/// \brief drop cutter at (cl.x, cl.y) against facet of Triangle t
/// calls xy_normal_length(), normal_length(), and center_height() on the subclass.
/// if cl.z is too low, updates cl.z so that cutter does not cut the facet.
/// CompositeCutter may be the only sub-class that needs to reimplement this function.
// general purpose facet-drop which calls xy_normal_length(), normal_length(),
// and center_height() on the subclass
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: virtual bool facetDrop(CLPoint &cl, const Triangle &t) const
public virtual bool facetDrop(CLPoint cl, Triangle t)
{ // Drop cutter at (cl.x, cl.y) against facet of Triangle t
Point normal = t.upNormal(); // facet surface normal
if (GlobalMembers.isZero_tol(normal.z)) // vertical surface
{
return(false); //can't drop against vertical surface
}
Debug.Assert(GlobalMembers.isPositive(normal.z));
if ((GlobalMembers.isZero_tol(normal.x)) && (GlobalMembers.isZero_tol(normal.y)))
{ // horizontal plane special case
CCPoint cc_tmp = new CCPoint(cl.x, cl.y, t.p[0].z, CCType.FACET);
return(cl.liftZ_if_inFacet(cc_tmp.z, cc_tmp, t));
}
else
{ // general case
// plane containing facet: a*x + b*y + c*z + d = 0, so
// d = -a*x - b*y - c*z, where (a,b,c) = surface normal
double d = -normal.dot(t.p[0]);
normal.normalize(); // make length of normal == 1.0
Point xyNormal = new Point(normal.x, normal.y, 0.0);
xyNormal.xyNormalize();
// define the radiusvector which points from the cc-point to the cutter-center
Point radiusvector = this.xy_normal_length * xyNormal + this.normal_length * normal;
CCPoint cc_tmp = new CCPoint(cl - radiusvector); // NOTE xy-coords right, z-coord is not.
cc_tmp.z = (1.0 / normal.z) * (-d - normal.x * cc_tmp.x - normal.y * cc_tmp.y); // cc-point lies in the plane.
cc_tmp.type = CCType.FACET;
double tip_z = cc_tmp.z + radiusvector.z - this.center_height;
return(cl.liftZ_if_inFacet(tip_z, cc_tmp, t));
}
}
// drop-cutter: vertex and facet are handled in base-class
// drop-cutter: Toroidal cutter edge-test handled here
// called from MillingCutter::singleEdgeDrop()
//
// the canonical geometry is one where (cl.x, cl.y) = (0,0)
// and the edge is rotated to lie along the x-axis.
// since the u1-u2 edge is along the x-axis, the points u1 u2 have the same y-coordinate.
//
// when a radius2 cylinder around the edge is sliced by an XY plane this
// results in an ellipse with a shorter axis of radius2, and a longer axis of radius2/sin(theta)
// where theta is the slope of the edge in the XZ plane
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: System.Tuple< double, double > singleEdgeDropCanonical(const Point& u1, const Point& u2) const
protected new Tuple <double, double> singleEdgeDropCanonical(Point u1, Point u2)
{
if (GlobalMembers.isZero_tol(u1.z - u2.z))
{ // horizontal edge special case
return(new Tuple <double, double>(0, u1.z - height(u1.y)));
}
else
{ // the general offset-ellipse case
double b_axis = radius2; // short axis of ellipse = radius2
double theta = Math.Atan((u2.z - u1.z) / (u2.x - u1.x)); // theta is the slope of the line
double a_axis = Math.Abs(radius2 / Math.Sin(theta)); // long axis of ellipse = radius2/sin(theta)
Point ellcenter = new Point(0, u1.y, 0);
Ellipse e = new Ellipse(ellcenter, a_axis, b_axis, radius1); // radius1 is the ellipse-offset
int iters = e.solver_brent(); // numerical solver that searches for a point on the ellipse
// such that a radius1-length normal-vector from this ellipse-point
// is at the CL point (0,0)
if (iters > 200)
{
Console.Write("WARNING: BullCutter::singleEdgeDropCanonical() iters>200 !!\n");
}
Debug.Assert(iters < 200);
e.setEllipsePositionHi(u1, u2); // this selects either EllipsePosition1 or
// EllipsePosition2 and sets it to EllipsePosition_hi
// pseudo cc-point on the ellipse/cylinder, in the CL=(0,0) system
Point ell_ccp = e.ePointHi();
Debug.Assert(Math.Abs(ell_ccp.xyNorm() - radius1) < 1E-5); // ell_ccp should be on the cylinder-circle
Point cc_tmp_u = ell_ccp.closestPoint(u1, u2); // find cc-point on u1-u2 edge
return(new Tuple <double, double>(cc_tmp_u.x, e.getCenterZ() - radius2));
}
}
/*
* /// string repr
* public static std::ostream operator << (std::ostream stream, BullCutter c)
* {
* stream << "BullCutter(d=" << c.diameter << ", r1=" << c.radius1 << " r2=" << c.radius2 << ", L=" << c.length << ")";
