/// <summary>
/// Finds a large inscribed rectangle. Tries to be maximal but this is
/// best effort. The algorithm used was inspired by the blog post
/// https://d3plus.org/blog/behind-the-scenes/2014/07/08/largest-rect/
/// Random points within the polygon are chosen, and then 2 lines are
/// drawn through those points. The midpoints of those lines are
/// used as the center of various rectangles, using a binary search to
/// vary the size, until the largest fit-able rectangle is found.
/// This is then repeated for predefined angles (0-180 in steps of 15)
/// and aspect ratios (1 to 15 in steps of 0.5).
/// </summary>
/// <param name="geometryEdges">The boundary geometry.</param>
/// <param name="randomSeed">Random number generator seed.</param>
/// <remarks>
/// For the most reproducible results, use the same randomSeed value
/// each time this method is called.
/// </remarks>
public InscribedRectangle(Edge[] geometryEdges, int randomSeed)
{
// Clear previous rectangle
Center = EdgeUtilities.InvalidPoint;
Width = 0;
Height = 0;
Angle = 0;
float minX = EdgeUtilities.maxWidth;
float minY = EdgeUtilities.maxWidth;
float maxX = -EdgeUtilities.maxWidth;
float maxY = -EdgeUtilities.maxWidth;
// Find min x, min y, max x, max y
for (int i = 0; i < geometryEdges.Length; i++)
{
Edge edge = geometryEdges[i];
if ((edge.PointA.x < minX) || (edge.PointB.x < minX))
{
minX = Mathf.Min(edge.PointA.x, edge.PointB.x);
}
if ((edge.PointA.y < minY) || (edge.PointB.y < minY))
{
minY = Mathf.Min(edge.PointA.y, edge.PointB.y);
}
if ((edge.PointA.x > maxX) || (edge.PointB.x > maxX))
{
maxX = Mathf.Max(edge.PointA.x, edge.PointB.x);
}
if ((edge.PointA.y > maxY) || (edge.PointB.y > maxY))
{
maxY = Mathf.Min(edge.PointA.y, edge.PointB.y);
}
}
// Generate random points until we have randomPointCount starting points
Vector2[] startingPoints = new Vector2[randomPointCount];
{
System.Random random = new System.Random(randomSeed);
for (int i = 0; i < startingPoints.Length; i++)
{
Vector2 candidatePoint;
do
{
candidatePoint.x = ((float)random.NextDouble() * (maxX - minX)) + minX;
candidatePoint.y = ((float)random.NextDouble() * (maxY - minY)) + minY;
}while (!EdgeUtilities.IsInsideBoundary(geometryEdges, candidatePoint));
startingPoints[i] = candidatePoint;
}
}
for (int angleIndex = 0; angleIndex < fitAngles.Length; angleIndex++)
{
for (int pointIndex = 0; pointIndex < startingPoints.Length; pointIndex++)
{
float angleRadians = MathUtilities.DegreesToRadians(fitAngles[angleIndex]);
// Find the collision point of a cross through the given point at the given angle.
// Note, we are ignoring the return value as we are checking each point's validity
// individually.
FindSurroundingCollisionPoints(
geometryEdges,
startingPoints[pointIndex],
angleRadians,
out Vector2 topCollisionPoint,
out Vector2 bottomCollisionPoint,
out Vector2 leftCollisionPoint,
out Vector2 rightCollisionPoint);
float newWidth;
float newHeight;
if (EdgeUtilities.IsValidPoint(topCollisionPoint) && EdgeUtilities.IsValidPoint(bottomCollisionPoint))
{
float aX = topCollisionPoint.x;
float aY = topCollisionPoint.y;
float bX = bottomCollisionPoint.x;
float bY = bottomCollisionPoint.y;
// Calculate the midpoint between the top and bottom collision points.
Vector2 verticalMidpoint = new Vector2((aX + bX) * 0.5f, (aY + bY) * 0.5f);
if (TryFixMaximumRectangle(
geometryEdges,
verticalMidpoint,
angleRadians,
Width * Height,
out newWidth,
out newHeight))
{
Center = verticalMidpoint;
Angle = fitAngles[angleIndex];
Width = newWidth;
Height = newHeight;
}
}
if (EdgeUtilities.IsValidPoint(leftCollisionPoint) && EdgeUtilities.IsValidPoint(rightCollisionPoint))
{
float aX = leftCollisionPoint.x;
float aY = leftCollisionPoint.y;
float bX = rightCollisionPoint.x;
float bY = rightCollisionPoint.y;
// Calculate the midpoint between the left and right collision points.
Vector2 horizontalMidpoint = new Vector2((aX + bX) * 0.5f, (aY + bY) * 0.5f);
if (TryFixMaximumRectangle(
geometryEdges,
horizontalMidpoint,
angleRadians,
Width * Height,
out newWidth,
out newHeight))
{
Center = horizontalMidpoint;
Angle = fitAngles[angleIndex];
Width = newWidth;
Height = newHeight;
}
}
}
}
}
/// <summary>
/// Find points at which there are collisions with the geometry around a given point.
