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我有一個線段(x1,y1,x2,y2)與半徑爲r的圓相交。我怎樣才能確定哪個交點最接近(x1,y1)?線段和圓交點
我有一個線段(x1,y1,x2,y2)與半徑爲r的圓相交。我怎樣才能確定哪個交點最接近(x1,y1)?線段和圓交點
要做到這一點首先找到與圓的交點,然後取最接近的一個線起點
所以檢查這個代碼
// CX,CY爲中心圓的點
public PointF ClosestIntersection(float cx, float cy, float radius,
PointF lineStart, PointF lineEnd)
{
PointF intersection1;
PointF intersection2;
int intersections = FindLineCircleIntersections(cx, cy, radius, lineStart, lineEnd, out intersection1, out intersection2);
if (intersections == 1)
return intersection1;//one intersection
if (intersections == 2)
{
double dist1 = Distance(intersection1, lineStart);
double dist2 = Distance(intersection2, lineStart);
if (dist1 < dist2)
return intersection1;
else
return intersection2;
}
return PointF.Empty;// no intersections at all
}
private double Distance(PointF p1, PointF p2)
{
return Math.Sqrt(Math.Pow(p2.X - p1.X, 2) + Math.Pow(p2.Y - p1.Y, 2));
}
// Find the points of intersection.
private int FindLineCircleIntersections(float cx, float cy, float radius,
PointF point1, PointF point2, out PointF intersection1, out PointF intersection2)
{
float dx, dy, A, B, C, det, t;
dx = point2.X - point1.X;
dy = point2.Y - point1.Y;
A = dx * dx + dy * dy;
B = 2 * (dx * (point1.X - cx) + dy * (point1.Y - cy));
C = (point1.X - cx) * (point1.X - cx) + (point1.Y - cy) * (point1.Y - cy) - radius * radius;
det = B * B - 4 * A * C;
if ((A <= 0.0000001) || (det < 0))
{
// No real solutions.
intersection1 = new PointF(float.NaN, float.NaN);
intersection2 = new PointF(float.NaN, float.NaN);
return 0;
}
else if (det == 0)
{
// One solution.
t = -B/(2 * A);
intersection1 = new PointF(point1.X + t * dx, point1.Y + t * dy);
intersection2 = new PointF(float.NaN, float.NaN);
return 1;
}
else
{
// Two solutions.
t = (float)((-B + Math.Sqrt(det))/(2 * A));
intersection1 = new PointF(point1.X + t * dx, point1.Y + t * dy);
t = (float)((-B - Math.Sqrt(det))/(2 * A));
intersection2 = new PointF(point1.X + t * dx, point1.Y + t * dy);
return 2;
}
}
路口代碼的形式在這裏LINK
距離的順序不會被sqrt改變,因此最好讓它們平方以獲得更好的速度。 – Preza8
你能解釋一下「最接近的交點」是什麼意思?這是圓上的一個點嗎?細分市場上的一個點?兩件事都沒有? – andand
這是一個基本的數學問題,將解決方案轉換爲C#非常簡單,並且不會使問題更具相關性。 –
@andand相交點屬於兩條線。 – Dmitry