// Checks to see if this line intersects with "line2". True is returned
// if they do intersect. The "ISectPt" is optional and can be NULL, but, if
// provided, it is filled with the point of intersection.
// IMPORTANT: If the two lines are equal then false is returned, not true.
// Do not call for degenerate lines (check with IsDegenerate).
public bool Intersects(NormalizedGeneralLine2D line2, ref EOFC.Vector2D ISectPt)
{
// If the two lines are parallel then they won't intersect
if (IsParallel(line2))
{
return(false);
}
float x, y;
// Handle special case
if (m_a == 0.0f)
{
y = -m_c / m_b;
x = (-line2.m_b * y - line2.m_c) / line2.m_a;
ISectPt = new EOFC.Vector2D(x, y);
return(true);
}
// else
float val1 = (-line2.m_a * m_b) / m_a + line2.m_b;
y = ((line2.m_a * m_c / m_a) - line2.m_c) / val1;
x = (-m_b * y - m_c) / m_a;
ISectPt = new EOFC.Vector2D(x, y);
return(true);
}
// ProjectPoint
// Returns the point on the line that has the shortest distance to the
// specified point. This equivalent to visually bringing the point "straight
// down" onto the line, somewhat like "projecting" it onto the line.
public EOFC.Vector2D ProjectPoint(EOFC.Vector2D point)
{
float distance = m_a * point.X + m_b * point.Y + m_c;
EOFC.Vector2D Norm = new EOFC.Vector2D(m_a, m_b);
return(point + Norm * (-distance));
}
public bool Intersects(GeneralLine2D line2, ref EOFC.Vector2D intersectionPt)
{
// If the two lines are parallel then they won't intersect
if (IsParallel(line2))
{
return(false);
}
float x, y;
// Handle special case
if (0.0f == A)
{
y = -C / B;
x = (-line2.B * y - line2.C) / line2.A;
intersectionPt = new EOFC.Vector2D(x, y);
return(true);
}
float val1 = (-line2.A * B) / A + line2.B;
y = ((line2.A * C / A) - line2.C) / val1;
x = (-B * y - C) / A;
intersectionPt = new EOFC.Vector2D(x, y);
return(true);
}
/// <summary>
/// Constructs a line instance from 2 different points that lie on the line.
/// </summary>
public GeneralLine2D(Vector2D point1, Vector2D point2)
{
EOFC.Vector2D LV = (point2 - point1);
LV.Normalize();
A = -LV.Y;
B = LV.X;
C = -(A * point1.X + B * point1.Y);
}
/// <summary>
/// Constructs a line instance from 2 different points that lie on the line.
/// </summary>
public NormalizedGeneralLine2D(EOFC.Vector2D point1, EOFC.Vector2D point2)
{
EOFC.Vector2D LV = (point2 - point1);
LV.Normalize();
m_a = -LV.Y;
m_b = LV.X;
m_c = -(m_a * point1.X + m_b * point1.Y);
}
public NormalizedGeneralLine2D(float x1, float y1, float x2, float y2)
{
EOFC.Vector2D LV = new EOFC.Vector2D(x2 - x1, y2 - y1);
LV.Normalize();
m_a = -LV.Y;
m_b = LV.X;
m_c = -(m_a * x1 + m_b * y1);
}
public EOFC.Vector2D ReflectPoint(EOFC.Vector2D pt)
{
float[] M = new float[9];
GetReflectionMatrix(M);
EOFC.Vector2D output = new EOFC.Vector2D(
M[0] * pt.X + M[1] * pt.Y + M[2],
M[3] * pt.X + M[4] * pt.Y + M[5]);
return(output);
}
/// <summary>
/// Tests if a point, WHICH IS ALREADY KNOWN TO BE ON THE INFINITE LINE, is on this segment.
/// </summary>
private bool IsPointOnSegment(EOFC.Vector2D pt)
{
// If distance (squared) from p1 to pt and distance (squared) from p2 to pt are
// both less than the distance (squared) from p1 to p2, then it's on the segment.
float lsqrd = m_l * m_l;
float l1 = (pt.X - m_p1.X) * (pt.X - m_p1.X) + (pt.Y - m_p1.Y) * (pt.Y - m_p1.Y);
float l2 = (pt.X - m_p2.X) * (pt.X - m_p2.X) + (pt.Y - m_p2.Y) * (pt.Y - m_p2.Y);
return(l1 <= lsqrd && l2 <= lsqrd);
}
/// <summary>
/// Returns the signed distance from the specified point to this line segment.
/// This will be the distance from the point to the closet point on the segment.
/// The sign is with respect to an arbitrary, but consistent, normal vector which
/// can be retrieved from the "GetUnitNormal" function.
