public static Desmos ToDesmos(this FrontChain frontChain)
{
// roughly estimate the size of the graph
var top = 0;
var bottom = 0;
var right = 0;
var left = 0;
var desmos = new Desmos();
var id = 0;
var current = frontChain.Head;
do
{
var layout = current.Value;
var expression = layout.ToString();
id++;
desmos.Add(id.ToString(), expression);
desmos.AddXY(layout.Center);
left = (int)Math.Min(left, layout.Center.X - layout.Radius);
right = (int)Math.Max(right, layout.Center.X + layout.Radius);
top = (int)Math.Max(top, layout.Center.Y + layout.Radius);
bottom = (int)Math.Min(bottom, layout.Center.Y - layout.Radius);
current = current.Next;
} while (current != frontChain.Head);
desmos.SetBounds(top, left, bottom, right);
return(desmos);
}
private CircularLayoutInfo CalculateEnclosingCircle(IHierarchicalData root, FrontChain frontChain)
{
// Get extreme points by extending the vector from origin to center by the radius
var layouts = frontChain.ToList();
var points = layouts.Select(x => Geometry.MovePointAlongLine(new Point(), x.Center, x.Radius)).ToList();
var layout = GetLayout(root);
Debug.Assert(layout.Center == new Point()); // Since we process bottom up this node was not considered yet.
double radius;
Point center;
if (frontChain.Head.Next == frontChain.Head) // Single element
{
center = frontChain.Head.Value.Center;
radius = frontChain.Head.Value.Radius;
}
else
{
// 2 and 3 points seem to be handled correctly.
Geometry.FindMinimalBoundingCircle(points, out center, out radius);
}
layout.Center = center;
Debug.Assert(Math.Abs(radius) > 0.00001);
layout.Radius = radius * 1.03; // Just a little larger 3%.
return(layout);
// Note that this is not exact. It is a difficult problem.
// We may have a little overlap. The larger the increment in radius
// the smaller this problem gets.
}
/// <summary>
/// Layouting of items starts with arranging the first three items around the center 0,0
/// Note that we do not set the radius. The radius was determined for the leaf nodes before.
/// The non leaf nodes don't reflect the sum of the children (area metric!).
/// </summary>
private FrontChain InitializeFrontChain(List <IHierarchicalData> children)
{
var frontChain = new FrontChain();
var left = new CircularLayoutInfo();
var right = new CircularLayoutInfo();
var top = new CircularLayoutInfo();
IHierarchicalData child;
if (children.Count >= 1)
{
// Left
child = children[0];
left = GetLayout(child);
// If child has children its origin is not (0,0) any more. So move this node to origin first.
var displacement = -(Vector)left.Center + new Vector(-left.Radius, 0);
left.Move(displacement);
}
if (children.Count >= 2)
{
// Right
child = children[1];
right = GetLayout(child);
// If child has children its origin is not (0,0) any more. So move this node to origin first.
var displacement = -(Vector)right.Center + new Vector(right.Radius, 0);
right.Move(displacement);
}
if (children.Count >= 3)
{
// Top
child = children[2];
top = GetLayout(child);
var solutions = Geometry.FindCircleCircleIntersections(
left.Center, left.Radius + top.Radius,
right.Center, right.Radius + top.Radius,
out var solution1, out var solution2);
// If not maybe you did not remove zero weights?
Debug.Assert(solutions == 2);
var solution = solution1.Y > solution2.Y ? solution1 : solution2;
var displacement = -(Vector)top.Center + (Vector)solution;
top.Move(displacement);
}
// This order makes a huge difference.
// left -> right -> top did not work and leads to overlapping circles!
frontChain.Add(left);
frontChain.Add(top);
frontChain.Add(right);
return(frontChain);
}
public static void WriteDebugOutput(FrontChain frontChain, string extra, params CircularLayoutInfo[] proposedSolutions)
{
var id = 1;
var d = frontChain.ToDesmos();
foreach (var circle in proposedSolutions)
{
d.Add("solution" + id++, circle.ToString());
}
if (extra == null)
{
d.Write($"d:\\circles_{_dbg:D3}.html");
}
else
{
d.Write($"d:\\circles_{_dbg:D3}_{extra}.html");
}
}
private Node FindOverlappingCircleOnFrontChain(FrontChain frontChain, CircularLayoutInfo tmpCircle)
{
return(frontChain.Find(node => IsOverlapping(node.Value, tmpCircle)));
}
/// <summary>
/// Usually we have two solutions for tangent circles. We have to decide which to use.