* return stream;
* }
*
* //C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
* //ORIGINAL LINE: string str() const
* public new string str()
* {
* std::ostringstream o = new std::ostringstream();
* o << this;
* return o.str();
* }
*/
// push-cutter: vertex and facet handled by base-class
// edge handled here
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool generalEdgePush(const Fiber& f, Interval& i, const Point& p1, const Point& p2) const
protected new bool generalEdgePush(Fiber f, Interval i, Point p1, Point p2)
{
//std::cout << " BullCutter::generalEdgePush() \n";
bool result = false;
if (GlobalMembers.isZero_tol((p2 - p1).xyNorm()))
{ // this would be a vertical edge
return(result);
}
if (GlobalMembers.isZero_tol(p2.z - p1.z)) // this would be a horizontal edge
{
return(result);
}
Debug.Assert(Math.Abs(p2.z - p1.z) > 0.0); // no horiz edges allowed hereafter
// p1+t*(p2-p1) = f.p1.z+radius2 =>
double tplane = (f.p1.z + radius2 - p1.z) / (p2.z - p1.z); // intersect edge with plane at z = ufp1.z
Point ell_center = p1 + tplane * (p2 - p1);
Debug.Assert(GlobalMembers.isZero_tol(Math.Abs(ell_center.z - (f.p1.z + radius2))));
Point major_dir = (p2 - p1);
Debug.Assert(major_dir.xyNorm() > 0.0);
major_dir.z = 0;
major_dir.xyNormalize();
Point minor_dir = major_dir.xyPerp();
double theta = Math.Atan((p2.z - p1.z) / (p2 - p1).xyNorm());
double major_length = Math.Abs(radius2 / Math.Sin(theta));
double minor_length = radius2;
AlignedEllipse e = new AlignedEllipse(ell_center, major_length, minor_length, radius1, major_dir, minor_dir);
if (e.aligned_solver(f))
{ // now we want the offset-ellipse point to lie on the fiber
Point pseudo_cc = e.ePoint1(); // pseudo cc-point on ellipse and cylinder
Point pseudo_cc2 = e.ePoint2();
CCPoint cc = new CCPoint(pseudo_cc.closestPoint(p1, p2));
CCPoint cc2 = new CCPoint(pseudo_cc2.closestPoint(p1, p2));
cc.type = CCType.EDGE_POS;
cc2.type = CCType.EDGE_POS;
Point cl = e.oePoint1() - new Point(0, 0, center_height);
Debug.Assert(GlobalMembers.isZero_tol(Math.Abs(cl.z - f.p1.z)));
Point cl2 = e.oePoint2() - new Point(0, 0, center_height);
Debug.Assert(GlobalMembers.isZero_tol(Math.Abs(cl2.z - f.p1.z)));
double cl_t = f.tval(cl);
double cl_t2 = f.tval(cl2);
if (i.update_ifCCinEdgeAndTrue(cl_t, cc, p1, p2, true))
{
result = true;
}
if (i.update_ifCCinEdgeAndTrue(cl_t2, cc2, p1, p2, true))
{
result = true;
}
}
//std::cout << " BullCutter::generalEdgePush() DONE result= " << result << "\n";
return(result);
}
/// return true if vector parallel to y-axis
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool yParallel() const
public bool yParallel()
{
if (GlobalMembers.isZero_tol(x) && GlobalMembers.isZero_tol(z))
{
return(true);
}
return(false);
}
// test for intersection with the fiber and a tip-tang line
// if there is an intersection in tip-tang, calculate the cc-point and update the interval
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool cone_CC(const Point& tang, const Point& tip, const Point& base, const Point& p1, const Point& p2, const Fiber& f, Interval& i) const
protected bool cone_CC(Point tang, Point tip, Point @base, Point p1, Point p2, Fiber f, Interval i)
{
double u = 0;
double t = 0;
if (GlobalMembers.xy_line_line_intersection(f.p1, f.p2, ref u, tang, tip, ref t))
{
if ((t >= 0.0) && (t <= 1.0))
{
CCPoint cc_tmp = new CCPoint(@base + t * (tip - @base));
cc_tmp.z_projectOntoEdge(p1, p2);
cc_tmp.type = CCType.EDGE_CONE;
return(i.update_ifCCinEdgeAndTrue(u, cc_tmp, p1, p2, (true)));
}
}
return(false);
}
/// return true if (s,t) is valid, i.e. lies on the unit circle
/// checks s^2 + t^2 == 1 (to within tolerance)
// check that s and t values are OK
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool isValid() const
public bool isValid()
{
if (GlobalMembers.isZero_tol(ocl.GlobalMembers.square(s) + ocl.GlobalMembers.square(t) - 1.0))
{
return(true);
}
else
{
Console.Write(" EllipsePosition=");
Console.Write(this);
Console.Write("\n");
Console.Write(" square(s) + square(t) - 1.0 = ");
Console.Write(ocl.GlobalMembers.square(s) + ocl.GlobalMembers.square(t) - 1.0);
Console.Write(" !!\n");
return(false);
}
}
/// push-cutter horizontal edge case
/// horizontal are much simpler than the general case.
