我目前正在编写 Convex Hull 算法的分而治之版本，它非常接近工作，但在合并两个凸包（以形成整体凸包）时遇到了麻烦。
我正在合并：
我不能 100% 确定这是否是正确的方法 - 任何用于查找组合的上/下船体的指导或伪代码？
【问题讨论】：
标签： java algorithm convex-hull
【讨论】：
虽然这是使用 XNA 库，但您绝对可以将其移植到 Java：
public static class PolygonUnion
{
public static bool PolyUnion(Vector2[] polya, Vector2[] polyb, out Vector2[] union, out Vector2[] intersection)
{
if (!Intersects(polya, polyb))
{
union = polya;
intersection = polyb;
return false;
}
LList a = new LList(polya), b = new LList(polyb);
List<Intersection> intersections = new List<Intersection>();
Vector2 vert;
VNode aNode = a.First, bNode = b.First;
//Find intersection points between the polygons
do
{
do
{
if (EdgeIntersects(aNode.Value, (aNode.Next == null) ? a.First.Value : aNode.Next.Value, bNode.Value,
(bNode.Next == null) ? b.First.Value : bNode.Next.Value, out vert))
{
//An intersection point has been found!
intersections.Add(new Intersection(vert, aNode, bNode, (aNode.Next == null) ? a.First : aNode.Next,
(bNode.Next == null) ? b.First : bNode.Next));
}
bNode = bNode.Next;
}
while (bNode != null);
bNode = b.First;
aNode = aNode.Next;
}
while (aNode != null);
//Perform surgery on these intersections
Intersection i;
for (int j = 0; j < intersections.Count; j++)
{
i = intersections[j];
i.aIn.Next = new VNode(i.Position, i.bOut, i.aIn);
i.bOut.Prev = i.aIn.Next;
i.bIn.Next = new VNode(i.Position, i.aOut, i.bIn);
i.aOut.Prev = i.bIn.Next;
}
//Decompose and simplify polygons into arrays
union = a.ToArray();
intersection = b.ToArray();
//Find exterior polygon
if (union.Length < intersection.Length)
{
//Polygons need swapping!
Vector2[] u = union;
union = intersection;
intersection = u;
}
return true;
}
private class Intersection
{
public Intersection(Vector2 position, VNode aIn, VNode bIn, VNode aOut, VNode bOut)
{
this.aIn = aIn;
this.bIn = bIn;
this.aOut = aOut;
this.bOut = bOut;
this.Position = position;
}
public VNode aIn, bIn, aOut, bOut;
public Vector2 Position;
}
private class LList
{
public LList(Vector2[] poly)
{
First = new VNode(poly[0], null, null);
current = First;
for (int i = 1; i < poly.Length; i++)
{
Add(current, poly[i]);
current = current.Next;
}
current = First;
}
private void Add(VNode prev, Vector2 pos)
{
prev.Next = new VNode(pos, null, prev);
}
public VNode First;
private VNode current;
public Vector2[] ToArray()
{
List<Vector2> ret = new List<Vector2>();
current = First;
int timeout = 1000;
bool starting = true;
while (current != null)
{
if (current.Prev != null && current.Value == current.Prev.Value)
{
current = current.Next;
if (current.Value == current.Next.Value && current.Value == current.Prev.Value) break;
continue;
}
if (!starting && current.Value == First.Value) break;
starting = false;
ret.Add(current.Value);
current = current.Next;
timeout--;
if (timeout <= 0) break;
}
return Simplify(ret.ToArray());
}
}
private class VNode
{
public VNode(Vector2 value, VNode next, VNode prev)
{
Value = value;
Next = next;
Prev = prev;
}
public VNode Next;
public VNode Prev;
public Vector2 Value;
public override string ToString()
{
return Value.ToString();
}
}
private static Vector2[] Simplify(Vector2[] poly)
{
const float tolerance = 25f;//5 pixels tolerance. (5^2 to save sqrt)
if (poly.Length == 0) return poly;
List<Vector2> ret = new List<Vector2>(1);
ret.Add(poly[0]);
float dist;
for (int i = 1; i < poly.Length; i++)
{
dist = (poly[ret.Count - 1] - poly[i]).LengthSquared();
if (dist < tolerance) continue;
if (ret.Contains(poly[i])) continue;
ret.Add(poly[i]);
}
return ret.ToArray();
}
/// <summary>
/// Checks if the line segments intersect.
