/// <summary>
/// 射线与圆相交交点
/// </summary>
/// <param name="rayOrigin"></param>
/// <param name="rayDirection"></param>
/// <param name="circleCenter"></param>
/// <param name="radius"></param>
/// <returns></returns>
public static IntersectionResult RayToCircleIntersection(Vector2 rayOrigin, Vector2 rayDirection, Vector2 circleCenter, float radius)
{
IntersectionResult result = new IntersectionResult();
rayDirection = rayDirection.normalized;
Vector2 rayOriginToCircleCenter = circleCenter - rayOrigin;
float rayOriginToCircleCenterLength = rayOriginToCircleCenter.sqrMagnitude;
float dot = Vector2.Dot(rayDirection, rayOriginToCircleCenter.normalized);
Vector2 pointOnRayVerticalWithCircleCenter = rayOrigin + rayDirection * (dot * Mathf.Sqrt(rayOriginToCircleCenterLength));
float squareDistanceToCenter = Vector2.Dot(pointOnRayVerticalWithCircleCenter - circleCenter, pointOnRayVerticalWithCircleCenter - circleCenter);
if (squareDistanceToCenter > radius * radius)
{
return(result);
}
if (squareDistanceToCenter == radius * radius)
{
result.AddIntersectionPoint(pointOnRayVerticalWithCircleCenter);
return(result);
}
float distanceToIntersection = 0f;
float distanceToCenter = 0f;
if (squareDistanceToCenter == 0)
{
distanceToIntersection = radius;
}
else
{
distanceToCenter = (float)Math.Sqrt(squareDistanceToCenter);
distanceToIntersection = (float)Math.Sqrt(radius * radius - squareDistanceToCenter);
}
float lineSegmentLength = 1 / Mathf.Sqrt(rayOriginToCircleCenterLength);
rayOriginToCircleCenter *= lineSegmentLength;
rayOriginToCircleCenter *= distanceToIntersection;
Vector2 solution1 = pointOnRayVerticalWithCircleCenter + rayOriginToCircleCenter;
if (Vector2.Distance(solution1, rayOrigin) > 0)
{
result.AddIntersectionPoint(solution1);
}
Vector2 solution2 = pointOnRayVerticalWithCircleCenter - rayOriginToCircleCenter;
if (Vector2.Distance(solution2, rayOrigin) > 0)
{
result.AddIntersectionPoint(solution2);
}
return(result);
}
/// <summary>
/// 两射线求交点
/// </summary>
/// <param name="rayOrigin1"></param>
/// <param name="rayDirection1"></param>
/// <param name="rayOrigin2"></param>
/// <param name="rayDirection2"></param>
/// <returns></returns>
public static IntersectionResult RayToRayIntersection(Vector2 rayOrigin1, Vector2 rayDirection1, Vector2 rayOrigin2, Vector2 rayDirection2)
{
IntersectionResult result = new IntersectionResult();
rayDirection1 = rayDirection1.normalized;
rayDirection2 = rayDirection2.normalized;
float r, s, d;
if (rayDirection1 != rayDirection2)
{
d = Cross(rayDirection1, rayDirection2);
if (d != 0)
{
Vector2 rayOrigin2ToRayOrigin1 = rayOrigin1 - rayOrigin2;
r = Cross(rayDirection2, rayOrigin2ToRayOrigin1) / d;
s = Cross(rayDirection1, rayOrigin2ToRayOrigin1) / d;
if (r >= 0)
{
if (s >= 0)
{
Vector2 intersectionPoint = rayOrigin1 + rayDirection1 * r;
result.AddIntersectionPoint(intersectionPoint);
}
}
}
}
return(result);
}
/// <summary>
/// 射线与线段的交点
/// </summary>
/// <param name="rayOrigin"></param>
/// <param name="rayDirection"></param>
/// <param name="lineStart"></param>
/// <param name="lineEnd"></param>
/// <returns></returns>
public static IntersectionResult RayToLineSegmentIntersection(Vector2 rayOrigin, Vector2 rayDirection, Vector2 lineStart, Vector2 lineEnd)
{
IntersectionResult result = new IntersectionResult();
Vector2 v1 = rayOrigin - lineStart;
Vector2 v2 = lineEnd - lineStart;
