///Returns whether a line segment intersects a polygon (given a list of vertices)
public static bool LineSegIntersectsPoly(LineSeg lns, List <Vector2> verts)
{
//Check to see if either end of the segment is in the polygon
if (PointInPoly(lns.CenterA, verts) || PointInPoly(lns.CenterB, verts))
{
return(true);
}
int j = verts.Count - 1;
LineSeg lnsCheck = new LineSeg();
//checks every line segment in the polygon until an intersection is found
for (int i = 0; i < verts.Count; i++)
{
lnsCheck.SetA(verts[i]);
lnsCheck.SetB(verts[j]);
if (LineSegIntersectsLineSeg(lns, lnsCheck))
{
return(true);
}
j = i;
}
return(false);
}
///Returns whether a line segment intersects a circle
public static bool LineSegIntersectsCircle(LineSeg lns, Circle c)
{
//for efficiency, check if either end of the line is in the circle first
if (PointInCircle(lns.CenterA, c) || PointInCircle(lns.CenterB, c))
{
return(true);
}
Vector2 point = Vector2.zero;
//do checks to see whether the slope is 0 or infinite
if (Mathf.Approximately(lns.Slope, 0f))
{
point = new Vector2(c.WorldCenter.x, lns.CenterA.y);
}
else if (lns.Slope == float.PositiveInfinity)
{
point = new Vector2(lns.CenterA.x, c.WorldCenter.y);
}
else
{
//get negative reciprocal of slope of line segment to find a new perpendicular line
float slope = -1f / lns.Slope;
//find the offset that the new line needs to also contain the center of the circle
float offset = -slope * c.WorldCenter.x + c.WorldCenter.y;
//calculate point of intersection between the perpendicular lines
point.x = (lns.Offset - offset) / (slope - lns.Slope);
point.y = slope * point.x + offset;
}
//check if the calculated point is on the line segment and in the circle
return(PointInCircle(point, c) && PointOnLineSeg(point, lns));
}
/* Poly methods */
#region
///Returns whether a polygon intersects another polygon (given a list of vertices)
public static bool PolyIntersectsPoly(List <Vector2> verts1, List <Vector2> verts2)
{
//check to see if any vertices exist inside either polygon (more efficient and catches most cases)
for (int i = 0; i < verts1.Count; i++)
{
Vector2 vert = verts1[i];
if (PointInPoly(vert, verts2))
{
return(true);
}
}
for (int i = 0; i < verts2.Count; i++)
{
Vector2 vert = verts2[i];
if (PointInPoly(vert, new List <Vector2>(verts1)))
{
return(true);
}
}
//check to see if any of the edges of a polygon intersect with the edges of the other
//this code ensures concave shapes work too but it's potentially slow
LineSeg lnsCheck = new LineSeg();
int j = verts1.Count - 1;
for (int i = 0; i < verts1.Count; i++)
{
lnsCheck.SetA(verts1[i]);
lnsCheck.SetB(verts1[j]);
if (LineSegIntersectsPoly(lnsCheck, verts2))
{
return(true);
}
j = i;
}
return(false);
}
///Returns whether a point lies on the perimeter of a polygon given its vertices
public static bool PointOnPolyPerimeter(Vector2 p, List <Vector2> verts)
{
LineSeg lineCheck = new LineSeg();
int j = verts.Count - 1;
//checks every line segment of the polygon to see if the point lies on any segment
for (int i = 0; i < verts.Count; i++)
{
lineCheck.SetA(verts[i]);
lineCheck.SetB(verts[j]);
if (PointOnLineSeg(p, lineCheck))
{
return(true);
}
j = i;
}
return(false);
}
///Returns whether a circle intersects a polygon (given a list of vertices)
public static bool CircleIntersectsPoly(Circle c, List <Vector2> verts)
{
//check to see if the center of the circle is in the poly
if (PointInPoly(c.WorldCenter, verts))
{
return(true);
}
//check to see if any points are in the circle
for (int i = 0; i < verts.Count; i++)
{
Vector2 vert = verts[i];
if (PointInCircle(vert, c))
{
return(true);
}
}
LineSeg lnsCheck = new LineSeg();
int j = verts.Count - 1;
//check each line segment of the polygon until an intersection is found
for (int i = 0; i < verts.Count; i++)
{
lnsCheck.SetA(verts[i]);
lnsCheck.SetB(verts[j]);
if (LineSegIntersectsCircle(lnsCheck, c))
{
return(true);
}
j = i;
}
return(false);
}
/* LineSeg methods */
#region
///Returns whether a line segment intersects another line segment
public static bool LineSegIntersectsLineSeg(LineSeg lns1, LineSeg lns2)
{
//if lines have the same slope (i.e. parallel or collinear)
if (Mathf.Approximately(lns1.Slope, lns2.Slope))
{
//returns whether the ends of either segment lies on either segment
return(PointOnLineSeg(lns1.CenterA, lns2) ||
PointOnLineSeg(lns1.CenterB, lns2) ||
PointOnLineSeg(lns2.CenterA, lns1) ||
PointOnLineSeg(lns2.CenterB, lns1));
}
Vector2 p;
//check to see if either line 1 or 2 are vertical (slope would be infinite)
//slope and offset are needed for slope intercept form calculation (y = mx + b)
if (lns1.Slope == float.PositiveInfinity)
{
p.x = lns1.Offset;
p.y = lns2.Slope * p.x + lns2.Offset;
}
else if (lns2.Slope == float.PositiveInfinity)
{
p.x = lns2.Offset;
p.y = lns1.Slope * p.x + lns1.Offset;
}
else
{
//find point of intersection for line equations
p.x = (lns2.Offset - lns1.Offset) / (lns1.Slope - lns2.Slope);
p.y = lns1.Slope * p.x + lns1.Offset;
}
//return whether the calculated point is on both line segments
return(PointOnLineSeg(p, lns1) && PointOnLineSeg(p, lns2));
}
///Returns whether a line segment intersects a polygon
public static bool LineSegIntersectsPoly(LineSeg lns, Poly p)
{
return(LineSegIntersectsPoly(lns, p.GetOffsetVerts()));
}
///Returns whether a point lies on a line segment
public static bool PointOnLineSeg(Vector2 p, LineSeg lns)
{
//if the distance between p and the segment ends is equal to the length of the segment, then point is on the segment
return(Mathf.Approximately(Vector2.Distance(p, lns.CenterA) + Vector2.Distance(p, lns.CenterB), lns.Length));
}
