}//end Solve3
public bool Solve2(double L1, double L2, cPointi target, cPointd J)
{
cPointi c1 = new cPointi(list.head.Point.X, list.head.Point.Y); // center of circle 1
int nsoln; // # of solns: 0,1,2,3(infinite)
nsoln = TwoCircles(c1, L1, target, L2, J);
return(nsoln != 0);
}// end Solve2
}//end Solve
public bool Solve3(double L1, double L2, double L3, cPointi target0)
{
cPointi target;
cPointd Jk; // coords of kinked joint returned by Solve2
cPointi J1; // Joint1 on x-axis
cPointi Ttarget; // translated target
target = new cPointi(target0.X, target0.Y);
System.Diagnostics.Debug.WriteLine("==>Solve3: links = " + L1 + ", " + L2 + ", " + L3);
Jk = new cPointd(0, 0);
if (Solve2(L1 + L2, L3, target, Jk))
{
firstlinks++;
nlinks = 2;
System.Diagnostics.Debug.WriteLine("Solve3: link1=" + (L1 + L2) + ", link2=" + L3 + ", joint=\n");
LineTo_d(Jk);
SetAChain(Jk, target);
return(true);
}
else if (Solve2(L1, L2 + L3, target, Jk))
{
System.Diagnostics.Debug.WriteLine("Solve3: link1= " + L1 + ", link2= " + (L2 + L3) + ", joint=\n");
nlinks = 2;
LineTo_d(Jk);
SetAChain(Jk, target);
return(true);
}
else
{ // pin J0 to 0.
// Shift so J1 is origin.
//J1.x = L1; J1.y = 0;
J1 = new cPointi(L1, 0);
Ttarget = new cPointi(0, 0);
SubVec(target, J1, Ttarget);
if (Solve2(L2, L3, Ttarget, Jk))
{
// Shift solution back to origin.
Jk.x += L1;
System.Diagnostics.Debug.WriteLine("Solve3: link1=" + L1 + ", link2= " + L2 + ", link3= " + L1 + ", joints=\n");
nlinks = 3;
LineTo_i(J1);
LineTo_d(Jk);
SetAChain(Jk, target);
cVertex VJ1 = new cVertex(list.head.Point.X + J1.X, list.head.Point.Y);
list.InsertBefore(VJ1, list.head.NextVertex);
return(true);
}
else
{
return(false);
}
}
}//end Solve3
private bool diagdrawn = true; //diag-s've been drawn after triang?
public cPolygoni(cVertexList list)
{
this.list = list;
listcopy = new cVertexList();
diaglist = new cDiagonalList();
CG = new cPointd(0, 0);
intCount = 0;
diagdrawn = true;
}
/*---------------------------------------------------------------------
* SegSegInt: Finds the point of intersection p between two closed
* segments ab and cd. Returns p and a char with the following meaning:
* 'e': The segments collinearly overlap, sharing a point.
* 'v': An endpoint (vertex) of one segment is on the other segment,
* but 'e' doesn't hold.
* '1': The segments intersect properly (i.e., they share a point and
* neither 'v' nor 'e' holds).
* '0': The segments do not intersect (i.e., they share no points).
* Note that two collinear segments that share just one point, an endpoint
* of each, returns 'e' rather than 'v' as one might expect.
* ---------------------------------------------------------------------*/
public char SegSegInt(cPointi a, cPointi b, cPointi c, cPointi d, cPointd p, cPointd q)
{
double s, t; /* The two parameters of the parametric eqns. */
double num, denom; /* Numerator and denoninator of equations. */
char code = '?'; /* Return char characterizing intersection. */
p.x = p.y = 100.0; /* For testing purposes only... */
denom = a.X * (double)(d.Y - c.Y) +
b.X * (double)(c.Y - d.Y) +
d.X * (double)(b.Y - a.Y) +
c.X * (double)(a.Y - b.Y);
/* If denom is zero, then segments are parallel: handle separately. */
if (denom == 0.0)
{
return(ParallelInt(a, b, c, d, p, q));
}
num = a.X * (double)(d.Y - c.Y) +
c.X * (double)(a.Y - d.Y) +
d.X * (double)(c.Y - a.Y);
if ((num == 0.0) || (num == denom))
{
code = 'v';
}
s = num / denom;
System.Diagnostics.Debug.WriteLine("SegSegInt: num=" + num + ",denom=" + denom + ",s=" + s);
num = -(a.X * (double)(c.Y - b.Y) +
b.X * (double)(a.Y - c.Y) +
c.X * (double)(b.Y - a.Y));
if ((num == 0.0) || (num == denom))
{
code = 'v';
}
t = num / denom;
System.Diagnostics.Debug.WriteLine("SegSegInt: num=" + num + ",denom=" + denom + ",t=" + t);
if ((0.0 < s) && (s < 1.0) &&
(0.0 < t) && (t < 1.0))
{
code = '1';
}
else if ((0.0 > s) || (s > 1.0) ||
(0.0 > t) || (t > 1.0))
{
code = '0';
}
p.x = a.X + s * (b.X - a.X);
p.y = a.Y + s * (b.Y - a.Y);
return(code);
}
//---------------------------------------------------------------------
//TwoCircles00 assumes circle centers are (0,0) and (a2,0).
