private Point FindNewLocationWithoutMaxAngle(Vertex torg, Vertex tdest, Vertex tapex,
ref double xi, ref double eta, bool offcenter, Otri badotri)
{
double offconstant = behavior.offconstant;
// for calculating the distances of the edges
double xdo, ydo, xao, yao, xda, yda;
double dodist, aodist, dadist;
// for exact calculation
double denominator;
double dx, dy, dxoff, dyoff;
////////////////////////////// HALE'S VARIABLES //////////////////////////////
// keeps the difference of coordinates edge
double xShortestEdge = 0, yShortestEdge = 0, xMiddleEdge, yMiddleEdge, xLongestEdge, yLongestEdge;
// keeps the square of edge lengths
double shortestEdgeDist = 0, middleEdgeDist = 0, longestEdgeDist = 0;
// keeps the vertices according to the angle incident to that vertex in a triangle
Point smallestAngleCorner, middleAngleCorner, largestAngleCorner;
// keeps the type of orientation if the triangle
int orientation = 0;
// keeps the coordinates of circumcenter of itself and neighbor triangle circumcenter
Point myCircumcenter, neighborCircumcenter;
// keeps if bad triangle is almost good or not
int almostGood = 0;
// keeps the cosine of the largest angle
double cosMaxAngle;
bool isObtuse; // 1: obtuse 0: nonobtuse
// keeps the radius of petal
double petalRadius;
// for calculating petal center
double xPetalCtr_1, yPetalCtr_1, xPetalCtr_2, yPetalCtr_2, xPetalCtr, yPetalCtr, xMidOfShortestEdge, yMidOfShortestEdge;
double dxcenter1, dycenter1, dxcenter2, dycenter2;
// for finding neighbor
Otri neighborotri = default(Otri);
double[] thirdPoint = new double[2];
//int neighborNotFound = -1;
bool neighborNotFound;
// for keeping the vertices of the neighbor triangle
Vertex neighborvertex_1;
Vertex neighborvertex_2;
Vertex neighborvertex_3;
// dummy variables
double xi_tmp = 0, eta_tmp = 0;
//vertex thirdVertex;
// for petal intersection
double vector_x, vector_y, xMidOfLongestEdge, yMidOfLongestEdge, inter_x, inter_y;
double[] p = new double[5], voronoiOrInter = new double[4];
bool isCorrect;
// for vector calculations in perturbation
double ax, ay, d;
double pertConst = 0.06; // perturbation constant
double lengthConst = 1; // used at comparing circumcenter's distance to proposed point's distance
double justAcute = 1; // used for making the program working for one direction only
// for smoothing
int relocated = 0;// used to differentiate between calling the deletevertex and just proposing a steiner point
double[] newloc = new double[2]; // new location suggested by smoothing
double origin_x = 0, origin_y = 0; // for keeping torg safe
Otri delotri; // keeping the original orientation for relocation process
// keeps the first and second direction suggested points
double dxFirstSuggestion, dyFirstSuggestion, dxSecondSuggestion, dySecondSuggestion;
// second direction variables
double xMidOfMiddleEdge, yMidOfMiddleEdge;
////////////////////////////// END OF HALE'S VARIABLES //////////////////////////////
Statistic.CircumcenterCount++;
// Compute the circumcenter of the triangle.
xdo = tdest.x - torg.x;
ydo = tdest.y - torg.y;
xao = tapex.x - torg.x;
yao = tapex.y - torg.y;
xda = tapex.x - tdest.x;
yda = tapex.y - tdest.y;
// keeps the square of the distances
dodist = xdo * xdo + ydo * ydo;
aodist = xao * xao + yao * yao;
dadist = (tdest.x - tapex.x) * (tdest.x - tapex.x) +
(tdest.y - tapex.y) * (tdest.y - tapex.y);
// checking if the user wanted exact arithmetic or not
if (Behavior.NoExact)
{
denominator = 0.5 / (xdo * yao - xao * ydo);
}
else
{
// Use the counterclockwise() routine to ensure a positive (and
// reasonably accurate) result, avoiding any possibility of
// division by zero.
denominator = 0.5 / Primitives.CounterClockwise(tdest, tapex, torg);
// Don't count the above as an orientation test.
