public void TestEvalXAt123()
{
int fX = 1;
int fY = 2;
int directrix = 3;
Assert.AreEqual(5.0 / 2, ParabolaMath.EvalParabola(fX, fY, directrix, 1), Epsilon);
Assert.AreEqual(-95.0 / 2, ParabolaMath.EvalParabola(fX, fY, directrix, 11), Epsilon);
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, -9), ParabolaMath.EvalParabola(fX, fY, directrix, 11), Epsilon);
}
public void TestEvalXAtFOne()
{
int fX = 1;
int fY = 1;
int directrix = 3;
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 1), 2, Epsilon);
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 15), -47, Epsilon);
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 15), ParabolaMath.EvalParabola(fX, fY, directrix, -13), Epsilon);
}
public void Test1()
{
int fX = 0;
int fY = 0;
int directrix = 2;
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 0), 1, Epsilon);
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 10), -24, Epsilon);
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 10), ParabolaMath.EvalParabola(fX, fY, directrix, -10), Epsilon);
}
public void TestEvalXAtFZero()
{
int fX = 0;
int fY = 0;
int directrix = 2;
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 0), 1, EPSILON);
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 10), -24, EPSILON);
Assert.AreEqual(ParabolaMath.EvalParabola(fX, fY, directrix, 10), ParabolaMath.EvalParabola(fX, fY, directrix, -10), EPSILON);
}
internal void AddBeachSection(FortuneSiteEvent siteEvent, MinHeap <FortuneEvent> eventQueue, HashSet <FortuneCircleEvent> deleted, LinkedList <VEdge> edges)
{
var site = siteEvent.Site;
var x = site.X;
var directrix = site.Y;
RBTreeNode <BeachSection> leftSection = null;
RBTreeNode <BeachSection> rightSection = null;
var node = beachLine.Root;
//find the parabola(s) above this site
while (node != null && leftSection == null && rightSection == null)
{
var distanceLeft = LeftBreakpoint(node, directrix) - x;
if (distanceLeft > 0)
{
//the new site is before the left breakpoint
if (node.Left == null)
{
rightSection = node;
}
else
{
node = node.Left;
}
continue;
}
var distanceRight = x - RightBreakpoint(node, directrix);
if (distanceRight > 0)
{
//the new site is after the right breakpoint
if (node.Right == null)
{
leftSection = node;
}
else
{
node = node.Right;
}
continue;
}
//the point lies below the left breakpoint
if (distanceLeft.ApproxEqual(0))
{
leftSection = node.Previous;
rightSection = node;
continue;
}
//the point lies below the right breakpoint
if (distanceRight.ApproxEqual(0))
{
leftSection = node;
rightSection = node.Next;
continue;
}
// distance Right < 0 and distance Left < 0
// this section is above the new site
leftSection = rightSection = node;
}
//our goal is to insert the new node between the
//left and right sections
var section = new BeachSection(site);
//left section could be null, in which case this node is the first
//in the tree
var newSection = beachLine.InsertSuccessor(leftSection, section);
//new beach section is the first beach section to be added
if (leftSection == null && rightSection == null)
{
return;
}
//main case:
//if both left section and right section point to the same valid arc
//we need to split the arc into a left arc and a right arc with our
//new arc sitting in the middle
if (leftSection != null && leftSection == rightSection)
{
//if the arc has a circle event, it was a false alarm.
