[CSharpTips]判断两条线段是否相交 - ToB企服应用市场:ToB评测及商务社交产业平台

using System;
using System.Collections.Generic;
using System.Windows;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace lineTest
{
class Program
{
public struct Point
{
public double X;
public double Y;
public Point(double x, double y)
{
X = x;
Y = y;
}
}
static void Main(string[] args)
{
Point a = new Point(0, 0);
Point b = new Point(100, 100);
Point c = new Point(100,0);
Point d = new Point(50,49);
var result = IsIntersect(a, b, c, d);
}
public static Point? GetIntersection(Point lineAStart, Point lineAEnd, Point lineBStart, Point lineBEnd)
{
double x1 = lineAStart.X, y1 = lineAStart.Y;
double x2 = lineAEnd.X, y2 = lineAEnd.Y;
double x3 = lineBStart.X, y3 = lineBStart.Y;
double x4 = lineBEnd.X, y4 = lineBEnd.Y;
//equations of the form x=c (two vertical lines)
if (x1 == x2 && x3 == x4 && x1 == x3)
{
return null;
}
//equations of the form y=c (two horizontal lines)
if (y1 == y2 && y3 == y4 && y1 == y3)
{
return null;
}
//equations of the form x=c (two vertical lines)
if (x1 == x2 && x3 == x4)
{
return null;
}
//equations of the form y=c (two horizontal lines)
if (y1 == y2 && y3 == y4)
{
return null;
}
double x, y;
if (x1 == x2)
{
double m2 = (y4 - y3) / (x4 - x3);
double c2 = -m2 * x3 + y3;
x = x1;
y = c2 + m2 * x1;
}
else if (x3 == x4)
{
double m1 = (y2 - y1) / (x2 - x1);
double c1 = -m1 * x1 + y1;
x = x3;
y = c1 + m1 * x3;
}
else
{
//compute slope of line 1 (m1) and c2
double m1 = (y2 - y1) / (x2 - x1);
double c1 = -m1 * x1 + y1;
//compute slope of line 2 (m2) and c2
double m2 = (y4 - y3) / (x4 - x3);
double c2 = -m2 * x3 + y3;
x = (c1 - c2) / (m2 - m1);
y = c2 + m2 * x;
}
if (IsInsideLine(lineAStart, lineAEnd, x, y) &&
IsInsideLine(lineBStart, lineBEnd, x, y))
{
return new Point(x, y);
}
//return default null (no intersection)
return null;
}
private static bool IsInsideLine(Point start, Point end, double x, double y)
{
return ((x >= start.X && x <= end.X)
|| (x >= end.Y && x <= start.Y))
&& ((y >= start.Y && y <= end.Y)
|| (y >= end.Y && y <= start.Y));
}
public static bool IsIntersect(Point p1, Point p2, Point q1, Point q2)
{
//排斥试验，判断p1p2在q1q2为对角线的矩形区之外
if (Math.Max(p1.X, p2.X) < Math.Min(q1.X, q2.X))
{//P1P2中最大的X比Q1Q2中的最小X还要小，说明P1P2在Q1Q2的最左点的左侧，不可能相交。
return false;
}
if (Math.Min(p1.X, p2.X) > Math.Max(q1.X, q2.X))
{//P1P2中最小的X比Q1Q2中的最大X还要大，说明P1P2在Q1Q2的最右点的右侧，不可能相交。
return false;
}
if (Math.Max(p1.Y, p2.Y) < Math.Min(q1.Y, q2.Y))
{//P1P2中最大的Y比Q1Q2中的最小Y还要小，说明P1P2在Q1Q2的最低点的下方，不可能相交。
return false;
}
if (Math.Min(p1.Y, p2.Y) > Math.Max(q1.Y, q2.Y))
{//P1P2中最小的Y比Q1Q2中的最大Y还要大，说明P1P2在Q1Q2的最高点的上方，不可能相交。
return false;
}
//跨立试验
var crossP1P2Q1 = VectorCross(p1, p2, q1);
var crossP1Q2P2 = VectorCross(p1, q2, p2);
var crossQ1Q2P1 = VectorCross(q1, q2, p1);
var crossQ1P2Q2 = VectorCross(q1, p2, q2);
bool isIntersect = (crossP1P2Q1 * crossP1Q2P2 >= 0) && (crossQ1Q2P1 * crossQ1P2Q2 >= 0);
return isIntersect;
}
private static double VectorCross(Point p1, Point p2, Point p3)
{
Vector vectorP1 = new Vector(p1.X, p1.Y);
Vector vectorP2 = new Vector(p2.X, p2.Y);
Vector vectorP3 = new Vector(p3.X, p3.Y);
Vector vectorP1P2 = Vector.Subtract(vectorP2, vectorP1);
Vector vectorP1P3 = Vector.Subtract(vectorP3, vectorP1);
return Vector.CrossProduct(vectorP1P2, vectorP1P3);
}
}
}

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