Statistic.CounterClockwiseCount--;
}
// calculate the circumcenter in terms of distance to origin point
dx = (yao * dodist - ydo * aodist) * denominator;
dy = (xdo * aodist - xao * dodist) * denominator;
// for debugging and for keeping circumcenter to use later
// coordinate value of the circumcenter
myCircumcenter = new Point(torg.x + dx, torg.y + dy);
delotri = badotri; // save for later
///////////////// FINDING THE ORIENTATION OF TRIANGLE //////////////////
// Find the (squared) length of the triangle's shortest edge. This
// serves as a conservative estimate of the insertion radius of the
// circumcenter's parent. The estimate is used to ensure that
// the algorithm terminates even if very small angles appear in
// the input PSLG.
// find the orientation of the triangle, basically shortest and longest edges
orientation = LongestShortestEdge(aodist, dadist, dodist);
//printf("org: (%f,%f), dest: (%f,%f), apex: (%f,%f)\n",torg[0],torg[1],tdest[0],tdest[1],tapex[0],tapex[1]);
/////////////////////////////////////////////////////////////////////////////////////////////
// 123: shortest: aodist // 213: shortest: dadist // 312: shortest: dodist //
// middle: dadist // middle: aodist // middle: aodist //
// longest: dodist // longest: dodist // longest: dadist //
// 132: shortest: aodist // 231: shortest: dadist // 321: shortest: dodist //
// middle: dodist // middle: dodist // middle: dadist //
// longest: dadist // longest: aodist // longest: aodist //
/////////////////////////////////////////////////////////////////////////////////////////////
switch (orientation)
{
case 123: // assign necessary information
/// smallest angle corner: dest
/// largest angle corner: apex
xShortestEdge = xao; yShortestEdge = yao;
xMiddleEdge = xda; yMiddleEdge = yda;
xLongestEdge = xdo; yLongestEdge = ydo;
shortestEdgeDist = aodist;
middleEdgeDist = dadist;
longestEdgeDist = dodist;
smallestAngleCorner = tdest;
middleAngleCorner = torg;
largestAngleCorner = tapex;
break;
case 132: // assign necessary information
/// smallest angle corner: dest
/// largest angle corner: org
xShortestEdge = xao; yShortestEdge = yao;
xMiddleEdge = xdo; yMiddleEdge = ydo;
xLongestEdge = xda; yLongestEdge = yda;
shortestEdgeDist = aodist;
middleEdgeDist = dodist;
longestEdgeDist = dadist;
smallestAngleCorner = tdest;
middleAngleCorner = tapex;
largestAngleCorner = torg;
break;
case 213: // assign necessary information
/// smallest angle corner: org
/// largest angle corner: apex
xShortestEdge = xda; yShortestEdge = yda;
xMiddleEdge = xao; yMiddleEdge = yao;
xLongestEdge = xdo; yLongestEdge = ydo;
shortestEdgeDist = dadist;
middleEdgeDist = aodist;
longestEdgeDist = dodist;
smallestAngleCorner = torg;
middleAngleCorner = tdest;
largestAngleCorner = tapex;
break;
case 231: // assign necessary information
/// smallest angle corner: org
/// largest angle corner: dest
xShortestEdge = xda; yShortestEdge = yda;
xMiddleEdge = xdo; yMiddleEdge = ydo;
xLongestEdge = xao; yLongestEdge = yao;
shortestEdgeDist = dadist;
middleEdgeDist = dodist;
longestEdgeDist = aodist;
smallestAngleCorner = torg;
middleAngleCorner = tapex;
largestAngleCorner = tdest;
break;
case 312: // assign necessary information
/// smallest angle corner: apex
/// largest angle corner: org
xShortestEdge = xdo; yShortestEdge = ydo;
xMiddleEdge = xao; yMiddleEdge = yao;
xLongestEdge = xda; yLongestEdge = yda;
shortestEdgeDist = dodist;
middleEdgeDist = aodist;
longestEdgeDist = dadist;
smallestAngleCorner = tapex;
middleAngleCorner = tdest;
largestAngleCorner = torg;
break;
case 321: // assign necessary information
default: // TODO: is this safe?