/// we can consider the cutter circular with an effective radius of this->width(h)
// this is the horizontal edge case
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool horizEdgePush(const Fiber& f, Interval& i, const Point& p1, const Point& p2) const
protected bool horizEdgePush(Fiber f, Interval i, Point p1, Point p2)
{
bool result = false;
double h = p1.z - f.p1.z; // height of edge above fiber
if ((h > 0.0))
{
if (GlobalMembers.isZero_tol(p2.z - p1.z))
{ // this is the horizontal-edge special case
double eff_radius = this.width(h); // the cutter acts as a cylinder with eff_radius
// contact this cylinder/circle against edge in xy-plane
double qt = 0; // fiber is f.p1 + qt*(f.p2-f.p1)
double qv = 0; // line is p1 + qv*(p2-p1)
if (GlobalMembers.xy_line_line_intersection(p1, p2, ref qv, f.p1, f.p2, ref qt))
{
Point q = p1 + qv * (p2 - p1); // the intersection point
// from q, go v-units along tangent, then eff_r*normal, and end up on fiber:
// q + ccv*tangent + r*normal = p1 + clt*(p2-p1)
double ccv = 0;
double clt = 0;
Point xy_tang = p2 - p1;
xy_tang.z = 0;
xy_tang.xyNormalize();
Point xy_normal = xy_tang.xyPerp();
Point q1 = q + eff_radius * xy_normal;
Point q2 = q1 + (p2 - p1);
if (GlobalMembers.xy_line_line_intersection(q1, q2, ref ccv, f.p1, f.p2, ref clt))
{
double t_cl1 = clt;
double t_cl2 = qt + (qt - clt);
if (calcCCandUpdateInterval(t_cl1, ccv, q, p1, p2, f, i, f.p1.z, CCType.EDGE_HORIZ))
{
result = true;
}
if (calcCCandUpdateInterval(t_cl2, -ccv, q, p1, p2, f, i, f.p1.z, CCType.EDGE_HORIZ))
{
result = true;
}
}
}
}
}
//std::cout << " horizEdgePush = " << result << "\n";
return(result);
}
/// Cone facet-drop is special, since we can make contact with either the tip or the circular rim
// because this checks for contact with both the tip and the circular edge it is hard to move to the base-class
// we either hit the tip, when the slope of the plane is smaller than angle
// or when the slope is steep, the circular edge between the cone and the cylindrical shaft
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool facetDrop(CLPoint &cl, const Triangle &t) const
public new bool facetDrop(CLPoint cl, Triangle t)
{
bool result = false;
Point normal = t.upNormal(); // facet surface normal
if (GlobalMembers.isZero_tol(normal.z)) // vertical surface
{
return(false); //can't drop against vertical surface
}
if ((GlobalMembers.isZero_tol(normal.x)) && (GlobalMembers.isZero_tol(normal.y)))
{ // horizontal plane special case
CCPoint cc_tmp = new CCPoint(cl.x, cl.y, t.p[0].z, CCType.FACET_TIP); // so any vertex is at the correct height
return(cl.liftZ_if_inFacet(cc_tmp.z, cc_tmp, t));
}
else
{
// define plane containing facet
// a*x + b*y + c*z + d = 0, so
// d = -a*x - b*y - c*z, where (a,b,c) = surface normal
double a = normal.x;
double b = normal.y;
double c = normal.z;
double d = -normal.dot(t.p[0]);
normal.xyNormalize(); // make xy length of normal == 1.0
// cylindrical contact point case
// find the xy-coordinates of the cc-point
CCPoint cyl_cc_tmp = new CCPoint(cl - radius * normal);
cyl_cc_tmp.z = (1.0 / c) * (-d - a * cyl_cc_tmp.x - b * cyl_cc_tmp.y);
double cyl_cl_z = cyl_cc_tmp.z - length; // tip positioned here
cyl_cc_tmp.type = CCType.FACET_CYL;
// tip contact with facet
CCPoint tip_cc_tmp = new CCPoint(cl.x, cl.y, 0.0);
tip_cc_tmp.z = (1.0 / c) * (-d - a * tip_cc_tmp.x - b * tip_cc_tmp.y);
double tip_cl_z = tip_cc_tmp.z;
tip_cc_tmp.type = CCType.FACET_TIP;
result = result || cl.liftZ_if_inFacet(tip_cl_z, tip_cc_tmp, t);
result = result || cl.liftZ_if_inFacet(cyl_cl_z, cyl_cc_tmp, t);
return(result);
}
}
/// push-cutter cylindrical shaft case.
/// This is called when the contact is above the sphere/toroid/cone shaped lower part of the cutter
// this is used for the cylindrical shaft of Cyl, Ball, Bull, Cone
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool shaftEdgePush(const Fiber& f, Interval& i, const Point& p1, const Point& p2) const
protected bool shaftEdgePush(Fiber f, Interval i, Point p1, Point p2)
{
// push cutter along Fiber f in contact with edge p1-p2
// contact with cylindrical cutter shaft
double u = 0;
double v = 0;
bool result = false;
if (GlobalMembers.xy_line_line_intersection(p1, p2, ref u, f.p1, f.p2, ref v))
{ // find XY-intersection btw fiber and edge
Point q = p1 + u * (p2 - p1); // edge/fiber intersection point, on edge
// Point q = f.p1 + v*(f.p2-f.p1); // q on fiber
// from q, go v_cc*xy_tangent, then r*xy_normal, and end up on fiber:
// q + v_cc*tangent + r*xy_normal = p1 + t_cl*(p2-p1)
Point xy_tang = p2 - p1;
xy_tang.z = 0;
xy_tang.xyNormalize();
Point xy_normal = xy_tang.xyPerp();
Point q1 = q + radius * xy_normal;
Point q2 = q1 + (p2 - p1);
double u_cc = 0;
double t_cl = 0;
if (GlobalMembers.xy_line_line_intersection(q1, q2, ref u_cc, f.p1, f.p2, ref t_cl))
{
double t_cl1 = t_cl; // cc_tmp1 = q +/- u_cc*(p2-p1);
double t_cl2 = v + (v - t_cl);
if (calcCCandUpdateInterval(t_cl1, u_cc, q, p1, p2, f, i, f.p1.z + center_height, CCType.EDGE_SHAFT))
{
result = true;
}
if (calcCCandUpdateInterval(t_cl2, -u_cc, q, p1, p2, f, i, f.p1.z + center_height, CCType.EDGE_SHAFT))
{
result = true;
}
}
}
//std::cout << " shaftEdgePush = " << result << "\n";
return(result);
}
/// return closest Point to line through p1 and p2. Works in the XY plane.
