// Calculate the projection of a polygon on an axis and returns it as a [min, max] interval
public void ProjectPolygon(Vector axis, Polygon polygon, ref float min, ref float max)
{
// To project a point on an axis use the dot product
float d = axis.DotProduct(polygon.Points[0]);
min = d;
max = d;
for (int i = 0; i < polygon.Points.Count; i++)
{
d = polygon.Points[i].DotProduct(axis);
if (d < min)
{
min = d;
}
else
{
if (d > max)
{
max = d;
}
}
}
}
// Check if polygon A is going to collide with polygon B for the given velocity
public PolygonCollisionResult PolygonCollision(Polygon polygonA, Polygon polygonB, Vector velocity)
{
PolygonCollisionResult result = new PolygonCollisionResult();
result.Intersect = false;
result.WillIntersect = true;
int edgeCountA = polygonA.Edges.Count;
int edgeCountB = polygonB.Edges.Count;
float minIntervalDistance = float.PositiveInfinity;
Vector translationAxis = new Vector();
Vector edge;
// Loop through all the edges of both polygons
for (int edgeIndex = 0; edgeIndex < edgeCountA + edgeCountB; edgeIndex++)
{
if (edgeIndex < edgeCountA)
{
edge = polygonA.Edges[edgeIndex];
}
else
{
edge = polygonB.Edges[edgeIndex - edgeCountA];
}
// ===== 1. Find if the polygons are currently intersecting =====
// Find the axis perpendicular to the current edge
Vector axis = new Vector(-edge.Y, edge.X);
axis.Normalize();
// Find the projection of the polygon on the current axis
float minA = 0; float minB = 0; float maxA = 0; float maxB = 0;
ProjectPolygon(axis, polygonA, ref minA, ref maxA);
ProjectPolygon(axis, polygonB, ref minB, ref maxB);
// Check if the polygon projections are currentlty intersecting
//if (IntervalDistance(minA, maxA, minB, maxB) > 0) result.Intersect = false;
// ===== 2. Now find if the polygons *will* intersect =====
// Project the velocity on the current axis
float velocityProjection = axis.DotProduct(velocity);
// Get the projection of polygon A during the movement
if (velocityProjection < 0)
{
minA += velocityProjection;
}
else
{
maxA += velocityProjection;
}
// Do the same test as above for the new projection
float intervalDistance = IntervalDistance(minA, maxA, minB, maxB);
if (intervalDistance > 0) result.WillIntersect = false;
// If the polygons are not intersecting and won't intersect, exit the loop
if (!result.Intersect && !result.WillIntersect) break;
// Check if the current interval distance is the minimum one. If so store
// the interval distance and the current distance.
// This will be used to calculate the minimum translation vector
intervalDistance = Math.Abs(intervalDistance);
if (intervalDistance < minIntervalDistance)
{
minIntervalDistance = intervalDistance;
translationAxis = axis;
Vector d = polygonA.Center - polygonB.Center;
if (d.DotProduct(translationAxis) < 0) translationAxis = -translationAxis;
}
}
// The minimum translation vector can be used to push the polygons appart.
// First moves the polygons by their velocity
// then move polygonA by MinimumTranslationVector.
if (result.WillIntersect) result.MinimumTranslationVector = translationAxis * minIntervalDistance;
return result;
}