using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace CommonLang.Geometry
{
/// <summary>
/// A code container for collision-related mathematical functions.
/// </summary>
static public class CollisionMath
{
/// <summary>
/// Data defining a circle/line collision result.
/// </summary>
/// <remarks>Also used for circle/rectangles.</remarks>
public struct CircleLineCollisionResult
{
public bool Collision;
public Vector2 Point;
public Vector2 Normal;
public float Distance;
}
/// <summary>
/// Determine if two circles intersect or contain each other.
/// </summary>
/// <param name="center1">The center of the first circle.</param>
/// <param name="radius1">The radius of the first circle.</param>
/// <param name="center2">The center of the second circle.</param>
/// <param name="radius2">The radius of the second circle.</param>
/// <returns>True if the circles intersect or contain one another.</returns>
public static bool CircleCircleIntersect(Vector2 center1, float radius1, Vector2 center2, float radius2)
{
Vector2 line = center2 - center1;
// we use LengthSquared to avoid a costly square-root call
return (line.LengthSquared() <= (radius1 + radius2) * (radius1 + radius2));
}
/// <summary>
/// Determines the point of intersection between two line segments,
/// as defined by four points.
/// </summary>
/// <param name="a">The first point on the first line segment.</param>
/// <param name="b">The second point on the first line segment.</param>
/// <param name="c">The first point on the second line segment.</param>
/// <param name="d">The second point on the second line segment.</param>
/// <param name="point">The output value with the interesection, if any.</param>
/// <remarks>The output parameter "point" is only valid
/// when the return value is true.</remarks>
/// <returns>True if intersecting, false otherwise.</returns>
public static bool LineLineIntersect(Vector2 a, Vector2 b, Vector2 c, Vector2 d, out Vector2 point)
{
point = Vector2.Zero;
double r, s;
double denominator = (b.X - a.X) * (d.Y - c.Y) - (b.Y - a.Y) * (d.X - c.X);
// If the denominator in above is zero, AB & CD are colinear
if (denominator == 0)
{
return false;
}
double numeratorR = (a.Y - c.Y) * (d.X - c.X) - (a.X - c.X) * (d.Y - c.Y);
r = numeratorR / denominator;
double numeratorS = (a.Y - c.Y) * (b.X - a.X) - (a.X - c.X) * (b.Y - a.Y);
s = numeratorS / denominator;
// non-intersecting
if (r < 0 || r > 1 || s < 0 || s > 1)
{
return false;
}
// find intersection point
point.X = (float)(a.X + (r * (b.X - a.X)));
point.Y = (float)(a.Y + (r * (b.Y - a.Y)));
return true;
}
public static bool LineLineIntersect(Vector2 a, Vector2 b, Vector2 c, Vector2 d)
{
double r, s;
double denominator = (b.X - a.X) * (d.Y - c.Y) - (b.Y - a.Y) * (d.X - c.X);
// If the denominator in above is zero, AB & CD are colinear
if (denominator == 0)
{
return false;
}
double numeratorR = (a.Y - c.Y) * (d.X - c.X) - (a.X - c.X) * (d.Y - c.Y);
r = numeratorR / denominator;
double numeratorS = (a.Y - c.Y) * (b.X - a.X) - (a.X - c.X) * (b.Y - a.Y);
s = numeratorS / denominator;
// non-intersecting
if (r < 0 || r > 1 || s < 0 || s > 1)
{
return false;
}
return true;
}
/// <summary>
/// Determines if a circle and line segment intersect, and if so, how they do.
/// </summary>
/// <param name="center">The center of the circle.</param>
/// <param name="radius">The radius of the circle.</param>
/// <param name="lineStart">The first point on the line segment.</param>
/// <param name="lineEnd">The second point on the line segment.</param>
/// <param name="result">The result data for the collision.</param>
/// <returns>True if a collision occurs, provided for convenience.</returns>
public static bool CircleLineCollide(Vector2 center, float radius, Vector2 lineStart, Vector2 lineEnd, ref CircleLineCollisionResult result)
{
Vector2 AC = center - lineStart;
Vector2 AB = lineEnd - lineStart;
float ab2 = AB.LengthSquared();
if (ab2 <= 0f)
{
return false;
}
float acab = Vector2.Dot(AC, AB);
float t = acab / ab2;
if (t < 0.0f)
t = 0.0f;
else if (t > 1.0f)
t = 1.0f;
result.Point = lineStart + t * AB;
result.Normal = center - result.Point;
float h2 = result.Normal.LengthSquared();
float r2 = radius * radius;
if ((h2 == 0) || (h2 <= r2))
{
result.Normal.Normalize();
result.Distance = (radius - (center - result.Point).Length());
result.Collision = true;
}
else
{
result.Collision = false;
}
return result.Collision;
}
public static bool CircleLineCollide(Vector2 center, float radius, Vector2 lineStart, Vector2 lineEnd)
{
Vector2 AC = center - lineStart;
Vector2 AB = lineEnd - lineStart;
float ab2 = AB.LengthSquared();
if (ab2 <= 0f)
{
return false;
}
float acab = Vector2.Dot(AC, AB);
float t = acab / ab2;
if (t < 0.0f)
t = 0.0f;
else if (t > 1.0f)
t = 1.0f;
Vector2 resultPoint = lineStart + t * AB;
Vector2 resultNormal = center - resultPoint;
float h2 = resultNormal.LengthSquared();
float r2 = radius * radius;
if ((h2 == 0) || (h2 <= r2))
{
return true;
}
else
{
return false;
}
}
/// <summary>
/// 点在凸多边形内部。
/// </summary>
/// <param name="center"></param>
/// <param name="list"></param>
/// <returns></returns>
public static bool PointInPolygon(Vector2 center, Vector2[] list)
{
int wn = 0, j = 0; //wn 计数器 j第二个
for (int i = 0; i < list.Length; i++)
{
//开始循环
if (i == list.Length - 1)
{
j = 0;//如果 循环到最后一点 第二个指针指向第一点
}
else
{
j = j + 1; //如果不是 ，则找下一点
}
if (list[i].Y <= center.Y) // 如果多边形的点 小于等于 选定点的 Y 坐标
{
if (list[j].Y > center.Y) // 如果多边形的下一点 大于于 选定点的 Y 坐标
{
if (isLeft(list[i], list[j], center) > 0)
{
wn++;
}
}
}
else
{
if (list[j].Y <= center.Y)
{
if (isLeft(list[i], list[j], center) < 0)
{
wn--;
}
}
}
}
if (wn == 0)
{
return false;
}
else
{
return true;
}
}
//判断点在线的一边
public static float isLeft(Vector2 P0, Vector2 P1, Vector2 P2)
{
float abc = ((P1.X - P0.X) * (P2.Y - P0.Y) - (P2.X - P0.X) * (P1.Y - P0.Y));
return abc;
}
public static Vector2 MoveToByRadians(Vector2 p, float degree, float distance)
{
return new Vector2(
p.X + (float)(Math.Cos(degree) * distance),
p.Y + (float)(Math.Sin(degree) * distance));
}
}
}