/// <summary>
/// Constructor for node model
/// </summary>
/// <param name="node1">The first of two nodes the line connects</param>
/// <param name="node2">The second of two nodes that the line connects</param>
/// <param name="color">The color of the line when drawn</param>
public Line(Node node1, Node node2, Color color)
{
if (node1.X < node2.X || node1.X == node2.X && node1.Y < node2.Y)
{
this.node1 = node1;
this.node2 = node2;
}
else
{
this.node1 = node2;
this.node2 = node1;
}
lineColor = color;
}
/// <summary>
/// Calculates the angle between two nodes
/// </summary>
/// <param name="nodeA">Base node, assumed to be lowest of both nodes</param>
/// <param name="nodeB">Measured node, should be equal to or higher in height than base node</param>
/// <returns>The angle, in degrees, between the two nodes; angle is on [0, 180] degrees</returns>
private double AngleBetweenPoints(Node nodeA, Node nodeB)
{
int yPrime = nodeA.Y - nodeB.Y;
int xPrime = nodeA.X - nodeB.X;
double z = Math.Sqrt(xPrime * xPrime + yPrime * yPrime);
double angle = (180 / Math.PI) * Math.Asin(yPrime / z);
if (xPrime == 0)
{
return 90;
}
else if (xPrime > 0)
{
return 180 - angle;
}
else
{
return angle;
}
}
/// <summary>
/// Draws a single node on the graph
/// </summary>
/// <param name="node">The node to draw</param>
private void DrawNode(Node node)
{
float halfRadius = radius / 2.0f;
using (Graphics g = Graphics.FromImage(self))
{
g.FillRectangle(new SolidBrush(node.NodeColor), node.X - halfRadius, node.Y - halfRadius, 2 * radius, 2 * radius);
}
}
/// <summary>
/// Computes the cross product of three points
/// </summary>
/// <param name="p1">First node</param>
/// <param name="p2">Second node</param>
/// <param name="p3">Third node</param>
/// <returns>Positive number if left turn, negative number if right turn, 0 if co-linear</returns>
private int CrossProduct(Node p1, Node p2, Node p3)
{
return (p3.X - p1.X) * (p2.Y - p1.Y) - (p2.X - p1.X) * (p3.Y - p1.Y);
}
/// <summary>
/// Determines if the line drawn from nodeA to nodeB split the other nodes such that all other nodes fall on one side
/// </summary>
/// <param name="nodes">List of nodes to check</param>
/// <param name="nodeA">First node of potential hull line</param>
/// <param name="nodeB">Second node of potential hull line</param>
/// <returns>True if line from nodeA to nodeB belongs in the Convex Hull</returns>
private bool ComputeStep(List<Node> nodes, Node nodeA, Node nodeB)
{
bool? IsLeftTurnExpected = null;
foreach (Node nodeC in nodes)
{
if (nodeA == nodeC || nodeB == nodeC)
{
continue;
}
int test = CrossProduct(nodeA, nodeB, nodeC);
if (IsLeftTurnExpected == null)
{
IsLeftTurnExpected = (test < 0);
}
if (test == 0)
{
continue;
}
if (IsLeftTurnExpected == true && test > 0)
{
return false;
}
else if (IsLeftTurnExpected == false && test < 0)
{
return false;
}
}
return true;
}
/// <summary>
/// Calculates and sorts a list of nodes by angel
/// </summary>
/// <param name="nodes">The nodes to sort</param>
/// <param name="baseNode">The node to sort with respect to</param>
/// <returns>A list of nodes sorted by angle from the base node counter-clockwise</returns>
private List<Node> SortByAngle(List<Node> nodes, Node baseNode)
{
var nodeAngles = new Dictionary<Node, Double>();
foreach (Node node in nodes)
{
if (node == baseNode)
{
continue;
}
double angle = AngleBetweenPoints(baseNode, node);
nodeAngles.Add(node, angle);
}
List<KeyValuePair<Node, Double>> nodeAngleList = nodeAngles.ToList();
nodeAngleList.Sort(
(firstPair, secondPair) =>
{
return firstPair.Value.CompareTo(secondPair.Value);
});
List<Node> sortedNodes = new List<Node>();
foreach (KeyValuePair<Node, Double> node in nodeAngleList)
{
sortedNodes.Add(node.Key);
}
return sortedNodes;
}