/// return Point on p1-p2 line which is closest in XY-plane to this
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: Point xyClosestPoint(const Point &p1, const Point &p2) const
public Point xyClosestPoint(Point p1, Point p2)
{
// one explanation is here
// http://local.wasp.uwa.edu.au/~pbourke/geometry/pointline/
Point pt1 = new Point(p1); // this required because of "const" arguments above.
Point pt2 = new Point(p2);
Point v = pt2 - pt1;
if (GlobalMembers.isZero_tol(v.xyNorm()))
{ // if p1 and p2 do not make a line in the xy-plane
Console.Write("point.cpp: xyClosestPoint ERROR!: can't calculate closest point from \n");
Console.Write("point.cpp: xyClosestPoint ERROR!: *this =");
Console.Write(this);
Console.Write(" to line through\n");
Console.Write("point.cpp: xyClosestPoint ERROR!: p1=");
Console.Write(p1);
Console.Write(" and \n");
Console.Write("point.cpp: xyClosestPoint ERROR!: p2=");
Console.Write(p2);
Console.Write("\n");
Console.Write("point.cpp: xyClosestPoint ERROR!: in the xy-plane\n");
Debug.Assert(false);
return(new Point(0, 0, 0));
}
double u;
// vector notation:
// u = (p3-p1) dot v / (v dot v)
u = (this.x - p1.x) * (v.x) + (this.y - p1.y) * (v.y);
u = u / (v.x * v.x + v.y * v.y);
// coordinates for closest point
double x = p1.x + u * v.x;
double y = p1.y + u * v.y;
return(new Point(x, y, 0));
}
/// \brief drop cutter at (cl.x, cl.y) against the three edges of input Triangle t.
/// calls the sub-class MillingCutter::singleEdgeDrop on each edge
/// if cl.z is too low, updates cl.z so that cutter does not cut any edge.
// edge-drop function which calls the sub-class MillingCutter::singleEdgeDrop on each
// edge of the input Triangle t.
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: virtual bool edgeDrop(CLPoint &cl, const Triangle &t) const
public virtual bool edgeDrop(CLPoint cl, Triangle t)
{
bool result = false;
for (int n = 0; n < 3; n++)
{ // loop through all three edges
int start = n; // index of the start-point of the edge
int end = (n + 1) % 3; // index of the end-point of the edge
Point p1 = t.p[start];
Point p2 = t.p[end];
if (!GlobalMembers.isZero_tol(p1.x - p2.x) || !GlobalMembers.isZero_tol(p1.y - p2.y))
{
double d = cl.xyDistanceToLine(p1, p2);
if (d <= radius) // potential contact with edge
{
if (this.singleEdgeDrop(cl, p1, p2, d))
{
result = true;
}
}
}
}
return(result);
}
// cone is pushed along Fiber f into contact with edge p1-p2
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool generalEdgePush(const Fiber& f, Interval& i, const Point& p1, const Point& p2) const
protected new bool generalEdgePush(Fiber f, Interval i, Point p1, Point p2)
{
bool result = false;
if (GlobalMembers.isZero_tol(p2.z - p1.z)) // guard against horizontal edge
{
return(result);
}
Debug.Assert((p2.z - p1.z) != 0.0);
// idea: as the ITO-cone slides along the edge it will pierce a z-plane at the height of the fiber
// the shaped of the pierced area is either a circle if the edge is steep
// or a 'half-circle' + cone shape if the edge is shallow (ice-cream cone...)
// we can now intersect this 2D shape with the fiber and get the CL-points.
// this is where the ITO cone pierces the z-plane of the fiber
// edge-line: p1+t*(p2-p1) = zheight
// => t = (zheight - p1)/ (p2-p1)
double t_tip = (f.p1.z - p1.z) / (p2.z - p1.z);
Point p_tip = p1 + t_tip * (p2 - p1);
Debug.Assert(GlobalMembers.isZero_tol(Math.Abs(p_tip.z - f.p1.z))); // p_tip should be in plane of fiber
// this is where the ITO cone base exits the plane
double t_base = (f.p1.z + center_height - p1.z) / (p2.z - p1.z);
Point p_base = p1 + t_base * (p2 - p1);
p_base.z = f.p1.z; // project to plane of fiber
double L = (p_base - p_tip).xyNorm();
//if ( L <= radius ){ // this is where the ITO-slice is a circle
// find intersection points, if any, between the fiber and the circle
// fiber is f.p1 - f.p2
// circle is centered at p_base
double d = p_base.xyDistanceToLine(f.p1, f.p2);
if (d <= radius)
{
// we know there is an intersection point.
