如何知道一条线是否与C#中的平面相交？
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How to know if a line intersects a plane in C#?
提问by Gelu
I have two points (a line segment) and a rectangle. I would like to know how to calculate if the line segment intersects the rectangle.
我有两个点（一个线段）和一个矩形。我想知道如何计算线段是否与矩形相交。
采纳答案by Chris Marasti-Georg
From my "Geometry" class:
从我的“几何”课：
public struct Line
{
public static Line Empty;
private PointF p1;
private PointF p2;
public Line(PointF p1, PointF p2)
{
this.p1 = p1;
this.p2 = p2;
}
public PointF P1
{
get { return p1; }
set { p1 = value; }
}
public PointF P2
{
get { return p2; }
set { p2 = value; }
}
public float X1
{
get { return p1.X; }
set { p1.X = value; }
}
public float X2
{
get { return p2.X; }
set { p2.X = value; }
}
public float Y1
{
get { return p1.Y; }
set { p1.Y = value; }
}
public float Y2
{
get { return p2.Y; }
set { p2.Y = value; }
}
}
public struct Polygon: IEnumerable<PointF>
{
private PointF[] points;
public Polygon(PointF[] points)
{
this.points = points;
}
public PointF[] Points
{
get { return points; }
set { points = value; }
}
public int Length
{
get { return points.Length; }
}
public PointF this[int index]
{
get { return points[index]; }
set { points[index] = value; }
}
public static implicit operator PointF[](Polygon polygon)
{
return polygon.points;
}
public static implicit operator Polygon(PointF[] points)
{
return new Polygon(points);
}
IEnumerator<PointF> IEnumerable<PointF>.GetEnumerator()
{
return (IEnumerator<PointF>)points.GetEnumerator();
}
public IEnumerator GetEnumerator()
{
return points.GetEnumerator();
}
}
public enum Intersection
{
None,
Tangent,
Intersection,
Containment
}
public static class Geometry
{
public static Intersection IntersectionOf(Line line, Polygon polygon)
{
if (polygon.Length == 0)
{
return Intersection.None;
}
if (polygon.Length == 1)
{
return IntersectionOf(polygon[0], line);
}
bool tangent = false;
for (int index = 0; index < polygon.Length; index++)
{
int index2 = (index + 1)%polygon.Length;
Intersection intersection = IntersectionOf(line, new Line(polygon[index], polygon[index2]));
if (intersection == Intersection.Intersection)
{
return intersection;
}
if (intersection == Intersection.Tangent)
{
tangent = true;
}
}
return tangent ? Intersection.Tangent : IntersectionOf(line.P1, polygon);
}
public static Intersection IntersectionOf(PointF point, Polygon polygon)
{
switch (polygon.Length)
{
case 0:
return Intersection.None;
case 1:
if (polygon[0].X == point.X && polygon[0].Y == point.Y)
{
return Intersection.Tangent;
}
else
{
return Intersection.None;
}
case 2:
return IntersectionOf(point, new Line(polygon[0], polygon[1]));
}
int counter = 0;
int i;
PointF p1;
int n = polygon.Length;
p1 = polygon[0];
if (point == p1)
{
return Intersection.Tangent;
}
for (i = 1; i <= n; i++)
{
PointF p2 = polygon[i % n];
if (point == p2)
{
return Intersection.Tangent;
}
if (point.Y > Math.Min(p1.Y, p2.Y))
{
if (point.Y <= Math.Max(p1.Y, p2.Y))
{
if (point.X <= Math.Max(p1.X, p2.X))
{
if (p1.Y != p2.Y)
{
double xinters = (point.Y - p1.Y) * (p2.X - p1.X) / (p2.Y - p1.Y) + p1.X;
if (p1.X == p2.X || point.X <= xinters)
counter++;
}
}
}
}
p1 = p2;
}
return (counter % 2 == 1) ? Intersection.Containment : Intersection.None;
}
public static Intersection IntersectionOf(PointF point, Line line)
{
float bottomY = Math.Min(line.Y1, line.Y2);
float topY = Math.Max(line.Y1, line.Y2);
bool heightIsRight = point.Y >= bottomY &&
point.Y <= topY;
//Vertical line, slope is divideByZero error!
if (line.X1 == line.X2)
{
if (point.X == line.X1 && heightIsRight)
{
return Intersection.Tangent;
}
else
{
return Intersection.None;
}
}
float slope = (line.X2 - line.X1)/(line.Y2 - line.Y1);
bool onLine = (line.Y1 - point.Y) == (slope*(line.X1 - point.X));
if (onLine && heightIsRight)
{
return Intersection.Tangent;
}
else
{
return Intersection.None;
}
}
}
回答by kokos
Do http://mathworld.wolfram.com/Line-LineIntersection.htmlfor the line and each side of the rectangle.
