예제 #1
0
/* approximates a bezier curve with a set of circular arcs.
 * returns approximation in carcs
 */
HIDDEN void
bezier_to_carcs(const ON_BezierCurve& bezier, const struct bn_tol *tol, std::vector<ON_Arc>& carcs)
{
    bool skip_while = true, curvature_changed = false;
    fastf_t inflection_pt, biarc_angle;
    ON_Arc biarc;
    ON_BezierCurve current, next;
    std::vector<ON_BezierCurve> rest;

    // find inflection point, if it exists
    if (bezier_inflection(bezier, inflection_pt)) {
	curvature_changed = true;
	bezier.Split(inflection_pt, current, next);
	rest.push_back(next);
    } else {
	current = bezier;
    }

    while (skip_while || !rest.empty()) {
    if (skip_while) skip_while = false;
    biarc = make_biarc(current);
    if ((biarc_angle = biarc.AngleRadians()) <= M_PI_2) {
	// approximate the current bezier segment and add its biarc
	// approximation to carcs
	approx_bezier(current, biarc, tol, carcs);
    } else if (biarc_angle <= M_PI) {
	// divide the current bezier segment in half
	current.Split(0.5, current, next);
	// approximate first bezier segment
	approx_bezier(current, biarc, tol, carcs);
	// approximate second bezier segment
	approx_bezier(next, biarc, tol, carcs);
    } else {
	fastf_t t = 1.0;
	ON_Arc test_biarc;
	ON_BezierCurve test_bezier;
	// divide the current bezier such that the first curve segment would
	// have an approximating biarc segment <=90 degrees
	do {
	    t *= 0.5;
	    current.Split(t, test_bezier, next);
	    test_biarc = make_biarc(test_bezier);
	} while(test_biarc.AngleRadians() > M_PI_2);

	approx_bezier(test_bezier, test_biarc, tol, carcs);
	current = next;
	skip_while = true;
	continue;
    }

    if (curvature_changed) {
	curvature_changed = false;
	current = rest.back();
	rest.pop_back();
	// continue even if we just popped the last element
	skip_while = true;
    }
    }
}
예제 #2
0
static ON_BOOL32 NurbsCurveArc ( const ON_Arc& arc, int dim, ON_NurbsCurve& nurb )
{ 
  if ( !arc.IsValid() )
    return false;
  // makes a quadratic nurbs arc
  const ON_3dPoint center = arc.Center();
  double angle = arc.AngleRadians();
  ON_Interval dom = arc.DomainRadians();
  const double angle0 = dom[0];
  const double angle1 = dom[1];
  ON_3dPoint start_point = arc.StartPoint();
  //ON_3dPoint mid_point   = arc.PointAt(angle0 + 0.5*angle);
  ON_3dPoint end_point   = arc.IsCircle() ? start_point : arc.EndPoint();

  ON_4dPoint CV[9];
  double knot[10];

	double a, b, c, w, winv;
	double *cv;
	int    j, span_count, cv_count;

	a = (0.5 + ON_SQRT_EPSILON)*ON_PI;

	if (angle <= a)
		span_count = 1;
	else if (angle <= 2.0*a)
		span_count = 2;
	else if (angle <= 3.0*a)
		span_count = 4; // TODO - make a 3 span case
	else
		span_count = 4;

	cv_count = 2*span_count + 1;
	
	switch(span_count) {
	case 1:
    CV[0] = start_point;
    CV[1] = arc.PointAt(angle0 + 0.50*angle);
    CV[2] = end_point;
		break;
	case 2:
    CV[0] = start_point;
    CV[1] = arc.PointAt(angle0 + 0.25*angle);
    CV[2] = arc.PointAt(angle0 + 0.50*angle);
    CV[3] = arc.PointAt(angle0 + 0.75*angle);
    CV[4] = end_point;
		angle *= 0.5;
		break;
	default: // 4 spans
    CV[0] = start_point;
    CV[1] = arc.PointAt(angle0 + 0.125*angle);
    CV[2] = arc.PointAt(angle0 + 0.250*angle);
    CV[3] = arc.PointAt(angle0 + 0.375*angle);
    CV[4] = arc.PointAt(angle0 + 0.500*angle);
    CV[5] = arc.PointAt(angle0 + 0.625*angle);
    CV[6] = arc.PointAt(angle0 + 0.750*angle);
    CV[7] = arc.PointAt(angle0 + 0.875*angle);
    CV[8] = end_point;
		angle *= 0.25;
		break;
	}

	a = cos(0.5*angle);
	b = a - 1.0;
	//c = (radius > 0.0) ? radius*angle : angle;
  c = angle;

	span_count *= 2;
	knot[0] = knot[1] = angle0; //0.0;
	for (j = 1; j < span_count; j += 2) {
    CV[j].x += b * center.x;
    CV[j].y += b * center.y;
    CV[j].z += b * center.z;
    CV[j].w = a;
		CV[j+1].w = 1.0;
		knot[j+1] = knot[j+2] = knot[j-1] + c;
	}
  knot[cv_count-1] = knot[cv_count] = angle1;
  for ( j = 1; j < span_count; j += 2 ) {
    w = CV[j].w;
    winv = 1.0/w;
    a = CV[j].x*winv;
    b = ArcDeFuzz(a);
    if ( a != b ) {
      CV[j].x = b*w;
    }
    a = CV[j].y*winv;
    b = ArcDeFuzz(a);
    if ( a != b ) {
      CV[j].y = b*w;
    }
    a = CV[j].z*winv;
    b = ArcDeFuzz(a);
    if ( a != b ) {
      CV[j].z = b*w;
    }
  }

  nurb.m_dim = (dim==2) ? 2 : 3;
  nurb.m_is_rat = 1;
  nurb.m_order = 3;
  nurb.m_cv_count = cv_count;
  nurb.m_cv_stride = (dim==2 ? 3 : 4);
  nurb.ReserveCVCapacity( nurb.m_cv_stride*cv_count );
  nurb.ReserveKnotCapacity( cv_count+1 );
  for ( j = 0; j < cv_count; j++ ) {
    cv = nurb.CV(j);
    cv[0] = CV[j].x;
    cv[1] = CV[j].y;
    if ( dim == 2 ) {
      cv[2] = CV[j].w;
    }
    else {
      cv[2] = CV[j].z;
      cv[3] = CV[j].w;
    }
    nurb.m_knot[j] = knot[j];
  }
  nurb.m_knot[cv_count] = knot[cv_count];
  return true;
}