
    }
    return false;
    */
  } else {
    // Yes.  Keep going.

    // Maybe the point is in the left half of the segment?
    if (r_find_length(target_length, found_t, t1, tmid, p1, pmid, left)) {
      return true;
    }

    // Maybe it's on the right half?
    if (r_find_length(target_length - left, found_t, tmid, t2, pmid, p2, right)) {
      return true;
    }

    // Neither.  Keep going.
    seglength = left + right;
    return false;
  }
}



////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::r_find_t
//       Access: Private
//  Description: computes the t value in the parametric domain of a 
//               target point along a straight section of a curve.
//               This is similar to r_calc_length, above.  
//               target_length is the length along the curve past t1 
//               that we hope to find.  If the indicated target_length 
//               falls within this segment, returns true and sets 
//               found_t to the point along the segment.  
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
r_find_t(PN_stdfloat target_length, PN_stdfloat &found_t,
         PN_stdfloat t1, PN_stdfloat t2,
         const LPoint3 &p1, const LPoint3 &p2) const {
  static const PN_stdfloat length_tolerance = 0.0001f;
  static const PN_stdfloat t_tolerance = 0.0001f;

  if (parametrics_cat.is_spam()) {
    parametrics_cat.spam()
      << "target_length " << target_length << " t1 " << t1 << " t2 " << t2 << "\n";
  }

  // Is the target point close to the near endpoint
  if (target_length < length_tolerance) {
    found_t = t1;
    return true;
  } 

  // No, compute distance between two endpoints
  PN_stdfloat point_dist;
  point_dist = (p2 - p1).length();

  // Is the target point past the far endpoint?
  if (point_dist < target_length) {
    return false;
  }
   
  // Is the target point close to far endpoint?
  if ( (point_dist - target_length ) < length_tolerance ) {
    found_t = t2;
    return true;
  }
  
  // are we running out of parametric precision?
  if ((t2 - t1) < t_tolerance) {
    found_t = t1;
    return true;
  }

  // No, subdivide and continue
  PN_stdfloat tmid;
  LPoint3 pmid;
  PN_stdfloat left;
  
  // Calculate the point on the curve midway between the two
  // endpoints.
  tmid = (t1+t2)*0.5f;
  get_point(tmid, pmid);
  
  // Maybe the point is in the left half of the segment?
  if (r_find_t(target_length, found_t, t1, tmid, p1, pmid)) {
    return true;
  }
  // Nope, must be in the right half
  left = (p1 - pmid).length();
  if (r_find_t(target_length - left, found_t, tmid, t2, pmid, p2)) {
    return true;
  }

  // not found in either half, keep looking
  return false;
}


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::find_t_linear
//       Access: Private
//  Description: non-recursive version of r_find_t (see above)
////////////////////////////////////////////////////////////////////
bool ParametricCurve::
find_t_linear(PN_stdfloat target_length, PN_stdfloat &found_t,
              PN_stdfloat t1, PN_stdfloat t2,
              const LPoint3 &p1, const LPoint3 &p2) const {
  const PN_stdfloat length_tolerance = (p1-p2).length()/tolerance_divisor;
  const PN_stdfloat t_tolerance = (t1+t2)/tolerance_divisor;

  if (parametrics_cat.is_spam()) {
    parametrics_cat.spam()
      << "target_length " << target_length << " t1 " << t1 << " t2 " << t2 << "\n";
  }

  // first, check to make sure this segment contains the point
  // we're looking for
  if (target_length > (p1 - p2).length()) {
    // segment is too short
    return false;
  }

  PN_stdfloat tleft = t1;
  PN_stdfloat tright = t2;
  PN_stdfloat tmid;
  LPoint3 pmid;
  PN_stdfloat len;

  while (1) {
    tmid = (tleft + tright) * 0.5f;
    get_point(tmid, pmid);
    len = (pmid - p1).length();

    /*
    if (parametrics_cat.is_spam()) {
      parametrics_cat.spam()
        << "tleft " << tleft << " tright " << tright <<
        " tmid " << tmid << " len " << len << endl;
    }
    */

    // is our midpoint at the right distance?
    if (fabs(len - target_length) < length_tolerance) {
      found_t = tmid;
      return true;
    }

    /*
    if (parametrics_cat.is_spam()) {
      parametrics_cat.spam()
        << "tright-tleft " << tright-tleft << " t_tolerance " << t_tolerance << endl;
    }
    */

    // are we out of parametric precision?
    if ((tright - tleft) < t_tolerance) {
      // unfortunately, we can't get any closer in parametric space
      found_t = tmid;
      return true;
    }

    // should we look closer or farther?
    if (len > target_length) {
      // look closer
      tright = tmid;
    } else {
      // look farther
      tleft = tmid;
    }
  }
}


////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::write_datagram
//       Access: Protected, Virtual
//  Description: Function to write the important information in
//               the particular object to a Datagram
////////////////////////////////////////////////////////////////////
void ParametricCurve::
write_datagram(BamWriter *manager, Datagram &me) {
  PandaNode::write_datagram(manager, me);

  me.add_int8(_curve_type);
  me.add_int8(_num_dimensions);
}

////////////////////////////////////////////////////////////////////
//     Function: ParametricCurve::fillin
//       Access: Protected
//  Description: Function that reads out of the datagram (or asks
//               manager to read) all of the data that is needed to
//               re-create this object and stores it in the appropiate
//               place
////////////////////////////////////////////////////////////////////
void ParametricCurve::
fillin(DatagramIterator &scan, BamReader *manager) {
  PandaNode::fillin(scan, manager);

  _curve_type = scan.get_int8();
  _num_dimensions = scan.get_int8();
}