/// <summary> /// Determines the distance along axis, if any, that polygon 1 should be shifted by /// to prevent intersection with polygon 2. Null if no intersection along axis. /// </summary> /// <param name="poly1">polygon 1</param> /// <param name="poly2">polygon 2</param> /// <param name="pos1">polygon 1 origin</param> /// <param name="pos2">polygon 2 origin</param> /// <param name="rot1">polygon 1 rotation</param> /// <param name="rot2">polygon 2 rotation</param> /// <param name="axis">Axis to check</param> /// <returns>a number to shift pos1 along axis by to prevent poly1 at pos1 from intersecting poly2 at pos2, or null if no int. along axis</returns> public static float?IntersectMtvAlongAxis(Polygon2 poly1, Polygon2 poly2, Vector2 pos1, Vector2 pos2, Rotation2 rot1, Rotation2 rot2, Vector2 axis) { var proj1 = ProjectAlongAxis(poly1, pos1, rot1, axis); var proj2 = ProjectAlongAxis(poly2, pos2, rot2, axis); return(AxisAlignedLine2.IntersectMtv(proj1, proj2)); }
/// <summary> /// Determines the mtv along axis to move rect at pos1 to prevent intersection with poly at pos2 /// </summary> /// <param name="rect">Rectangle</param> /// <param name="poly">polygon</param> /// <param name="pos1">Origin of rectangle</param> /// <param name="pos2">Origin of polygon</param> /// <param name="rot2">Rotation of the polygon in radians</param> /// <param name="axis">Axis to check</param> /// <returns>Number if rect intersects poly along axis, null otherwise</returns> public static float?IntersectMtvAlongAxis(Rect2 rect, Polygon2 poly, Vector2 pos1, Vector2 pos2, Rotation2 rot2, Vector2 axis) { var proj1 = Rect2.ProjectAlongAxis(rect, pos1, axis); var proj2 = Polygon2.ProjectAlongAxis(poly, pos2, rot2, axis); return(AxisAlignedLine2.IntersectMtv(proj1, proj2)); }
/// <summary> /// Determines the minimum translation vector to be applied to the circle to /// prevent overlap with the rectangle, when they are at their given positions. /// </summary> /// <param name="circle">The circle</param> /// <param name="rect">The rectangle</param> /// <param name="pos1">The top-left of the circles bounding box</param> /// <param name="pos2">The rectangles origin</param> /// <returns>MTV for circle at pos1 to prevent overlap with rect at pos2</returns> public static Tuple <Vector2, float> IntersectMtv(Circle2 circle, Rect2 rect, Vector2 pos1, Vector2 pos2) { // Same as polygon rect, just converted to rects points HashSet <Vector2> checkedAxis = new HashSet <Vector2>(); Vector2 bestAxis = Vector2.Zero; float shortestOverlap = float.MaxValue; Func <Vector2, bool> checkAxis = (axis) => { var standard = Math2.MakeStandardNormal(axis); if (!checkedAxis.Contains(standard)) { checkedAxis.Add(standard); var circleProj = Circle2.ProjectAlongAxis(circle, pos1, axis); var rectProj = Rect2.ProjectAlongAxis(rect, pos2, axis); var mtv = AxisAlignedLine2.IntersectMtv(circleProj, rectProj); if (!mtv.HasValue) { return(false); } if (Math.Abs(mtv.Value) < Math.Abs(shortestOverlap)) { bestAxis = axis; shortestOverlap = mtv.Value; } } return(true); }; var circleCenter = new Vector2(pos1.X + circle.Radius, pos1.Y + circle.Radius); int last = 4; var lastVec = rect.UpperRight + pos2; for (int curr = 0; curr < 4; curr++) { Vector2 currVec = Vector2.Zero; switch (curr) { case 0: currVec = rect.Min + pos2; break; case 1: currVec = rect.LowerLeft + pos2; break; case 2: currVec = rect.Max + pos2; break; case 3: currVec = rect.UpperRight + pos2; break; } // Test along circle center -> vector if (!checkAxis(Vector2.Normalize(currVec - circleCenter))) { return(null); } // Test along line normal if (!checkAxis(Vector2.Normalize(Math2.Perpendicular(currVec - lastVec)))) { return(null); } last = curr; lastVec = currVec; } return(Tuple.Create(bestAxis, shortestOverlap)); }
/// <summary> /// Determines the minimum translation that must be applied the specified polygon (at the given position /// and rotation) to prevent intersection with the circle (at its given rotation). If the two are not overlapping, /// returns null. /// /// Returns a tuple of the axis to move the polygon in (unit vector) and the distance to move the polygon. /// </summary> /// <param name="poly">The polygon</param> /// <param name="circle">The circle</param> /// <param name="pos1">The origin of the polygon</param> /// <param name="pos2">The top-left of the circles bounding box</param> /// <param name="rot1">The rotation of the polygon</param> /// <returns></returns> public static Tuple <Vector2, float> IntersectMtv(Polygon2 poly, Circle2 circle, Vector2 pos1, Vector2 pos2, Rotation2 rot1) { // We have two situations, either the circle is not strictly intersecting the polygon, or // there exists at least one shortest line that you could push the polygon to prevent // intersection with the circle. // That line will either go from a vertix of the polygon to a point on the edge of the circle, // or it will go from a point on a line of the polygon to the edge of the circle. // If the line comes from a vertix of the polygon, the MTV will be along the line produced // by going from the center of the circle to the vertix, and the distance can be found by // projecting the cirle on that axis and the polygon on that axis and doing 1D overlap. // If the line comes from a point on the edge of the polygon, the MTV will be along the // normal of that line, and the distance can be found by projecting the circle on that axis // and the polygon on that axis and doing 1D overlap. // As with all SAT, if we find any axis that the circle and polygon do not overlap, we've // proven they do not intersect. // The worst case performance is related to 2x the number of vertices of the polygon, the same speed // as for 2 polygons of equal number of vertices. HashSet <Vector2> checkedAxis = new HashSet <Vector2>(); Vector2 bestAxis = Vector2.Zero; float shortestOverlap = float.MaxValue; Func <Vector2, bool> checkAxis = (axis) => { var standard = Math2.MakeStandardNormal(axis); if (!checkedAxis.Contains(standard)) { checkedAxis.Add(standard); var polyProj = Polygon2.ProjectAlongAxis(poly, pos1, rot1, axis); var circleProj = Circle2.ProjectAlongAxis(circle, pos2, axis); var mtv = AxisAlignedLine2.IntersectMtv(polyProj, circleProj); if (!mtv.HasValue) { return(false); } if (Math.Abs(mtv.Value) < Math.Abs(shortestOverlap)) { bestAxis = axis; shortestOverlap = mtv.Value; } } return(true); }; var circleCenter = new Vector2(pos2.X + circle.Radius, pos2.Y + circle.Radius); int last = poly.Vertices.Length - 1; var lastVec = Math2.Rotate(poly.Vertices[last], poly.Center, rot1) + pos1; for (int curr = 0; curr < poly.Vertices.Length; curr++) { var currVec = Math2.Rotate(poly.Vertices[curr], poly.Center, rot1) + pos1; // Test along circle center -> vector if (!checkAxis(Vector2.Normalize(currVec - circleCenter))) { return(null); } // Test along line normal if (!checkAxis(Vector2.Normalize(Math2.Perpendicular(currVec - lastVec)))) { return(null); } last = curr; lastVec = currVec; } return(Tuple.Create(bestAxis, shortestOverlap)); }