// http://mathworld.wolfram.com/Circle-LineIntersection.html
// subtract circle center, math is for circle centered at (0,0)
double dx = f.p2.x - f.p1.x;
double dy = f.p2.y - f.p1.y;
double dr = Math.Sqrt(ocl.GlobalMembers.square(dx) + ocl.GlobalMembers.square(dy));
double det = (f.p1.x - p_base.x) * (f.p2.y - p_base.y) - (f.p2.x - p_base.x) * (f.p1.y - p_base.y);
// intersection given by:
// x = det*dy +/- sign(dy) * dx * sqrt( r^2 dr^2 - det^2 ) / dr^2
// y = -det*dx +/- abs(dy) * sqrt( r^2 dr^2 - det^2 ) / dr^2
double discr = ocl.GlobalMembers.square(radius) * ocl.GlobalMembers.square(dr) - ocl.GlobalMembers.square(det);
if (discr >= 0.0)
{
if (discr == 0.0)
{ // tangent case
double x_tang = (det * dy) / ocl.GlobalMembers.square(dr);
double y_tang = -(det * dx) / ocl.GlobalMembers.square(dr);
Point p_tang = new Point(x_tang + p_base.x, y_tang + p_base.y); // translate back from (0,0) system!
double t_tang = f.tval(p_tang);
if (circle_CC(t_tang, p1, p2, f, i))
{
result = true;
}
}
else
{
// two intersection points with the base-circle
double x_pos = (det * dy + Math.Sign(dy) * dx * Math.Sqrt(discr)) / ocl.GlobalMembers.square(dr);
double y_pos = (-det * dx + Math.Abs(dy) * Math.Sqrt(discr)) / ocl.GlobalMembers.square(dr);
Point cl_pos = new Point(x_pos + p_base.x, y_pos + p_base.y);
double t_pos = f.tval(cl_pos);
// the same with "-" sign:
double x_neg = (det * dy - Math.Sign(dy) * dx * Math.Sqrt(discr)) / ocl.GlobalMembers.square(dr);
double y_neg = (-det * dx - Math.Abs(dy) * Math.Sqrt(discr)) / ocl.GlobalMembers.square(dr);
Point cl_neg = new Point(x_neg + p_base.x, y_neg + p_base.y);
double t_neg = f.tval(cl_neg);
if (circle_CC(t_pos, p1, p2, f, i))
{
result = true;
}
if (circle_CC(t_neg, p1, p2, f, i))
{
result = true;
}
}
}
}
//} // circle-case
if (L > radius)
{
// ITO-slice is cone + "half-circle"
// lines from p_tip to tangent points of the base-circle
// this page has an analytic solution:
// http://mathworld.wolfram.com/CircleTangentLine.html
// this page has a geometric construction:
// http://www.mathopenref.com/consttangents.html
// circle p_base, radius
// top p_tip
// tangent point at intersection of base-circle with this circle:
Point p_mid = 0.5 * (p_base + p_tip);
p_mid.z = f.p1.z;
double r_tang = L / 2;
// circle-circle intersection to find tangent-points
// three cases: no intersection point
// one intersection point
// two intersection points
//d is the distance between the circle centers
Point pd = p_mid - p_base;
pd.z = 0;
double dist = pd.xyNorm(); //distance between the circles
//Check for special cases which do not lead to solutions we want
bool case1 = (GlobalMembers.isZero_tol(dist) && GlobalMembers.isZero_tol(Math.Abs(radius - r_tang)));
bool case2 = (dist > (radius + r_tang)); //no solution. circles do not intersect
bool case3 = (dist < Math.Abs(radius - r_tang)); //no solution. one circle is contained in the other
bool case4 = (GlobalMembers.isZero_tol(dist - (radius + r_tang))); // tangent case
if (case1 || case2 || case3 || case4)
{
}
else
{
// here we know we have two solutions.
//Determine the distance from point 0 to point 2
// law of cosines (http://en.wikipedia.org/wiki/Law_of_cosines)
// rt^2 = d^2 + r^2 -2*d*r*cos(gamma)
// so cos(gamma) = (rt^2-d^2-r^2)/ -(2*d*r)
// and the sought distance is
// a = r*cos(gamma) = (-rt^2+d^2+r^2)/ (2*d)
double a = (-ocl.GlobalMembers.square(r_tang) + ocl.GlobalMembers.square(radius) + ocl.GlobalMembers.square(dist)) / (2.0 * dist);
Debug.Assert(a >= 0.0);
Point v2 = p_base + (a / dist) * pd; // v2 is the point where the line through the circle intersection points crosses the line between the circle centers.
//Determine the distance from v2 to either of the intersection points
double h = Math.Sqrt(ocl.GlobalMembers.square(radius) - ocl.GlobalMembers.square(a));
//Now determine the offsets of the intersection points from point 2
Point ofs = new Point(-pd.y * (h / dist), pd.x * (h / dist));
// now we know the tangent-points
Point tang1 = v2 + ofs;
Point tang2 = v2 - ofs;
if (cone_CC(tang1, p_tip, p_base, p1, p2, f, i))
{
result = true;
}
if (cone_CC(tang2, p_tip, p_base, p1, p2, f, i))
{
result = true;
}
}
} // end circle+cone case
return(result);
}
/// string repr
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: string str() const;
//C++ TO C# CONVERTER TODO TASK: The implementation of the following method could not be found:
// string str();
/// build and return a KDNode containing list *tris at depth dep.
protected KDNode <Triangle> build_node(LinkedList <Triangle> tris, int dep, KDNode <Triangle> par)
{ // parent node
//std::cout << "KDNode::build_node list.size()=" << tris->size() << "\n";
if (tris.Count == 0)
{ //this is a fatal error.