/// smallest angle corner: apex
/// largest angle corner: dest
xShortestEdge = xdo; yShortestEdge = ydo;
xMiddleEdge = xda; yMiddleEdge = yda;
xLongestEdge = xao; yLongestEdge = yao;
shortestEdgeDist = dodist;
middleEdgeDist = dadist;
longestEdgeDist = aodist;
smallestAngleCorner = tapex;
middleAngleCorner = torg;
largestAngleCorner = tdest;
break;
}// end of switch
// check for offcenter condition
if (offcenter && (offconstant > 0.0))
{
// origin has the smallest angle
if (orientation == 213 || orientation == 231)
{
// Find the position of the off-center, as described by Alper Ungor.
dxoff = 0.5 * xShortestEdge - offconstant * yShortestEdge;
dyoff = 0.5 * yShortestEdge + offconstant * xShortestEdge;
// If the off-center is closer to destination than the
// circumcenter, use the off-center instead.
/// doubleLY BAD CASE ///
if (dxoff * dxoff + dyoff * dyoff <
(dx - xdo) * (dx - xdo) + (dy - ydo) * (dy - ydo))
{
dx = xdo + dxoff;
dy = ydo + dyoff;
}
/// ALMOST GOOD CASE ///
else
{
almostGood = 1;
}
// destination has the smallest angle
}
else if (orientation == 123 || orientation == 132)
{
// Find the position of the off-center, as described by Alper Ungor.
dxoff = 0.5 * xShortestEdge + offconstant * yShortestEdge;
dyoff = 0.5 * yShortestEdge - offconstant * xShortestEdge;
// If the off-center is closer to the origin than the
// circumcenter, use the off-center instead.
/// doubleLY BAD CASE ///
if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy)
{
dx = dxoff;
dy = dyoff;
}
/// ALMOST GOOD CASE ///
else
{
almostGood = 1;
}
// apex has the smallest angle
}
else
{//orientation == 312 || orientation == 321
// Find the position of the off-center, as described by Alper Ungor.
dxoff = 0.5 * xShortestEdge - offconstant * yShortestEdge;
dyoff = 0.5 * yShortestEdge + offconstant * xShortestEdge;
// If the off-center is closer to the origin than the
// circumcenter, use the off-center instead.
/// doubleLY BAD CASE ///
if (dxoff * dxoff + dyoff * dyoff < dx * dx + dy * dy)
{
dx = dxoff;
dy = dyoff;
}
/// ALMOST GOOD CASE ///
else
{
almostGood = 1;
}
}
}
// if the bad triangle is almost good, apply our approach
if (almostGood == 1)
{
/// calculate cosine of largest angle ///
cosMaxAngle = (middleEdgeDist + shortestEdgeDist - longestEdgeDist) / (2 * Math.Sqrt(middleEdgeDist) * Math.Sqrt(shortestEdgeDist));
if (cosMaxAngle < 0.0)
{
// obtuse
isObtuse = true;
}
else if (Math.Abs(cosMaxAngle - 0.0) <= EPS)
{
// right triangle (largest angle is 90 degrees)
isObtuse = true;
}
else
{
// nonobtuse
isObtuse = false;
}
/// RELOCATION (LOCAL SMOOTHING) ///
/// check for possible relocation of one of triangle's points ///
relocated = DoSmoothing(delotri, torg, tdest, tapex, ref newloc);
/// if relocation is possible, delete that vertex and insert a vertex at the new location ///
if (relocated > 0)
{
Statistic.RelocationCount++;
dx = newloc[0] - torg.x;
dy = newloc[1] - torg.y;
origin_x = torg.x; // keep for later use
origin_y = torg.y;
switch (relocated)
{
case 1:
//printf("Relocate: (%f,%f)\n", torg[0],torg[1]);
mesh.DeleteVertex(ref delotri);
break;
case 2:
//printf("Relocate: (%f,%f)\n", tdest[0],tdest[1]);
delotri.LnextSelf();
mesh.DeleteVertex(ref delotri);
break;
case 3:
//printf("Relocate: (%f,%f)\n", tapex[0],tapex[1]);
delotri.LprevSelf();
