/// <summary>
/// Usually we have two solutions for tangent circles. We have to decide which to use.
/// I assume the polygon goes always in direction m to n.
/// We chose the solution that is outside the polygon. I want to grow outside.
/// 1. Calculate segment m-n
/// 2. Calculate normal vector form
/// 3. Chose m as vector to the segment
/// 4. Use vector normal form to check if solution1 or solution2 is outside or inside.
/// Both scalars may be positive or negative. So I chose the larger on. Not quite sure if this is ok.
/// </summary>
private CircularLayoutInfo SelectCircle(CircularLayoutInfo m, CircularLayoutInfo n, CircularLayoutInfo circle1, CircularLayoutInfo circle2)
{
Debug.Assert(IsPointValid(circle1.Center) || IsPointValid(circle2.Center));
// If only one point is valid, take it
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?
var segment_m_n = m.Center - n.Center;
var anyNormal = new Vector(-segment_m_n.Y, segment_m_n.X)
- new Vector(segment_m_n.Y, -segment_m_n.X);
var value1 = Vector.Multiply(circle1.Center - m.Center, anyNormal);
var value2 = Vector.Multiply(circle2.Center - m.Center, anyNormal);
if (value1 > 0 && value2 < 0)
{
return(circle2);
}
if (value2 > 0 && value1 < 0)
{
return(circle1);
}
return(value1 > value2 ? circle2 : circle1);
}
/// <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);
}
private CircularLayoutInfo GetLayout(IHierarchicalData item)
{
if (item.Layout == null)
{
var layout = new CircularLayoutInfo();
item.Layout = layout;
}
return(item.Layout as CircularLayoutInfo);
}
private CircularLayoutInfo SelectCircleWithLargerDistanceFromOrigin(CircularLayoutInfo circle1, CircularLayoutInfo circle2)
{
Debug.Assert(IsPointValid(circle1.Center) && IsPointValid(circle2.Center));
Debug.Assert(circle1.Radius.Equals(circle2.Radius));
if (((Vector)circle1.Center).Length > ((Vector)circle2.Center).Length)
{
return(circle1);
}
return(circle2);
}
private bool IsOverlapping(CircularLayoutInfo layout1, CircularLayoutInfo layout2)
{
if (layout1 == layout2)
{
return(true);
}
var intersections = Geometry.FindCircleCircleIntersections(layout1.Center, layout1.Radius,
layout2.Center, layout2.Radius, out var intersection1, out var intersection2);
// Two solutions or one circle inside the other.
return(intersections == 2 || intersections == -1);
}
public Node InsertAfter(Node node, CircularLayoutInfo layout)
{
var newNode = new Node(layout);
// Fix new node
newNode.Next = node.Next;
newNode.Previous = node;
// Fix successor
var successor = node.Next;
successor.Previous = newNode;
// Fix node
node.Next = newNode;
return(newNode);
}
/// <summary>
/// Find the circle tangent with the two others.
/// </summary>
private Tuple <CircularLayoutInfo, CircularLayoutInfo> FindTangentCircle(CircularLayoutInfo circle1, CircularLayoutInfo circle2, double radiusOfTangentCircle)
{
var solutions = Geometry.FindCircleCircleIntersections(circle1.Center, circle1.Radius + radiusOfTangentCircle,
circle2.Center, circle2.Radius + radiusOfTangentCircle, out var solution1
, out var solution2);
Debug.Assert(solutions >= 1);
return(new Tuple <CircularLayoutInfo, CircularLayoutInfo>(
new CircularLayoutInfo
{
Center = solution1, Radius = radiusOfTangentCircle
},
new CircularLayoutInfo
{
Center = solution2,
Radius = radiusOfTangentCircle
}));
}
public Node Add(CircularLayoutInfo layout)
{
var newNode = new Node(layout);
if (Head == null)
{
Head = newNode;
newNode.Next = Head;
newNode.Previous = Head;
}
else
{
// Add to the end (before head)
var tail = Head.Previous;
tail.Next = newNode;
newNode.Previous = tail;
newNode.Next = Head;
Head.Previous = newNode;
}
return(newNode);
}
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));
}
public Node(CircularLayoutInfo value)
{
Value = value;
}