//remove it
if (leftSection.Data.CircleEvent != null)
{
deleted.Add(leftSection.Data.CircleEvent);
leftSection.Data.CircleEvent = null;
}
//we leave the existing arc as the left section in the tree
//however we need to insert the right section defined by the arc
var copy = new BeachSection(leftSection.Data.Site);
rightSection = beachLine.InsertSuccessor(newSection, copy);
//grab the projection of this site onto the parabola
var y = ParabolaMath.EvalParabola(leftSection.Data.Site.X, leftSection.Data.Site.Y, directrix, x);
var intersection = new VPoint(x, y);
//create the two half edges corresponding to this intersection
var leftEdge = new VEdge(intersection, site, leftSection.Data.Site);
var rightEdge = new VEdge(intersection, leftSection.Data.Site, site);
leftEdge.Neighbor = rightEdge;
//put the edge in the list
edges.AddFirst(leftEdge);
//store the left edge on each arc section
newSection.Data.Edge = leftEdge;
rightSection.Data.Edge = rightEdge;
//store neighbors for delaunay
leftSection.Data.Site.Neighbors.Add(newSection.Data.Site);
newSection.Data.Site.Neighbors.Add(leftSection.Data.Site);
//create circle events
CheckCircle(leftSection, eventQueue);
CheckCircle(rightSection, eventQueue);
}
//site is the last beach section on the beach line
//this can only happen if all previous sites
//had the same y value
else if (leftSection != null && rightSection == null)
{
var start = new VPoint((leftSection.Data.Site.X + site.X) / 2, double.MinValue);
var infEdge = new VEdge(start, leftSection.Data.Site, site);
var newEdge = new VEdge(start, site, leftSection.Data.Site);
newEdge.Neighbor = infEdge;
edges.AddFirst(newEdge);
leftSection.Data.Site.Neighbors.Add(newSection.Data.Site);
newSection.Data.Site.Neighbors.Add(leftSection.Data.Site);
newSection.Data.Edge = newEdge;
//cant check circles since they are colinear
}
//site is directly above a break point
else if (leftSection != null && leftSection != rightSection)
{
//remove false alarms
if (leftSection.Data.CircleEvent != null)
{
deleted.Add(leftSection.Data.CircleEvent);
leftSection.Data.CircleEvent = null;
}
if (rightSection.Data.CircleEvent != null)
{
deleted.Add(rightSection.Data.CircleEvent);
rightSection.Data.CircleEvent = null;
}
//the breakpoint will dissapear if we add this site
//which means we will create an edge
//we treat this very similar to a circle event since
//an edge is finishing at the center of the circle
//created by circumscribing the left center and right
//sites
//bring a to the origin
var leftSite = leftSection.Data.Site;
var ax = leftSite.X;
var ay = leftSite.Y;
var bx = site.X - ax;
var by = site.Y - ay;
var rightSite = rightSection.Data.Site;
var cx = rightSite.X - ax;
var cy = rightSite.Y - ay;
var d = bx * cy - by * cx;
var magnitudeB = bx * bx + by * by;
var magnitudeC = cx * cx + cy * cy;
var vertex = new VPoint(
(cy * magnitudeB - by * magnitudeC) / (2 * d) + ax,
(bx * magnitudeC - cx * magnitudeB) / (2 * d) + ay);
rightSection.Data.Edge.End = vertex;
//next we create a two new edges
newSection.Data.Edge = new VEdge(vertex, site, leftSection.Data.Site);
rightSection.Data.Edge = new VEdge(vertex, rightSection.Data.Site, site);
edges.AddFirst(newSection.Data.Edge);
edges.AddFirst(rightSection.Data.Edge);
//add neighbors for delaunay
newSection.Data.Site.Neighbors.Add(leftSection.Data.Site);
leftSection.Data.Site.Neighbors.Add(newSection.Data.Site);
newSection.Data.Site.Neighbors.Add(rightSection.Data.Site);
rightSection.Data.Site.Neighbors.Add(newSection.Data.Site);
CheckCircle(leftSection, eventQueue);
CheckCircle(rightSection, eventQueue);
}
}
public void AddSection(FortuneSiteEvent siteEvent, MinHeap <FortuneEvent> eventQueue, HashSet <FortuneCircleEvent> deleted, LinkedList <Edge> edges)
{
FortuneSite site = siteEvent.site;
double x = site.x;
double directrix = site.y;