mesh.DeleteVertex(ref delotri);
break;
}
}
else
{
// calculate radius of the petal according to angle constraint
// first find the visible region, PETAL
// find the center of the circle and radius
petalRadius = Math.Sqrt(shortestEdgeDist) / (2 * Math.Sin(behavior.MinAngle * Math.PI / 180.0));
/// compute two possible centers of the petal ///
// finding the center
// first find the middle point of smallest edge
xMidOfShortestEdge = (middleAngleCorner.x + largestAngleCorner.x) / 2.0;
yMidOfShortestEdge = (middleAngleCorner.y + largestAngleCorner.y) / 2.0;
// two possible centers
xPetalCtr_1 = xMidOfShortestEdge + Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (middleAngleCorner.y -
largestAngleCorner.y) / Math.Sqrt(shortestEdgeDist);
yPetalCtr_1 = yMidOfShortestEdge + Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (largestAngleCorner.x -
middleAngleCorner.x) / Math.Sqrt(shortestEdgeDist);
xPetalCtr_2 = xMidOfShortestEdge - Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (middleAngleCorner.y -
largestAngleCorner.y) / Math.Sqrt(shortestEdgeDist);
yPetalCtr_2 = yMidOfShortestEdge - Math.Sqrt(petalRadius * petalRadius - (shortestEdgeDist / 4)) * (largestAngleCorner.x -
middleAngleCorner.x) / Math.Sqrt(shortestEdgeDist);
// find the correct circle since there will be two possible circles
// calculate the distance to smallest angle corner
dxcenter1 = (xPetalCtr_1 - smallestAngleCorner.x) * (xPetalCtr_1 - smallestAngleCorner.x);
dycenter1 = (yPetalCtr_1 - smallestAngleCorner.y) * (yPetalCtr_1 - smallestAngleCorner.y);
dxcenter2 = (xPetalCtr_2 - smallestAngleCorner.x) * (xPetalCtr_2 - smallestAngleCorner.x);
dycenter2 = (yPetalCtr_2 - smallestAngleCorner.y) * (yPetalCtr_2 - smallestAngleCorner.y);
// whichever is closer to smallest angle corner, it must be the center
if (dxcenter1 + dycenter1 <= dxcenter2 + dycenter2)
{
xPetalCtr = xPetalCtr_1; yPetalCtr = yPetalCtr_1;
}
else
{
xPetalCtr = xPetalCtr_2; yPetalCtr = yPetalCtr_2;
}
/// find the third point of the neighbor triangle ///
neighborNotFound = GetNeighborsVertex(badotri, middleAngleCorner.x, middleAngleCorner.y,
smallestAngleCorner.x, smallestAngleCorner.y, ref thirdPoint, ref neighborotri);
/// find the circumcenter of the neighbor triangle ///
dxFirstSuggestion = dx; // if we cannot find any appropriate suggestion, we use circumcenter
dyFirstSuggestion = dy;
// if there is a neighbor triangle
if (!neighborNotFound)
{
neighborvertex_1 = neighborotri.Org();
neighborvertex_2 = neighborotri.Dest();
neighborvertex_3 = neighborotri.Apex();
// now calculate neighbor's circumcenter which is the voronoi site
neighborCircumcenter = Primitives.FindCircumcenter(neighborvertex_1, neighborvertex_2, neighborvertex_3,
ref xi_tmp, ref eta_tmp);
/// compute petal and Voronoi edge intersection ///
// in order to avoid degenerate cases, we need to do a vector based calculation for line
vector_x = (middleAngleCorner.y - smallestAngleCorner.y);//(-y, x)
vector_y = smallestAngleCorner.x - middleAngleCorner.x;
vector_x = myCircumcenter.x + vector_x;
vector_y = myCircumcenter.y + vector_y;
// by intersecting bisectors you will end up with the one you want to walk on
// then this line and circle should be intersected
CircleLineIntersection(myCircumcenter.x, myCircumcenter.y, vector_x, vector_y,