Console.Write("ERROR: KDTree::build_node() called with tris->size()==0 !");
Debug.Assert(false);
return(null);
}
Spread spr = calc_spread(tris); // calculate spread in order to know how to cut
double cutvalue = spr.start + spr.val / 2; // cut in the middle
//std::cout << " cutvalue= " << cutvalue << "\n";
if ((tris.Count <= bucketSize) || GlobalMembers.isZero_tol(spr.val))
{ // then return a bucket/leaf node
//std::cout << "KDNode::build_node BUCKET list.size()=" << tris->size() << "\n";
KDNode <Triangle> bucket; // dim cutv parent hi lo triangles depth
bucket = new KDNode <Triangle>(spr.d, cutvalue, par, null, null, tris, dep);
Debug.Assert(bucket.isLeaf);
spr = null;
return(bucket); // this is the leaf/end of the recursion-tree
}
// build lists of triangles for hi and lo child nodes
LinkedList <Triangle> lolist = new LinkedList <Triangle>();
LinkedList <Triangle> hilist = new LinkedList <Triangle>();
foreach (Triangle t in tris)
{ // loop through each triangle and put it in either lolist or hilist
if (t.bb[spr.d] > cutvalue)
{
hilist.AddLast(t);
}
else
{
lolist.AddLast(t);
}
}
/*
* if (hilist->empty() || lolist->empty()) {// an error ??
* std::cout << "kdtree: hilist.size()==0! or lolist.size()==0! \n";
* std::cout << "kdtree: tris->size()= " << tris->size()<< "\n";
* std::cout << "kdtree: hilist.size()= " << hilist->size()<< "\n";
* std::cout << "kdtree: lolist.size()= " << lolist->size()<< "\n";
* BOOST_FOREACH(Triangle t, *tris) {
* std::cout << t << "\n";
* std::cout << t.bb << "\n";
* }
* std::cout << "kdtree: spr->d= " << spr->d << "\n";
* std::cout << "kdtree: cutvalue= " << cutvalue << "\n";
* assert(0);
* }*/
// create the current node dim value parent hi lo trilist depth
KDNode <Triangle> node = new KDNode <Triangle>(spr.d, cutvalue, par, null, null, null, dep);
// create the child-nodes through recursion
// list depth parent
if (hilist.Count > 0)
{
node.hi = build_node(hilist, dep + 1, node);
}
//else
//std::cout << "hilist empty!\n";
if (lolist.Count > 0)
{
node.lo = build_node(lolist, dep + 1, node);
}
else
{
//std::cout << "lolist empty!\n";
}
lolist.Clear();
hilist.Clear();
spr = null;
lolist = null;
hilist = null;
return(node); // return a new node
}
/// aligned offset-ellipse solver. callsn Numeric::brent_solver()
// used by BullCutter pushcutter edge-test
public bool aligned_solver(Fiber f)
{
error_dir.CopyFrom(f.dir.xyPerp()); // now calls to error(diangle) will give the right error
Debug.Assert(error_dir.xyNorm() > 0.0);
target.CopyFrom(f.p1); // target is either x or y-coord of f.p1
// find position(s) where ellipse tangent is parallel to fiber. Here error() will be minimized/maximized.
// tangent at point is: -a t + b s = -a*major_dir*t + b*minor_dir*s
// -at ma.y + bs mi.y = 0 for X-fiber
// s = sqrt(1-t^2)
// -a*ma.y * t + b*mi.y* sqrt(1-t^2) = 0
// => t^2 = b^2 / (a^2 + b^2)
double t1 = 0.0;
if (f.p1.y == f.p2.y)
{
t1 = Math.Sqrt(ocl.GlobalMembers.square(b * minor_dir.y) / (ocl.GlobalMembers.square(a * major_dir.y) + ocl.GlobalMembers.square(b * minor_dir.y)));
}
else if (f.p1.x == f.p2.x)
{
t1 = Math.Sqrt(ocl.GlobalMembers.square(b * minor_dir.x) / (ocl.GlobalMembers.square(a * major_dir.x) + ocl.GlobalMembers.square(b * minor_dir.x)));
}
else
{
Debug.Assert(false);
}
// bracket root
EllipsePosition tmp = new EllipsePosition();
EllipsePosition apos = new EllipsePosition();
EllipsePosition bpos = new EllipsePosition();
double s1 = Math.Sqrt(1.0 - ocl.GlobalMembers.square(t1));
bool found_positive = false;
bool found_negative = false;
tmp.setDiangle(GlobalMembers.xyVectorToDiangle(s1, t1));
if (error(tmp.diangle) > 0)
{
found_positive = true;
apos.CopyFrom(tmp);
}
else if (error(tmp.diangle) < 0)
{
found_negative = true;
bpos.CopyFrom(tmp);
}
tmp.setDiangle(GlobalMembers.xyVectorToDiangle(s1, -t1));
if (error(tmp.diangle) > 0)
{
found_positive = true;
apos.CopyFrom(tmp);
}
else if (error(tmp.diangle) < 0)
{
found_negative = true;
bpos.CopyFrom(tmp);
}
tmp.setDiangle(GlobalMembers.xyVectorToDiangle(-s1, t1));
if (error(tmp.diangle) > 0)
{
found_positive = true;
apos.CopyFrom(tmp);
}
else if (error(tmp.diangle) < 0)
{
found_negative = true;
bpos.CopyFrom(tmp);
}
tmp.setDiangle(GlobalMembers.xyVectorToDiangle(-s1, -t1));
if (error(tmp.diangle) > 0)
{
found_positive = true;
apos.CopyFrom(tmp);
}
else if (error(tmp.diangle) < 0)
{
found_negative = true;
bpos.CopyFrom(tmp);
}
if (found_positive)
{
if (found_negative)
{
Debug.Assert(this.error(apos.diangle) * this.error(bpos.diangle) < 0.0); // root is now bracketed.