RedBlackTreeNode <BeachSection> leftSection = null;
RedBlackTreeNode <BeachSection> rightSection = null;
RedBlackTreeNode <BeachSection> root = sections.root;
while (root != null && leftSection != null && rightSection != null)
{
double distanceLeft = LeftBreakpoint(root, directrix) - x;
if (distanceLeft > 0)
{
if (root.left == null)
{
rightSection = root;
}
else
{
root = root.left;
}
continue;
}
double distanceRight = x - RightBreakpoint(root, directrix);
if (distanceRight > 0)
{
if (root.right == null)
{
leftSection = root;
}
root = root.right;
continue;
}
if (distanceLeft.ApproxEqual(0))
{
leftSection = root.previous;
rightSection = root;
continue;
}
if (distanceRight.ApproxEqual(0))
{
leftSection = root;
rightSection = root.next;
continue;
}
leftSection = rightSection = root;
}
BeachSection section = new BeachSection(site);
RedBlackTreeNode <BeachSection> newSectionNode = sections.Insert(leftSection, section);
if (leftSection == null && rightSection == null)
{
return;
}
if (leftSection != null && leftSection == rightSection)
{
if (leftSection.data.circleEvent != null)
{
deleted.Add(leftSection.data.circleEvent);
leftSection.data.circleEvent = null;
}
BeachSection copy = new BeachSection(leftSection.data.site);
rightSection = sections.Insert(newSectionNode, copy);
double y = ParabolaMath.EvalParabola(leftSection.data.site.x, leftSection.data.site.y, directrix, x);
Point intersection = new Point(x, y);
Edge leftEdge = new Edge(intersection, site, leftSection.data.site);
Edge rightEdge = new Edge(intersection, leftSection.data.site, site);
leftEdge.neighbour = rightEdge;
edges.AddFirst(leftEdge);
newSectionNode.data.edge = leftEdge;
rightSection.data.edge = rightEdge;
leftSection.data.site.neighbours.Add(newSectionNode.data.site);
newSectionNode.data.site.neighbours.Add(leftSection.data.site);
CheckCircle(leftSection, eventQueue);
CheckCircle(rightSection, eventQueue);
}
else if (leftSection != null && rightSection != null)
{
Point start = new Point((leftSection.data.site.x + site.x) / 2, double.MinValue);
Edge infiniteEdge = new Edge(start, leftSection.data.site, site);
Edge newEdge = new Edge(start, site, leftSection.data.site);
newEdge.neighbour = infiniteEdge;
edges.AddFirst(newEdge);
leftSection.data.site.neighbours.Add(newSectionNode.data.site);
newSectionNode.data.site.neighbours.Add(leftSection.data.site);
newSectionNode.data.edge = newEdge;
}
else if (leftSection != null && leftSection != rightSection)
{
if (leftSection.data.circleEvent != null)
{
deleted.Add(leftSection.data.circleEvent);
leftSection.data.circleEvent = null;
}
if (rightSection.data.circleEvent != null)
{
deleted.Add(rightSection.data.circleEvent);
rightSection.data.circleEvent = null;
}
FortuneSite leftSite = leftSection.data.site;
double aX = leftSite.x;
double aY = leftSite.y;
double bX = site.x - aX;
double bY = site.y - aY;
FortuneSite rightSite = rightSection.data.site;
double cX = rightSite.x - aX;
double cY = rightSite.y - aY;
double delta = bX * cY - bY * cX;
double magnitudeB = bX * bX + bY * bY;
double magnitudeC = cX * cX + cY * cY;
Point vertex = new Point(
(cY * magnitudeB - bY * magnitudeC) / (2 * delta) + aX,
(bX * magnitudeC - cX * magnitudeB) / (2 * delta) + aY
);
rightSection.data.edge.end = vertex;
newSectionNode.data.edge = new Edge(vertex, site, leftSection.data.site);
rightSection.data.edge = new Edge(vertex, rightSection.data.site, site);
edges.AddFirst(newSectionNode.data.edge);
edges.AddFirst(rightSection.data.edge);
newSectionNode.data.site.neighbours.Add(leftSection.data.site);
leftSection.data.site.neighbours.Add(newSectionNode.data.site);
newSectionNode.data.site.neighbours.Add(rightSection.data.site);
rightSection.data.site.neighbours.Add(newSectionNode.data.site);
CheckCircle(leftSection, eventQueue);
CheckCircle(rightSection, eventQueue);
}
}