Vector2 v3 = new Vector2(-rayDirection.y, rayDirection.x);
var dot = Vector2.Dot(v2, v3);
if (Math.Abs(dot) < float.Epsilon)
{
return(result);
}
var t1 = Cross(v2, v1) / dot;
var t2 = Vector2.Dot(v1, v3) / dot;
if (t1 >= 0.0 && (t2 >= 0.0 && t2 <= 1.0))
{
result.AddIntersectionPoint(rayOrigin + t1 * rayDirection);
}
return(result);
}
/// <summary>
/// 射线与圆相交交点
/// </summary>
/// <param name="rayOrigin"></param>
/// <param name="rayDirection"></param>
/// <param name="circleCenter"></param>
/// <param name="radius"></param>
/// <returns></returns>
public static IntersectionResult RayToCircleIntersection(Vector2 rayOrigin, Vector2 rayDirection, Vector2 circleCenter, float radius, bool includeRayExtension = false)
{
IntersectionResult result = new IntersectionResult();
Vector2 d = rayOrigin - circleCenter;
float a = Vector2.Dot(rayDirection, rayDirection);
float b = Vector2.Dot(d, rayDirection);
float c = Vector2.Dot(d, d) - radius * radius;
float disc = b * b - a * c;
if (disc < 0.0f)
{
return(result);
}
float sqrtDisc = Mathf.Sqrt(disc);
float invA = 1.0f / a;
float t = (-b - sqrtDisc) * invA;
float s = (-b + sqrtDisc) * invA;
float invRadius = 1.0f / radius;
//相切，一个交点
if (sqrtDisc == 0)
{
if (includeRayExtension)
{
result.AddIntersectionPoint(rayOrigin + t * rayDirection);
}
else
{
if (t > 0)
{
result.AddIntersectionPoint(rayOrigin + t * rayDirection);
}
}
return(result);
}
if (includeRayExtension)
{
result.AddIntersectionPoint(rayOrigin + t * rayDirection);
result.AddIntersectionPoint(rayOrigin + s * rayDirection);
}
else
{
if (t > 0)
{
result.AddIntersectionPoint(rayOrigin + t * rayDirection);
}
if (s > 0)
{
result.AddIntersectionPoint(rayOrigin + s * rayDirection);
}
}
return(result);
}
/// <summary>
/// 两直线求交点
/// </summary>
/// <param name="line1Start"></param>
/// <param name="line1End"></param>
/// <param name="isSegmentLine1"></param>
/// <param name="line2Start"></param>
/// <param name="line2End"></param>
/// <param name="isSegmentLine2"></param>
/// <returns></returns>
public static IntersectionResult LineToLineIntersection(Vector2 line1Start, Vector2 line1End, bool isSegmentLine1, Vector2 line2Start, Vector2 line2End, bool isSegmentLine2)
{
IntersectionResult result = new IntersectionResult();
Vector2 line1Direction = line1End - line1Start;
Vector2 line2Direction = line2End - line2Start;
if (line2Direction != line1Direction)
{
float d = Cross(line1Direction, line2Direction);
if (d != 0)
{
Vector2 line1StartToLine2Start = line2Start - line1Start;
float r = Cross(line1StartToLine2Start, line2Direction) / d;
float s = Cross(line1StartToLine2Start, line1Direction) / d;
Vector2 intersection = default(Vector2);
//两条直线
if (!isSegmentLine1 && !isSegmentLine2)
{
intersection = line1Start + line1Direction * r;
result.AddIntersectionPoint(intersection);
return(result);
}
//两条线段
if (isSegmentLine1 && isSegmentLine2)
{
if (r >= 0 && r <= 1 && s >= 0 && s <= 1)
{
intersection = line1Start + line1Direction * r;
result.AddIntersectionPoint(intersection);
return(result);
}
}
//第一个是线段，第二个是直线
if (isSegmentLine1 && !isSegmentLine2)
{
if (r >= 0 && r <= 1)
{
intersection = line1Start + line1Direction * r;
result.AddIntersectionPoint(intersection);
return(result);
}
}
if (!isSegmentLine1 && isSegmentLine2)
{
if (r >= 0 && r <= 1)
{
intersection = line1Start + line1Direction * r;
result.AddIntersectionPoint(intersection);
return(result);
}
}
}
}
return(result);
}