double lolim = 0.0;
double hilim = 0.0;
if (apos.diangle > bpos.diangle)
{
lolim = bpos.diangle;
hilim = apos.diangle;
}
else if (bpos.diangle > apos.diangle)
{
hilim = bpos.diangle;
lolim = apos.diangle;
}
double dia_sln = ocl.GlobalMembers.brent_zero(lolim, hilim, 3E-16, DefineConstants.OE_ERROR_TOLERANCE, this);
double dia_sln2 = ocl.GlobalMembers.brent_zero(hilim - 4.0, lolim, 3E-16, DefineConstants.OE_ERROR_TOLERANCE, this);
EllipsePosition1.setDiangle(dia_sln);
EllipsePosition2.setDiangle(dia_sln2);
Debug.Assert(EllipsePosition1.isValid());
Debug.Assert(EllipsePosition2.isValid());
/*
* // FIXME. This assert fails in some cases (30sphere.stl z=0, for example)
* // FIXME. The allowed error should probably be in proportion to the difficulty of the case.
*
* if (!isZero_tol( error(EllipsePosition1.diangle) )) {
* std::cout << "AlignedEllipse::aligned_solver() ERROR \n";
* std::cout << "error(EllipsePosition1.diangle)= "<< error(EllipsePosition1.diangle) << " (expected zero)\n";
*
* }
* assert( isZero_tol( error(EllipsePosition1.diangle) ) );
* assert( isZero_tol( error(EllipsePosition2.diangle) ) );
*/
return(true);
}
}
return(false);
}
// push-cutter: vertex and facet handled in base-class
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool generalEdgePush(const Fiber& f, Interval& i, const Point& p1, const Point& p2) const
protected new bool generalEdgePush(Fiber f, Interval i, Point p1, Point p2)
{
bool result = false;
if (GlobalMembers.isZero_tol((p2 - p1).xyNorm()))
{ // this would be a vertical edge
return(result);
}
Point ufp1 = f.p1 + new Point(0, 0, radius); // take a fiber which is raised up by radius
Point ufp2 = f.p2 + new Point(0, 0, radius); // and intersect it with a cylinder around the edge p1-p2
// Ray : P(t) = O + t*V from point O, in direction V
// Cylinder [A, B, r] from point A to point B, radius r
// Point P on infinite cylinder if ((P - A) x (B - A))^2 = r^2 * (B - A)^2
// expand : ((O - A) x (B - A) + t * (V x (B - A)))^2 = r^2 * (B - A)^2
// equation in the form (X + t * Y)^2 = d , where:
// X = (O - A) x (B - A)
// Y = V x (B - A)
// d = r^2 * (B - A)^2
// expand the equation :
// t^2 * (Y . Y) + t * (2 * (X . Y)) + (X . X) - d = 0
// => second order equation in the form : a*t^2 + b*t + c = 0 where
// a = (Y . Y)
// b = 2 * (X . Y)
// c = (X . X) - d
Point ab = p2 - p1; // axis of the cylinder
Point ao = (ufp1 - p1); // cyl start to ray start
Point ao_x_ab = ao.cross(ab); // cross product
Point v_x_ab = (ufp2 - ufp1).cross(ab); // cross product
double ab2 = ab.dot(ab); // dot product
double a = v_x_ab.dot(v_x_ab); // dot product
double b = 2 * (v_x_ab.dot(ao_x_ab)); // dot product
double c = ao_x_ab.dot(ao_x_ab) - (radius * radius * ab2);
// solve second order equation : a*t^2 + b*t + c = 0
// t = (-b +/- sqrt( b^2 - 4ac ) ) / 2a
double discr = b * b - 4 * a * c;
double t1;
double t2;
if (GlobalMembers.isZero_tol(discr))
{ // tangent case, only one root
t1 = -b / (2 * a);
if (calcCCandUpdateInterval(t1, p1, p2, f, i))
{
result = true;
}
}
else if (discr > 0.0)
{ // two roots
t1 = (-b + Math.Sqrt(discr)) / (2 * a);
t2 = (-b - Math.Sqrt(discr)) / (2 * a);
if (calcCCandUpdateInterval(t1, p1, p2, f, i))
{
result = true;
}
if (calcCCandUpdateInterval(t2, p1, p2, f, i))
{
result = true;
}
}
return(result);
}
/// push cutter with given normal/center/xy_length into contact with Triangle facet
// general purpose facetPush
//C++ TO C# CONVERTER WARNING: 'const' methods are not available in C#:
//ORIGINAL LINE: bool generalFacetPush(double normal_length, double center_height, double xy_normal_length, const Fiber& fib, Interval& i, const Triangle& t) const
protected bool generalFacetPush(double normal_length, double center_height, double xy_normal_length, Fiber fib, Interval i, Triangle t)
{
bool result = false;
Point normal = t.upNormal(); // facet surface normal, pointing up
if (normal.zParallel()) // normal points in z-dir
{
return(result); //can't push against horizontal plane, stop here.