/// </summary>
/// <param name="geometryEdges">The boundary geometry.</param>
/// <param name="point">The point around which collisions will be identified.</param>
/// <param name="angleRadians">The angle, in radians, at which the collision points will be oriented.</param>
/// <param name="topCollisionPoint">Receives the coordinates of the upper collision point.</param>
/// <param name="bottomCollisionPoint">Receives the coordinates of the lower collision point.</param>
/// <param name="leftCollisionPoint">Receives the coordinates of the left collision point.</param>
/// <param name="rightCollisionPoint">Receives the coordinates of the right collision point.</param>
/// <returns>
/// True if all of the required collision points are located, false otherwise.
/// If a point is unable to be found, the appropriate out parameter will be set to <see cref="EdgeUtilities.InvalidPoint"/>.
/// </returns>
private bool FindSurroundingCollisionPoints(
Edge[] geometryEdges,
Vector2 point,
float angleRadians,
out Vector2 topCollisionPoint,
out Vector2 bottomCollisionPoint,
out Vector2 leftCollisionPoint,
out Vector2 rightCollisionPoint)
{
// Initialize out parameters.
topCollisionPoint = EdgeUtilities.InvalidPoint;
bottomCollisionPoint = EdgeUtilities.InvalidPoint;
leftCollisionPoint = EdgeUtilities.InvalidPoint;
rightCollisionPoint = EdgeUtilities.InvalidPoint;
// Check to see if the point is inside the geometry.
if (!EdgeUtilities.IsInsideBoundary(geometryEdges, point))
{
return(false);
}
// Define values that are outside of the maximum boundary size.
float largeValue = EdgeUtilities.maxWidth;
float smallValue = -largeValue;
// Find the top and bottom collision points by creating a large line segment that goes through the point to MAX and MIN values on Y
Vector2 topEndpoint = new Vector2(point.x, largeValue);
Vector2 bottomEndpoint = new Vector2(point.x, smallValue);
topEndpoint = RotatePoint(topEndpoint, point, angleRadians);
bottomEndpoint = RotatePoint(bottomEndpoint, point, angleRadians);
Edge verticalLine = new Edge(topEndpoint, bottomEndpoint);
// Find the left and right collision points by creating a large line segment that goes through the point to MAX and Min values on X
Vector2 rightEndpoint = new Vector2(largeValue, point.y);
Vector2 leftEndpoint = new Vector2(smallValue, point.y);
rightEndpoint = RotatePoint(rightEndpoint, point, angleRadians);
leftEndpoint = RotatePoint(leftEndpoint, point, angleRadians);
Edge horizontalLine = new Edge(rightEndpoint, leftEndpoint);
for (int i = 0; i < geometryEdges.Length; i++)
{
// Look for a vertical collision
Vector2 verticalIntersectionPoint = EdgeUtilities.GetIntersectionPoint(geometryEdges[i], verticalLine);
if (EdgeUtilities.IsValidPoint(verticalIntersectionPoint))
{
// Is the intersection above or below the point?
if (RotatePoint(verticalIntersectionPoint, point, -angleRadians).y > point.y)
{
// Update the top collision point
if (!EdgeUtilities.IsValidPoint(topCollisionPoint) ||
(Vector2.SqrMagnitude(point - verticalIntersectionPoint) < Vector2.SqrMagnitude(point - topCollisionPoint)))
{
topCollisionPoint = verticalIntersectionPoint;
}
}
else
{
// Update the bottom collision point
if (!EdgeUtilities.IsValidPoint(bottomCollisionPoint) ||
(Vector2.SqrMagnitude(point - verticalIntersectionPoint) < Vector2.SqrMagnitude(point - bottomCollisionPoint)))
{
bottomCollisionPoint = verticalIntersectionPoint;
}
}
}
// Look for a horizontal collision
Vector2 horizontalIntersection = EdgeUtilities.GetIntersectionPoint(geometryEdges[i], horizontalLine);
if (EdgeUtilities.IsValidPoint(horizontalIntersection))
{
// Is this intersection to the left or the right of the point?
if (RotatePoint(horizontalIntersection, point, -angleRadians).x < point.x)
{
// Update the left collision point
if (!EdgeUtilities.IsValidPoint(leftCollisionPoint) ||
(Vector2.SqrMagnitude(point - horizontalIntersection) < Vector2.SqrMagnitude(point - leftCollisionPoint)))
{
leftCollisionPoint = horizontalIntersection;
}
}
else
{
// Update the right collision point
if (!EdgeUtilities.IsValidPoint(rightCollisionPoint) ||
(Vector2.SqrMagnitude(point - horizontalIntersection) < Vector2.SqrMagnitude(point - rightCollisionPoint)))
{
rightCollisionPoint = horizontalIntersection;
}
}
}
}
// Each corner of the rectangle must intersect with the geometry.
if (!EdgeUtilities.IsValidPoint(topCollisionPoint) ||
!EdgeUtilities.IsValidPoint(bottomCollisionPoint) ||
!EdgeUtilities.IsValidPoint(leftCollisionPoint) ||
!EdgeUtilities.IsValidPoint(rightCollisionPoint))
{
return(false);
}
return(true);
}
