Esempio n. 1
0
        private static double RightBreakpoint(RBTreeNode <BeachSection> node, double directrix)
        {
            var rightNode = node.Next;

            //degenerate parabola
            if ((node.Data.Site.Y - directrix).ApproxEqual(0))
            {
                return(node.Data.Site.X);
            }
            //node is the last piece of the beach line
            if (rightNode == null)
            {
                return(double.PositiveInfinity);
            }
            //left node is degenerate
            if ((rightNode.Data.Site.Y - directrix).ApproxEqual(0))
            {
                return(rightNode.Data.Site.X);
            }
            var site      = node.Data.Site;
            var rightSite = rightNode.Data.Site;

            return(ParabolaMath.IntersectParabolaX(site.X, site.Y, rightSite.X, rightSite.Y, directrix));
        }
Esempio n. 2
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        private static double LeftBreakpoint(RBTreeNode <BeachSection> node, double directrix)
        {
            var leftNode = node.Previous;

            //degenerate parabola
            if ((node.Data.Site.Y - directrix).ApproxEqual(0))
            {
                return(node.Data.Site.X);
            }
            //node is the first piece of the beach line
            if (leftNode == null)
            {
                return(double.NegativeInfinity);
            }
            //left node is degenerate
            if ((leftNode.Data.Site.Y - directrix).ApproxEqual(0))
            {
                return(leftNode.Data.Site.X);
            }
            var site     = node.Data.Site;
            var leftSite = leftNode.Data.Site;

            return(ParabolaMath.IntersectParabolaX(leftSite.X, leftSite.Y, site.X, site.Y, directrix));
        }
Esempio n. 3
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        private static void CheckCircle(RBTreeNode <BeachSection> section, MinHeap <FortuneEvent> eventQueue)
        {
            //if (section == null)
            //    return;
            var left  = section.Previous;
            var right = section.Next;

            if (left == null || right == null)
            {
                return;
            }

            var leftSite   = left.Data.Site;
            var centerSite = section.Data.Site;
            var rightSite  = right.Data.Site;

            //if the left arc and right arc are defined by the same
            //focus, the two arcs cannot converge
            if (leftSite == rightSite)
            {
                return;
            }

            // http://mathforum.org/library/drmath/view/55002.html
            // because every piece of this program needs to be demoed in maple >.<

            //MATH HACKS: place center at origin and
            //draw vectors a and c to
            //left and right respectively
            double bx = centerSite.X,
                   by = centerSite.Y,
                   ax = leftSite.X - bx,
                   ay = leftSite.Y - by,
                   cx = rightSite.X - bx,
                   cy = rightSite.Y - by;

            //The center beach section can only dissapear when
            //the angle between a and c is negative
            var d = ax * cy - ay * cx;

            if (d.ApproxGreaterThanOrEqualTo(0))
            {
                return;
            }

            var magnitudeA = ax * ax + ay * ay;
            var magnitudeC = cx * cx + cy * cy;
            var x          = (cy * magnitudeA - ay * magnitudeC) / (2 * d);
            var y          = (ax * magnitudeC - cx * magnitudeA) / (2 * d);

            //add back offset
            var ycenter = y + by;
            //y center is off
            var circleEvent = new FortuneCircleEvent(
                new VPoint(x + bx, ycenter + Math.Sqrt(x * x + y * y)),
                ycenter, section
                );

            section.Data.CircleEvent = circleEvent;
            eventQueue.Insert(circleEvent);
        }
Esempio n. 4
0
        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);
            }
        }