//---------------------------------------------------------------------
public void TwoCircles00(double r1, double a2, double r2, cPointd p)
{
double r1sq, r2sq;
r1sq = r1 * r1;
r2sq = r2 * r2;
// Return only positive-y soln in p.
p.x = (a2 + (r1sq - r2sq) / a2) / 2;
p.y = Math.Sqrt(r1sq - p.x * p.x);
}//end TwoCircles00
public void SetAChain(cPointd Jk, cPointi target)
{
cPointi vaux1;
cPointi vaux2;
vaux1 = new cPointi(list.head.Point.X, list.head.Point.Y);
vaux2 = new cPointi(target.X, target.Y);
list.ClearVertexList();
list.SetVertex(vaux1.X, vaux1.Y);
list.SetVertex((int)(Jk.x + .5), (int)(Jk.y + .5));
list.SetVertex(vaux2.X, vaux2.Y);
}
}// end Solve2
//---------------------------------------------------------------------
//TwoCircles finds an intersection point between two circles.
//General routine: no assumptions. Returns # of intersections; point in p.
//---------------------------------------------------------------------
public int TwoCircles(cPointi c1, double r1, cPointi c2, double r2, cPointd p)
{
cPointi c;
cPointd q;
int nsoln = -1;
// Translate so that c1={0,0}.
c = new cPointi(0, 0);
SubVec(c2, c1, c);
q = new cPointd(0, 0);
nsoln = TwoCircles0a(r1, c, r2, p);//p instead of
// Translate back.
p.x = p.x + c1.X;
p.y = p.y + c1.Y;
return(nsoln);
}
/*---------------------------------------------------------------------
* Prints out the double point of intersection, and toggles in/out flag.
* ---------------------------------------------------------------------*/
public cInFlag InOut(cPointd p, cInFlag inflag, int aHB, int bHA)
{
InsertInters(p.x, p.y);
/* Update inflag. */
if (aHB > 0)
{
inflag.f = cInFlag.Pin; return(inflag);
}
else if (bHA > 0)
{
inflag.f = cInFlag.Qin; return(inflag);
}
else /* Keep status quo. */
{
return(inflag);
}
}
}//end TwoCircles0a
//---------------------------------------------------------------------
//TwoCircles0b also assumes that the 1st circle is origin-centered.
//---------------------------------------------------------------------
public int TwoCircles0b(double r1, cPointi c2, double r2, cPointd p)
{
double a2; // center of 2nd circle when rotated to x-axis
cPointd q; // one solution when c2 on x-axis
double cost, sint; // sine and cosine of angle of c2
// Rotate c2 to a2 on x-axis.
a2 = Math.Sqrt(Length2(c2));
cost = c2.X / a2;
sint = c2.Y / a2;
q = new cPointd(0, 0);
TwoCircles00(r1, a2, r2, q);
// Rotate back
p.x = cost * q.x + -sint * q.y;
p.y = sint * q.x + cost * q.y;
return(2);
}
//---------------------------------------------------------------------
//TwoCircles0a assumes that the first circle is centered on the origin.
//Returns # of intersections: 0, 1, 2, 3 (inf); point in p.
//-----------------------------------------------------------------------
public int TwoCircles0a(double r1, cPointi c2, double r2, cPointd p)
{
double dc2; // dist to center 2 squared
double rplus2, rminus2; // (r1 +/- r2)^2
double f; // fraction along c2 for nsoln=1
// Handle special cases.
dc2 = Length2(c2);
rplus2 = (r1 + r2) * (r1 + r2);
rminus2 = (r1 - r2) * (r1 - r2);
// No solution if c2 out of reach + or -.
if ((dc2 > rplus2) || (dc2 < rminus2))
{
return(0);
}
// One solution if c2 just reached.