/// Theoretically that is the one that is outside the front chain polygon.
/// However there are many edge cases. So I do not have an exact mathematical solution to this problem.
/// Therefore I use different heuristics.
/// </summary>
private CircularLayoutInfo SelectCircle(FrontChain frontChain, CircularLayoutInfo circle1, CircularLayoutInfo circle2)
{
var poly = frontChain.ToList().Select(x => x.Center).ToList();
Debug.Assert(IsPointValid(circle1.Center) || IsPointValid(circle2.Center));
// ----------------------------------------------------------------------------
// If exactly one of the two points is valid that is the solution.
// ----------------------------------------------------------------------------
if (IsPointValid(circle1.Center) && !IsPointValid(circle2.Center))
{
return(circle1);
}
if (!IsPointValid(circle1.Center) && IsPointValid(circle2.Center))
{
return(circle2);
}
// We have two solutions. Which point to chose?
// ----------------------------------------------------------------------------
// If one center is inside and one outside the polygon take the outside.
// ----------------------------------------------------------------------------
var center1Inside = MathHelper.PointInPolygon(poly, circle1.Center.X, circle1.Center.Y);
var center2Inside = MathHelper.PointInPolygon(poly, circle2.Center.X, circle2.Center.Y);
if (center1Inside && !center2Inside)
{
return(circle2);
}
if (!center1Inside && center2Inside)
{
return(circle1);
}
// Both centers outside: Examples\Both_centers_outside_polygon.html.
// Note that the purple circle (center) may also be inside the polygon if it was a little bit smaller.
// Debug.Assert(center2Inside && center2Inside);
// Both centers inside: Examples\Both_centers_inside_polygon.html
// Happens when centers are on the polygon edges.
// Debug.Assert(!center2Inside && !center2Inside);
// ----------------------------------------------------------------------------
// If one circle is crossed by an polygon edge and the other is not,
// take the other.
// ----------------------------------------------------------------------------
var circle1HitByEdge = false;
var circle2HitByEdge = false;
var iter = frontChain.Head;
while (iter != null)
{
var first = iter.Value;
var second = iter.Next.Value;
Point intersect1;
Point intersect2;
// Note we consider a line here, not a line segment
var solutions = MathHelper.FindLineCircleIntersections(circle1.Center.X,
circle1.Center.Y, circle1.Radius, first.Center, second.Center, out intersect1, out intersect2);
if (solutions > 0)
{
circle1HitByEdge |= MathHelper.PointOnLineSegment(first.Center, second.Center, intersect1);
}
if (solutions > 1)
{
circle1HitByEdge |= MathHelper.PointOnLineSegment(first.Center, second.Center, intersect2);
}
solutions = MathHelper.FindLineCircleIntersections(circle2.Center.X,
circle2.Center.Y, circle2.Radius, first.Center, second.Center, out intersect1, out intersect2);
if (solutions > 0)
{
circle2HitByEdge |= MathHelper.PointOnLineSegment(first.Center, second.Center, intersect1);
}
if (solutions > 1)
{
circle2HitByEdge |= MathHelper.PointOnLineSegment(first.Center, second.Center, intersect2);
}
iter = iter.Next;
if (iter == frontChain.Head)
{
// Ensure that the segment from tail to head is also processed.
iter = null;
}
}
if (circle1HitByEdge && !circle2HitByEdge)
{
return(circle2);
}
if (!circle1HitByEdge && circle2HitByEdge)
{
return(circle1);
}
if (DebugEnabled)
{
DebugHelper.WriteDebugOutput(frontChain, "not_sure_which_circle", circle1, circle2);
}
// Still inconclusive which solution to take.
// I choose the one with the largst distance from the origin.
// Background is following example: Inconclusive_solution.html
// I need to get rid of the inner (green) circle If I want to grow outwards.
// In my understanding this inner node is always m. We chose it because it had the smallest distance to the origin.
// My hope is that the selected solution leads to removal of m. Cannot prove it, but I think so.
return(SelectCircleWithLargerDistanceFromOrigin(circle1, circle2));
}