xPetalCtr, yPetalCtr, petalRadius, ref p);
/// choose the correct intersection point ///
// calculate middle point of the longest edge(bisector)
xMidOfLongestEdge = (middleAngleCorner.x + smallestAngleCorner.x) / 2.0;
yMidOfLongestEdge = (middleAngleCorner.y + smallestAngleCorner.y) / 2.0;
// we need to find correct intersection point, since line intersects circle twice
isCorrect = ChooseCorrectPoint(xMidOfLongestEdge, yMidOfLongestEdge, p[3], p[4],
myCircumcenter.x, myCircumcenter.y, isObtuse);
// make sure which point is the correct one to be considered
if (isCorrect)
{
inter_x = p[3];
inter_y = p[4];
}
else
{
inter_x = p[1];
inter_y = p[2];
}
/// check if there is a Voronoi vertex between before intersection ///
// check if the voronoi vertex is between the intersection and circumcenter
PointBetweenPoints(inter_x, inter_y, myCircumcenter.x, myCircumcenter.y,
neighborCircumcenter.x, neighborCircumcenter.y, ref voronoiOrInter);
/// determine the point to be suggested ///
if (p[0] > 0.0)
{ // there is at least one intersection point
// if it is between circumcenter and intersection
// if it returns 1.0 this means we have a voronoi vertex within feasible region
if (Math.Abs(voronoiOrInter[0] - 1.0) <= EPS)
{
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, neighborCircumcenter.x, neighborCircumcenter.y))
{
// go back to circumcenter
dxFirstSuggestion = dx;
dyFirstSuggestion = dy;
}
else
{ // we are not creating a bad triangle
// neighbor's circumcenter is suggested
dxFirstSuggestion = voronoiOrInter[2] - torg.x;
dyFirstSuggestion = voronoiOrInter[3] - torg.y;
}
}
else
{ // there is no voronoi vertex between intersection point and circumcenter
if (IsBadTriangleAngle(largestAngleCorner.x, largestAngleCorner.y, middleAngleCorner.x, middleAngleCorner.y, inter_x, inter_y))
{
// if it is inside feasible region, then insert v2
// apply perturbation
// find the distance between circumcenter and intersection point
d = Math.Sqrt((inter_x - myCircumcenter.x) * (inter_x - myCircumcenter.x) +
(inter_y - myCircumcenter.y) * (inter_y - myCircumcenter.y));
// then find the vector going from intersection point to circumcenter
ax = myCircumcenter.x - inter_x;
ay = myCircumcenter.y - inter_y;
ax = ax / d;
ay = ay / d;
// now calculate the new intersection point which is perturbated towards the circumcenter
inter_x = inter_x + ax * pertConst * Math.Sqrt(shortestEdgeDist);
inter_y = inter_y + ay * pertConst * Math.Sqrt(shortestEdgeDist);
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, inter_x, inter_y))
{
// go back to circumcenter
dxFirstSuggestion = dx;
dyFirstSuggestion = dy;
}
else
{
// intersection point is suggested
dxFirstSuggestion = inter_x - torg.x;
dyFirstSuggestion = inter_y - torg.y;
}
}
else
{
// intersection point is suggested
dxFirstSuggestion = inter_x - torg.x;
dyFirstSuggestion = inter_y - torg.y;
}
}
/// if it is an acute triangle, check if it is a good enough location ///
// for acute triangle case, we need to check if it is ok to use either of them
if ((smallestAngleCorner.x - myCircumcenter.x) * (smallestAngleCorner.x - myCircumcenter.x) +
(smallestAngleCorner.y - myCircumcenter.y) * (smallestAngleCorner.y - myCircumcenter.y) >
lengthConst * ((smallestAngleCorner.x - (dxFirstSuggestion + torg.x)) *