// Then solution is r1-of-the-way (f) to c2.
if (dc2 == rplus2)
{
f = r1 / (double)(r1 + r2);
p.x = f * c2.X; p.y = f * c2.Y;
return(1);
}
if (dc2 == rminus2)
{
if (rminus2 == 0)
{ // Circles coincide.
p.x = r1; p.y = 0;
return(3);
}
f = r1 / (double)(r1 - r2);
p.x = f * c2.X; p.x = f * c2.Y;
return(1);
}
// Two intersections.
int auxint = TwoCircles0b(r1, c2, r2, p);
return(auxint);
}//end TwoCircles0a
//**************************************
public bool Solven(double x, double y)
/*Is called when the user drags the last point of the link or releases it.
* Corresponds to the Solven method in C*/
{
double halfLength; //floor of half os total
cPointi target; //point for storing the target
cPointd Jk; // coords of kinked joint returned by Solve2
cPointi J1; // Joint1 on x-axis
//create target
target = new cPointi(x, y);
//Compute Length array and # of links
cVertex v0;
v1 = list.head;
for (i = 0; i < list.n - 1; i++)
{
linklen[i] = (Length(v1.Point, v1.NextVertex.Point) + .5);
v1 = v1.NextVertex;
}
nlinks = list.n - 1;
//Compute total&half Length
totLength = 0;
for (i = 0; i < nlinks; i++)
{
totLength += linklen[i];
}
halfLength = totLength / 2;
//Find median link
if (nlinks > 2)
{
L1 = 0;
for (m = 0; m < nlinks; m++)
{
if ((L1 + linklen[m]) > halfLength)
{
break;
}
L1 += linklen[m];
}//end for
L2 = linklen[m];
L3 = totLength - L1 - L2;
firstlinks = m;
for (i = 0; i < nlinks; i++)
{
linklenback[i] = linklen[i];
}
nlinksback = nlinks;
}
else if (nlinks == 2)
{
L1 = linklen[0];
L2 = linklen[1];
L3 = 0;
}
else
{
System.Diagnostics.Debug.WriteLine("Just one link!!!");
L1 = L2 = L3 = 0;
}
if ((nlinks == 3) && (nlinksback == 0))
{
nlinksback = 3;
}
if (nlinks == 2)
{
Jk = new cPointd(0, 0);
if (Solve2(L1, L2, target, Jk))
{
System.Diagnostics.Debug.WriteLine("Solve2 for 2 links: link1= " + L1 + ", link2= " + L2 + ", joint=\n");
LineTo_d(Jk);
SetAChain(Jk, target);
return(true);
}
else
{
return(false);
}
}//end if nlinks==2
else
{
if (Solve3(L1, L2, L3, target))
{
return(true);
}
else
{
return(false);
}
}
}//end Solve
public void LineTo_d(cPointd p)
{
System.Diagnostics.Debug.WriteLine(" Line to d" + p.x + ", " + p.y);
}
public void Assigndi(cPointd p, cPointi a)
{
p.x = a.X;
p.y = a.Y;
}
public char ParallelInt(cPointi a, cPointi b, cPointi c, cPointi d, cPointd p, cPointd q)
{
if (!a.Collinear(a, b, c))
{
return('0');
}
if (Between1(a, b, c) && Between1(a, b, d))
{
Assigndi(p, c);
Assigndi(q, d);
return('e');
}
if (Between1(c, d, a) && Between1(c, d, b))
{
Assigndi(p, a);
Assigndi(q, b);
return('e');
}
if (Between1(a, b, c) && Between1(c, d, b))
{
Assigndi(p, c);
Assigndi(q, b);
return('e');
}
if (Between1(a, b, c) && Between1(c, d, a))
{
Assigndi(p, c);
Assigndi(q, a);
return('e');
}
if (Between1(a, b, d) && Between1(c, d, b))
{
Assigndi(p, d);
Assigndi(q, b);
return('e');
}
if (Between1(a, b, d) && Between1(c, d, a))
{
Assigndi(p, d);
Assigndi(q, a);
return('e');
}
return('0');
/*
* if ( Between1( a, b, c ) ) {
* Assigndi( p, c );
* return 'e';
* }
* if ( Between1( a, b, d ) ) {
* Assigndi( p, d );
* return 'e';
* }
* if ( Between1( c, d, a ) ) {
* Assigndi( p, a );
* return 'e';
* }
* if ( Between1( c, d, b ) ) {
* Assigndi( p, b );
* return 'e';
* }
* return '0';
*/
}
/*---------------------------------------------------------------------
* Consult the book for explanations