}
normal.normalize();
Point xy_normal = new Point(normal);
xy_normal.z = 0;
xy_normal.xyNormalize();
// find a point on the plane from which radius2*normal+radius1*xy_normal lands on the fiber+radius2*Point(0,0,1)
// (u,v) locates a point on the triangle facet v0+ u*(v1-v0)+v*(v2-v0) u,v in [0,1]
// t locates a point along the fiber: p1 + t*(p2-p1) t in [0,1]
//
// facet-point + r2 * n + r1* xy_n = fiber-point + r2*Point(0,0,1)
// =>
// v0+ u*(v1-v0)+v*(v2-v0) + r2 * n + r1* xy_n = p1 + t*(p2-p1) + r2*Point(0,0,1)
//
// v0x + u*(v1x-v0x) + v*(v2x-v0x) + r2*nx + r1*xy_n.x = p1x + t*(p2x-p1x) p2x-p1x==0 for Y-fiber
// v0y + u*(v1y-v0y) + v*(v2y-v0y) + r2*ny + r1*xy_n.y = p1y + t*(p2y-p1y) p2y-p1y==0 for X-fiber
// v0z + u*(v1z-v0z) + v*(v2z-v0z) + r2*nz = p1z + t*(p2z-p1z) + r2 (p2z-p1z)==0 for XY-fibers!!
// X-fiber:
// v0x + u*(v1x-v0x) + v*(v2x-v0x) + r2*nx + r1*xy_n.x = p1x + t*(p2x-p1x)
// v0y + u*(v1y-v0y) + v*(v2y-v0y) + r2*ny + r1*xy_n.y = p1y solve these two for (u,v)
// v0z + u*(v1z-v0z) + v*(v2z-v0z) + r2*nz = p1z + r2 and substitute above for t
// or
// [ (v1y-v0y) (v2y-v0y) ] [ u ] = [ -v0y - r2*ny - r1*xy_n.y + p1y ]
// [ (v1z-v0z) (v2z-v0z) ] [ v ] = [ -v0z - r2*nz + p1z + r2 ]
//
// Y-fiber:
// [ (v1x-v0x) (v2x-v0x) ] [ u ] = [ -v0x - r2*nx - r1*xy_n.x + p1x ]
double a;
double b;
double c = t.p[1].z - t.p[0].z;
double d = t.p[2].z - t.p[0].z;
double e;
double f = -t.p[0].z - normal_length * normal.z + fib.p1.z + center_height;
// note: the xy_normal does not have a z-component, so omitted here.
double u = 0; // u and v are coordinates of the cc-point within the triangle facet
double v = 0;
// a,b,e depend on the fiber:
if (fib.p1.y == fib.p2.y)
{ // XFIBER
a = t.p[1].y - t.p[0].y;
b = t.p[2].y - t.p[0].y;
e = -t.p[0].y - normal_length * normal.y - xy_normal_length * xy_normal.y + fib.p1.y;
if (!GlobalMembers.two_by_two_solver(a, b, c, d, e, f, ref u, ref v))
{
return(result);
}
CCPoint cc = new CCPoint(t.p[0] + u * (t.p[1] - t.p[0]) + v * (t.p[2] - t.p[0]));
cc.type = CCType.FACET;
if (!cc.isInside(t))
{
return(result);
}
// v0x + u*(v1x-v0x) + v*(v2x-v0x) + r2*nx + r1*xy_n.x = p1x + t*(p2x-p1x)
// =>
// t = 1/(p2x-p1x) * ( v0x + r2*nx + r1*xy_n.x - p1x + u*(v1x-v0x) + v*(v2x-v0x) )
Debug.Assert(!GlobalMembers.isZero_tol(fib.p2.x - fib.p1.x)); // guard against division by zero
double tval = (1.0 / (fib.p2.x - fib.p1.x)) * (t.p[0].x + normal_length * normal.x + xy_normal_length * xy_normal.x - fib.p1.x + u * (t.p[1].x - t.p[0].x) + v * (t.p[2].x - t.p[0].x));
if (tval < 0.0 || tval > 1.0)
{
Console.Write("MillingCutter::facetPush() tval= ");
Console.Write(tval);
Console.Write(" error!?\n");
//std::cout << " cutter: " << *this << "\n";
Console.Write(" triangle: ");
Console.Write(t);
Console.Write("\n");
Console.Write(" fiber: ");
Console.Write(fib);
Console.Write("\n");
}
Debug.Assert(tval > 0.0 && tval < 1.0);
i.update(tval, cc);
result = true;
}
else if (fib.p1.x == fib.p2.x)
{ // YFIBER
a = t.p[1].x - t.p[0].x;
b = t.p[2].x - t.p[0].x;
e = -t.p[0].x - normal_length * normal.x - xy_normal_length * xy_normal.x + fib.p1.x;
if (!GlobalMembers.two_by_two_solver(a, b, c, d, e, f, ref u, ref v))
{
return(result);
}
CCPoint cc = new CCPoint(t.p[0] + u * (t.p[1] - t.p[0]) + v * (t.p[2] - t.p[0]));
cc.type = CCType.FACET;
if (!cc.isInside(t))
{
return(result);
}
Debug.Assert(!GlobalMembers.isZero_tol(fib.p2.y - fib.p1.y));
double tval = (1.0 / (fib.p2.y - fib.p1.y)) * (t.p[0].y + normal_length * normal.y + xy_normal_length * xy_normal.y - fib.p1.y + u * (t.p[1].y - t.p[0].y) + v * (t.p[2].y - t.p[0].y));
if (tval < 0.0 || tval > 1.0)
{
Console.Write("MillingCutter::facetPush() tval= ");
Console.Write(tval);
Console.Write(" error!?\n");
Console.Write(" (most probably a user error, the fiber is too short compared to the STL model?)\n");
}
Debug.Assert(tval > 0.0 && tval < 1.0);
i.update(tval, cc);
result = true;
}
else
{
Debug.Assert(false);
}
return(result);
}