(smallestAngleCorner.x - (dxFirstSuggestion + torg.x)) +
(smallestAngleCorner.y - (dyFirstSuggestion + torg.y)) *
(smallestAngleCorner.y - (dyFirstSuggestion + torg.y))))
{
// use circumcenter
dxFirstSuggestion = dx;
dyFirstSuggestion = dy;
}// else we stick to what we have found
}// intersection point
}// if it is on the boundary, meaning no neighbor triangle in this direction, try other direction
/// DO THE SAME THING FOR THE OTHER DIRECTION ///
/// find the third point of the neighbor triangle ///
neighborNotFound = GetNeighborsVertex(badotri, largestAngleCorner.x, largestAngleCorner.y,
smallestAngleCorner.x, smallestAngleCorner.y, ref thirdPoint, ref neighborotri);
/// find the circumcenter of the neighbor triangle ///
dxSecondSuggestion = dx; // if we cannot find any appropriate suggestion, we use circumcenter
dySecondSuggestion = dy;
// if there is a neighbor triangle
if (!neighborNotFound)
{
neighborvertex_1 = neighborotri.Org();
neighborvertex_2 = neighborotri.Dest();
neighborvertex_3 = neighborotri.Apex();
// now calculate neighbor's circumcenter which is the voronoi site
neighborCircumcenter = Primitives.FindCircumcenter(neighborvertex_1, neighborvertex_2, neighborvertex_3,
ref xi_tmp, ref eta_tmp);
/// compute petal and Voronoi edge intersection ///
// in order to avoid degenerate cases, we need to do a vector based calculation for line
vector_x = (largestAngleCorner.y - smallestAngleCorner.y);//(-y, x)
vector_y = smallestAngleCorner.x - largestAngleCorner.x;
vector_x = myCircumcenter.x + vector_x;
vector_y = myCircumcenter.y + vector_y;
// by intersecting bisectors you will end up with the one you want to walk on
// then this line and circle should be intersected
CircleLineIntersection(myCircumcenter.x, myCircumcenter.y, vector_x, vector_y,
xPetalCtr, yPetalCtr, petalRadius, ref p);
/// choose the correct intersection point ///
// calcuwedgeslate middle point of the longest edge(bisector)
xMidOfMiddleEdge = (largestAngleCorner.x + smallestAngleCorner.x) / 2.0;
yMidOfMiddleEdge = (largestAngleCorner.y + smallestAngleCorner.y) / 2.0;
// we need to find correct intersection point, since line intersects circle twice
// this direction is always ACUTE
isCorrect = ChooseCorrectPoint(xMidOfMiddleEdge, yMidOfMiddleEdge, p[3], p[4],
myCircumcenter.x, myCircumcenter.y, false/*(isObtuse+1)%2*/);
// make sure which point is the correct one to be considered
if (isCorrect)
{
inter_x = p[3];
inter_y = p[4];
}
else
{
inter_x = p[1];
inter_y = p[2];
}
/// check if there is a Voronoi vertex between before intersection ///
// check if the voronoi vertex is between the intersection and circumcenter
PointBetweenPoints(inter_x, inter_y, myCircumcenter.x, myCircumcenter.y,
neighborCircumcenter.x, neighborCircumcenter.y, ref voronoiOrInter);
/// determine the point to be suggested ///
if (p[0] > 0.0)
{ // there is at least one intersection point
// if it is between circumcenter and intersection
// if it returns 1.0 this means we have a voronoi vertex within feasible region
if (Math.Abs(voronoiOrInter[0] - 1.0) <= EPS)
{
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, neighborCircumcenter.x, neighborCircumcenter.y))
{
// go back to circumcenter
dxSecondSuggestion = dx;
dySecondSuggestion = dy;
}
else
{ // we are not creating a bad triangle
// neighbor's circumcenter is suggested