*--------------------------------------------------------------------*/
private void ConvexIntersect(cVertexList P, cVertexList Q, int n, int m)
/* P has n pointCloud, Q has m pointCloud. */
{
/* Initialize variables. */
a = new cVertex();
b = new cVertex();
a = P.head; b = Q.head;
aa = ba = 0;
Origin = new cPointi(); /* (0,0) */
inflag = new cInFlag();
FirstPoint = true;
cVertex a1, b1;
A = new cPointi();
B = new cPointi();
p = new cPointd();
q = new cPointd();
p0 = new cPointd();
do
{
/* System.Diagnostics.Debug.WriteLine("Before Advances:a="+a.v.x+","+a.v.y+
* ", b="+b.v.x+","+b.v.y+"; aa="+aa+", ba="+ba+"; inflag="+
* inflag.f); */
/* Computations of key variables. */
a1 = a.PrevVertex;
b1 = b.PrevVertex;
SubVec(a.Point, a1.Point, A);
SubVec(b.Point, b1.Point, B);
cross = Origin.TriangleSign(Origin, A, B);
aHB = b1.Point.TriangleSign(b1.Point, b.Point, a.Point);
bHA = a1.Point.TriangleSign(a1.Point, a.Point, b.Point);
System.Diagnostics.Debug.WriteLine("cross=" + cross + ", aHB=" + aHB + ", bHA=" + bHA);
/* If A & B intersect, update inflag. */
code = a1.Point.SegSegInt(a1.Point, a.Point, b1.Point, b.Point, p, q);
System.Diagnostics.Debug.WriteLine("SegSegInt: code = " + code);
if (code == '1' || code == 'v')
{
if (inflag.f == cInFlag.Unknown && FirstPoint)
{
aa = ba = 0;
FirstPoint = false;
p0.x = p.x; p0.y = p.y;
InsertInters(p0.x, p0.y);
}
inflag = InOut(p, inflag, aHB, bHA);
System.Diagnostics.Debug.WriteLine("InOut sets inflag=" + inflag.f);
}
/*-----Advance rules-----*/
/* Special case: A & B overlap and oppositely oriented. */
if ((code == 'e') && (Dot(A, B) < 0))
{
InsertSharedSeg(p, q);
return;
}
/* Special case: A & B parallel and separated. */
if ((cross == 0) && (aHB < 0) && (bHA < 0))
{
System.Diagnostics.Debug.WriteLine("P and Q are disjoint.");
return;
}
/* Special case: A & B collinear. */
else if ((cross == 0) && (aHB == 0) && (bHA == 0))
{
/* Advance but do not output point. */
if (inflag.f == cInFlag.Pin)
{
b = Advance(b, "ba", inflag.f == cInFlag.Qin, b.Point);
}
else
{
a = Advance(a, "aa", inflag.f == cInFlag.Pin, a.Point);
}
}
/* Generic cases. */
else if (cross >= 0)
{
if (bHA > 0)
{
a = Advance(a, "aa", inflag.f == cInFlag.Pin, a.Point);
}
else
{
b = Advance(b, "ba", inflag.f == cInFlag.Qin, b.Point);
}
}
else /* if ( cross < 0 ) */
{
if (aHB > 0)
{
b = Advance(b, "ba", inflag.f == cInFlag.Qin, b.Point);
}
else
{
a = Advance(a, "aa", inflag.f == cInFlag.Pin, a.Point);
}
}
System.Diagnostics.Debug.WriteLine("After advances:a=(" + a.Point.X + ", " + a.Point.Y +
"), b=(" + b.Point.X + ", " + b.Point.Y + "); aa=" + aa +
", ba=" + ba + "; inflag=" + inflag.f);
/* Quit when both adv. indices have cycled, or one has cycled twice. */
} while (((aa < n) || (ba < m)) && (aa < 2 * n) && (ba < 2 * m));
if (!FirstPoint) /* If at least one point output, close up. */
{
InsertInters(p0.x, p0.y);
}
/* Deal with special cases: not implemented. */
if (inflag.f == cInFlag.Unknown)
{
System.Diagnostics.Debug.WriteLine("The boundaries of P and Q do not cross.");
intersection = false;
}
}
public void InsertSharedSeg(cPointd p, cPointd q)
{
InsertInters((int)p.x, (int)p.y);
InsertInters((int)q.x, (int)q.y);
}
char code = '0'; /* intersection code returned by SegSegInt*/
public cSegSeg(cVertexList list)
{
p = new cPointd(0, 0);
this.list = list;
}