// Calculate the projection of a polygon on an axis and returns it as a [min, max] interval
private static void ProjectPolygon(FixVec2 axis, FixPolygon polygon, out Fix min, out Fix max)
{
// To project a point on an axis use the dot product
var d = axis.Dot(polygon.Points[0]);
min = d;
max = d;
for (var i = 0; i < polygon.Points.Length; i++)
{
d = polygon.Points[i].Dot(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 static PolygonCollisionResult CheckCollision(FixPolygon polygonA, FixPolygon polygonB, FixVec2 velocity)
{
var result = new PolygonCollisionResult {
Intersect = true, WillIntersect = true
};
var edgeCountA = polygonA.Edges.Length;
var edgeCountB = polygonB.Edges.Length;
var minIntervalDistance = Fix.MaxValue;
var translationAxis = new FixVec2();
// Loop through all the edges of both polygons
for (var edgeIndex = 0; edgeIndex < edgeCountA + edgeCountB; edgeIndex++)
{
var edge = edgeIndex < edgeCountA ? polygonA.Edges[edgeIndex] : polygonB.Edges[edgeIndex - edgeCountA];
// ===== 1. Find if the polygons are currently intersecting =====
// Find the axis perpendicular to the current edge
var axis = new FixVec2(-edge.Y, edge.X).Normalize();
// Find the projection of the polygon on the current axis
Fix minA;
Fix maxA;
Fix minB;
Fix maxB;
ProjectPolygon(axis, polygonA, out minA, out maxA);
ProjectPolygon(axis, polygonB, out minB, out maxB);
// Check if the polygon projections are currently 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
var velocityProjection = axis.Dot(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
var 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 FixVec2
intervalDistance = FixMath.Abs(intervalDistance);
if (intervalDistance < minIntervalDistance)
{
minIntervalDistance = intervalDistance;
translationAxis = axis;
var d = polygonA.Center - polygonB.Center;
if (d.Dot(translationAxis) < 0)
{
translationAxis = -translationAxis;
}
}
}
// The minimum translation FixVec2 can be used to push the polygons apart.
// First moves the polygons by their velocity
// then move polygonA by MinimumTranslationVector.
if (result.WillIntersect)
{
result.MinimumTranslationVector = translationAxis * minIntervalDistance;
}
return(result);
}