/// </summary>
private static bool EdgeIntersects(Vector2 x, Vector2 y, Vector2 a, Vector2 b, out Vector2 i)
{
i = Vector2.Zero;
float dx, dy, da, db, t, s;
dx = y.X - x.X;
dy = y.Y - x.Y;
da = b.X - a.X;
db = b.Y - a.Y;
if ((da * dy - db * dx) == 0) return false;
s = (dx * (a.Y - x.Y) + dy * (x.X - a.X)) / (da * dy - db * dx);
t = (da * (x.Y - a.Y) + db * (a.X - x.X)) / (db * dx - da * dy);
i = new Vector2(x.X + t * dx, x.Y + t * dy);
return (bool)(s >= 0 && s <= 1 && t >= 0 && t <= 1);
}
#region Intersection Test
/// <summary>
/// Checks if two polygons intersect.
/// </summary>
public static bool Intersects(Vector2[] aPoints, Vector2[] bPoints)
{
Vector2 edge, axis;
float minA, maxA, minB, maxB, overlap;
//Loop through all edges until a seperating axis is found
for (int x = 0; x < aPoints.Length + bPoints.Length; x++)
{
//Calculate the current edge
if (x < aPoints.Length) edge = aPoints[(x == aPoints.Length - 1 ? 0 : x + 1)] - aPoints[x];
else
{
x -= aPoints.Length;
edge = bPoints[(x == bPoints.Length - 1 ? 0 : x + 1)] - bPoints[x];
x += aPoints.Length;
}
//Find the axis perpendicular to current edge
axis = new Vector2(-edge.Y, edge.X);
axis.Normalize();
//Project the two shapes onto this axis
//Project this
ProjectPoly(aPoints, axis, out maxA, out minA);
ProjectPoly(bPoints, axis, out maxB, out minB);
//Find the overlap between them
if (minA < minB) overlap = minB - maxA;
else overlap = minA - maxB;
//If the overlap is negative then they are overlapping and the smallest
//overlap must be found to find the minumum translation.
//If it is bigger than 0 then they won't overlap at all.
if (overlap < 0) return true;
}
return false;
}
/// <summary>
/// Projects a polygon onto the axis, giving the maximum and minimum positions.
/// </summary>
/// <param name="points">Points that are in world space with origin at the centre</param>
private static void ProjectPoly(Vector2[] points, Vector2 axis, out float max, out float min)
{
//Projecting a point onto an axis uses a dot product.
float dotProduct = Vector2.Dot(axis, points[0]);
min = dotProduct;
max = dotProduct;
//Now project the rest of the polygon...
for (int i = 1; i < points.Length; i++)
{
dotProduct = Vector2.Dot(axis, points[i]);
if (dotProduct < min) min = dotProduct;
else if (dotProduct > max) max = dotProduct;
}
}
#endregion
}
【讨论】：
我不确定你所说的低和高是什么意思，最好指定它是 2D 还是 3D。
对于 2D 凸包。我做了一个算法，根据我的测试，它是最快的（至少是 Chan 的两倍），并且两者都在 O(n log h) 中。
但我的另一个不同之处在于，它支持“在线”喂食。我的意思是您可以一次动态地添加一个点（尚不支持删除）。每一点都保持在 O (log h) 内，这实际上是您可以获得的最快速度。我认为，它也是唯一一个在线并在该性能范围内的。
关于凸包的文章是：Fast and improved 2D Convex Hull algorithm and its implementation in O(n log h)。但是“在线”部分尚未记录。我今天才完成（2018-01-25）。但是所有代码都可以在GitHub 访问。
为简单起见，您只能使用在线部分将任何内容与此代码动态合并（您可以添加凸包点或任何点）：
OuelletConvexHullAvl2Online.ConvexHullOnline convexHullOnline = new OuelletConvexHullAvl2Online.ConvexHullOnline();
foreach (Point pt in points)
{
convexHullOnline.DynamicallyAddAnotherPointToConvexHullIfAppropriate(pt);
}
return convexHullOnline.GetResultsAsArrayOfPoint();
【讨论】：