Or: http://mathworld.wolfram.com/Line-PlaneIntersection.html
为直线和矩形的每一边做http://mathworld.wolfram.com/Line-LineIntersection.html。
或：http: //mathworld.wolfram.com/Line-PlaneIntersection.html
回答by Nathan DeWitt
If it is 2d, then all lines are on the only plane.
如果是 2d，那么所有的线都在唯一的平面上。
So, this is basic 3-D geometry. You should be able to do this with a straightforward equation.
所以，这是基本的 3-D 几何。你应该能够用一个简单的等式来做到这一点。
Check out this page:
看看这个页面：
The second solution should be easy to implement, as long as you translate the coordinates of your rectangle into the equation of a plane.
第二种解决方案应该很容易实现，只要您将矩形的坐标转换为平面方程即可。
Furthermore, check that your denominator isn't zero (line doesn't intersect or is contained in the plane).
此外，检查您的分母是否不为零（线不相交或包含在平面中）。
回答by fortran
I hate browsing the MSDN docs (they're awfully slow and weird :-s) but I think they should have something similar to this Java method... and if they haven't, bad for them! XD (btw, it works for segments, not lines).
我讨厌浏览 MSDN 文档（它们非常慢而且很奇怪 :-s），但我认为他们应该有类似于这种 Java 方法的东西……如果没有，对他们不利！XD（顺便说一句，它适用于段，而不是线）。
In any case, you can peek the open source Java SDK to see how is it implemented, maybe you'll learn some new trick (I'm always surprised when I look other people's code)
无论如何，你可以偷看一下开源的Java SDK，看看它是如何实现的，也许你会学到一些新的技巧（看别人的代码总是很惊讶）
回答by Jaguar
since it is missing i'll just add it for completeness
因为它丢失了，我只是为了完整性而添加它
public static Intersection IntersectionOf(Line line1, Line line2)
{
// Fail if either line segment is zero-length.
if (line1.X1 == line1.X2 && line1.Y1 == line1.Y2 || line2.X1 == line2.X2 && line2.Y1 == line2.Y2)
return Intersection.None;
if (line1.X1 == line2.X1 && line1.Y1 == line2.Y1 || line1.X2 == line2.X1 && line1.Y2 == line2.Y1)
return Intersection.Intersection;
if (line1.X1 == line2.X2 && line1.Y1 == line2.Y2 || line1.X2 == line2.X2 && line1.Y2 == line2.Y2)
return Intersection.Intersection;
// (1) Translate the system so that point A is on the origin.
line1.X2 -= line1.X1; line1.Y2 -= line1.Y1;
line2.X1 -= line1.X1; line2.Y1 -= line1.Y1;
line2.X2 -= line1.X1; line2.Y2 -= line1.Y1;
// Discover the length of segment A-B.
double distAB = Math.Sqrt(line1.X2 * line1.X2 + line1.Y2 * line1.Y2);
// (2) Rotate the system so that point B is on the positive X axis.
double theCos = line1.X2 / distAB;
double theSin = line1.Y2 / distAB;
double newX = line2.X1 * theCos + line2.Y1 * theSin;
line2.Y1 = line2.Y1 * theCos - line2.X1 * theSin; line2.X1 = newX;
newX = line2.X2 * theCos + line2.Y2 * theSin;
line2.Y2 = line2.Y2 * theCos - line2.X2 * theSin; line2.X2 = newX;
// Fail if segment C-D doesn't cross line A-B.
if (line2.Y1 < 0 && line2.Y2 < 0 || line2.Y1 >= 0 && line2.Y2 >= 0)
return Intersection.None;
// (3) Discover the position of the intersection point along line A-B.
double posAB = line2.X2 + (line2.X1 - line2.X2) * line2.Y2 / (line2.Y2 - line2.Y1);
// Fail if segment C-D crosses line A-B outside of segment A-B.
if (posAB < 0 || posAB > distAB)
return Intersection.None;
// (4) Apply the discovered position to line A-B in the original coordinate system.
return Intersection.Intersection;
}
note that the method rotates the line segments so as to avoid direction-related problems
请注意，该方法旋转线段以避免与方向相关的问题
回答by Imran
Isn't it possible to check the line against each side of the rectangle using simple line segment formula.
是否可以使用简单的线段公式根据矩形的每一边检查线。
回答by lestival
Use class:
使用类：
System.Drawing.Rectangle
Method:
方法：
IntersectsWith();
