public static bool LineLineIntersect(Line lineA, Line lineB, out Point intersectPoint)
{
if (lineA.a == 0)
{
return(LineLineIntersect(lineB, lineA, out intersectPoint)); //because the f(y) can return NaN if lineA is vertical...
}
var output = new List <Point>();
float yQuotient = lineA.a * lineB.b - lineB.a * lineA.b;
if (yQuotient == 0)
{
intersectPoint = new Point(float.NaN, float.NaN);
return(false);
}
float yNumerator = lineB.a * lineA.c - lineA.a * lineB.c;
float y = yNumerator / yQuotient;
float x = lineA.fY(y);
intersectPoint = new Point(x, y);
return(true);
}
public static List <Point> LineCircleIntersect(Line line, Circle circle)
{
Vector2 linePointA, linePointB;
float xA = -1;
float yA = line.fX(xA);
float xB, yB;
if (!float.IsNaN(yA))
{
xB = 1;
yB = line.fX(xB);
}
else
{
yA = -1;
xA = line.fY(yA);
yB = 1;
xB = line.fY(yB);
}
linePointA = new Vector2(xA, yA);
linePointB = new Vector2(xB, yB);
//circle is at 0, 0 for this...
var localPA = linePointA - circle.center;
var localPB = linePointB - circle.center;
//http://mathworld.wolfram.com/Circle-LineIntersection.html
float r = circle.radius;
float x1 = localPA.x;
float x2 = localPB.x;
float y1 = localPA.y;
float y2 = localPB.y;
float dx = x2 - x1;
float dy = y2 - y1;
float dr = Mathf.Sqrt((dx * dx) + (dy * dy));
float bigD = x1 * y2 - x2 * y1;
var localIntersects = new List <Point>();
float discriminant = (r * r) * (dr * dr) - (bigD * bigD);
if (!(discriminant < 0))
{
float xNumeratorSummand1 = bigD * dy;
float xNumeratorSummand2 = sgn(dy) * dx * Mathf.Sqrt(discriminant);
float xQuotient = dr * dr;
float yNumeratorSummand1 = -bigD * dx;
float yNumeratorSummand2 = Mathf.Abs(dy) * Mathf.Sqrt(discriminant);
float yQuotient = dr * dr;
localIntersects.Add(new Point(
(xNumeratorSummand1 + xNumeratorSummand2) / xQuotient,
(yNumeratorSummand1 + yNumeratorSummand2) / yQuotient)
);
if (discriminant > 0)
{
localIntersects.Add(new Point(
(xNumeratorSummand1 - xNumeratorSummand2) / xQuotient,
(yNumeratorSummand1 - yNumeratorSummand2) / yQuotient)
);
}
}
var output = new List <Point>();
//revert transformation into local space of circle
foreach (var intersect in localIntersects)
{
output.Add((Vector2)intersect + circle.center);
}
return(output);
//since regular sign function returns 0 at input 0
float sgn(float inputValue)
{
return(inputValue < 0 ? -1 : 1);
}
}