dxSecondSuggestion = voronoiOrInter[2] - torg.x;
dySecondSuggestion = voronoiOrInter[3] - torg.y;
}
}
else
{ // there is no voronoi vertex between intersection point and circumcenter
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, inter_x, inter_y))
{
// if it is inside feasible region, then insert v2
// apply perturbation
// find the distance between circumcenter and intersection point
d = Math.Sqrt((inter_x - myCircumcenter.x) * (inter_x - myCircumcenter.x) +
(inter_y - myCircumcenter.y) * (inter_y - myCircumcenter.y));
// then find the vector going from intersection point to circumcenter
ax = myCircumcenter.x - inter_x;
ay = myCircumcenter.y - inter_y;
ax = ax / d;
ay = ay / d;
// now calculate the new intersection point which is perturbated towards the circumcenter
inter_x = inter_x + ax * pertConst * Math.Sqrt(shortestEdgeDist);
inter_y = inter_y + ay * pertConst * Math.Sqrt(shortestEdgeDist);
if (IsBadTriangleAngle(middleAngleCorner.x, middleAngleCorner.y, largestAngleCorner.x, largestAngleCorner.y, inter_x, inter_y))
{
// go back to circumcenter
dxSecondSuggestion = dx;
dySecondSuggestion = dy;
}
else
{
// intersection point is suggested
dxSecondSuggestion = inter_x - torg.x;
dySecondSuggestion = inter_y - torg.y;
}
}
else
{
// intersection point is suggested
dxSecondSuggestion = inter_x - torg.x;
dySecondSuggestion = inter_y - torg.y;
}
}
/// if it is an acute triangle, check if it is a good enough location ///
// for acute triangle case, we need to check if it is ok to use either of them
if ((smallestAngleCorner.x - myCircumcenter.x) * (smallestAngleCorner.x - myCircumcenter.x) +
(smallestAngleCorner.y - myCircumcenter.y) * (smallestAngleCorner.y - myCircumcenter.y) >
lengthConst * ((smallestAngleCorner.x - (dxSecondSuggestion + torg.x)) *
(smallestAngleCorner.x - (dxSecondSuggestion + torg.x)) +
(smallestAngleCorner.y - (dySecondSuggestion + torg.y)) *
(smallestAngleCorner.y - (dySecondSuggestion + torg.y))))
{
// use circumcenter
dxSecondSuggestion = dx;
dySecondSuggestion = dy;
}// else we stick on what we have found
}
}// if it is on the boundary, meaning no neighbor triangle in this direction, the other direction might be ok
if (isObtuse)
{
//obtuse: do nothing
dx = dxFirstSuggestion;
dy = dyFirstSuggestion;
}
else
{ // acute : consider other direction
if (justAcute * ((smallestAngleCorner.x - (dxSecondSuggestion + torg.x)) *
(smallestAngleCorner.x - (dxSecondSuggestion + torg.x)) +
(smallestAngleCorner.y - (dySecondSuggestion + torg.y)) *
(smallestAngleCorner.y - (dySecondSuggestion + torg.y))) >
(smallestAngleCorner.x - (dxFirstSuggestion + torg.x)) *
(smallestAngleCorner.x - (dxFirstSuggestion + torg.x)) +
(smallestAngleCorner.y - (dyFirstSuggestion + torg.y)) *
(smallestAngleCorner.y - (dyFirstSuggestion + torg.y)))
{
dx = dxSecondSuggestion;
dy = dySecondSuggestion;
}
else
{
dx = dxFirstSuggestion;
dy = dyFirstSuggestion;
}
}// end if obtuse
}// end of relocation
}// end of almostGood
Point circumcenter = new Point();
if (relocated <= 0)
{
circumcenter.x = torg.x + dx;
circumcenter.y = torg.y + dy;
}
else
{
circumcenter.x = origin_x + dx;
circumcenter.y = origin_y + dy;
}
xi = (yao * dx - xao * dy) * (2.0 * denominator);
eta = (xdo * dy - ydo * dx) * (2.0 * denominator);
return circumcenter;
}