/// </summary>
public float Distance(EOFC.Vector2D point)
{
if (DoesPointProjectOnto(point))
{
EOFC.Vector2D unorm = GetUnitNormal();
return((point - m_p1).DotProduct(unorm));
}
// If the point doesn't project onto the segment, then the smallest distance
// will be from one of the endpoints.
return(Math.Min((point - m_p1).Length, (point - m_p2).Length));
}
public bool IsParallel(LineSegment2D seg2)
{
// The two segments will be parallel if their line vectors are the same
// or one is the negative of the other.
EOFC.Vector2D v1 = GetVector();
EOFC.Vector2D v2 = seg2.GetVector();
v1.Normalize();
v2.Normalize();
if (v1.DotProduct(v2) == 1.0f)
{
return(true);
}
return(false);
}
public bool Intersects(LineSegment2D segment2, ref EOFC.Vector2D outISectPt)
{
float t = 0.0f;
if (!Intersects(segment2, ref t))
{
return(false);
}
// Fill the intersection point
float dx1 = m_p2.X - m_p1.X;
float dy1 = m_p2.Y - m_p1.Y;
outISectPt.Set(m_p1.X + t * dx1, m_p1.Y + t * dy1);
return(true);
}
/// <summary>
/// Returns the shortest unsigned distance from the specified point to this arc.
/// </summary>
public float DistanceU(EOFC.Vector2D point)
{
// Start by getting the angle of the point with respect to the circle center
double angle = (point - m_circle.Center).GetCCWAngle();
// If the angle is in the angle range for this arc then the shortest distance will
// be from the point to the edge of the circle.
if (IsAngleInRange(angle, m_startAngle, m_sweepAngle))
{
return(Math.Abs(m_circle.Radius - (point - m_circle.Center).Length));
}
// Otherwise the distance is the smaller of the two distances between the point and the
// arc endpoints.
return(Math.Min(
(point - m_circle.GetPointOnPerimeter(m_startAngle)).Length,
(point - m_circle.GetPointOnPerimeter(m_startAngle + m_sweepAngle)).Length));
}
public bool Intersects(NormalizedGeneralLine2D line, ref EOFC.Vector2D outISectPt)
{
NormalizedGeneralLine2D thisInfLine = GetInfiniteLine();
EOFC.Vector2D temp = new Vector2D();
if (!thisInfLine.Intersects(line, ref temp))
{
return(false);
}
// The two infinite lines intersect, now see if the intersection point
// is on this segment
if (this.IsPointOnSegment(temp))
{
outISectPt = temp;
return(true);
}
return(false);
}
/// <summary>
/// Gets the point on this line segment with the specified y-value. If no such point
/// exists on the segment then false is returned. Note that if the segment is horizontal,
/// even if it has a y-value of "y", then false is returned.
/// </summary>
public bool GetPointWithYValue(float y, ref EOFC.Vector2D outPt)
{
// If this segment is horizontal, return false.
if (m_p1.Y == m_p2.Y)
{
return(false);
}
NormalizedGeneralLine2D infLine = GetInfiniteLine();
float x = infLine.GetXCoord(y);
EOFC.Vector2D pt = new EOFC.Vector2D(x, y);
if (IsPointOnSegment(pt))
{
outPt.Set(pt);
return(true);
}
return(false);
}
/// <summary>
/// Gets the point on this line segment with the specified x-value. If no such point
/// exists on the segment then false is returned. Note that if the segment is vertical,
/// even if it has a x-value of "x", then false is returned.
/// </summary>
public bool GetPointWithXValue(float x, ref EOFC.Vector2D outPt)
{
// If this segment is vertical, return false.
if (m_p1.X == m_p2.X)
{
return(false);
}
NormalizedGeneralLine2D infLine = GetInfiniteLine();
float y = infLine.GetYCoord(x);
EOFC.Vector2D pt = new EOFC.Vector2D(x, y);
if (IsPointOnSegment(pt))
{
outPt.Set(pt);
return(true);
}
return(false);
}
/// <summary>
/// Returns the unsigned distance from the specified point to this line segment
/// </summary>
public float DistanceU(Vector2D point)
{
EOFC.Vector2D pointMinusP1 = (point - m_p1);
float p = pointMinusP1.ScalarProjectOnto(m_p2 - m_p1);
if (p >= 0.0f && p <= m_l)
{
float s = pointMinusP1.LengthSquared - (p * p);
if (s <= 0.0f)
{
// This should only ever occur because of rounding errors
return(0.0f);
}
return((float)Math.Sqrt(s));
}
float d1 = pointMinusP1.Length;
float d2 = (point - m_p2).Length;
return((d1 < d2) ? d1 : d2);
}
public bool Contains(EOFC.Vector2D point)
{
return((point - m_center).Length <= m_radius);
}
public bool IsPointOnLine(EOFC.Vector2D pt)
{
return(0.0f == (m_a * pt.X + m_b * pt.Y + m_c));
}
public LineSegment2D(EOFC.Vector2D point1, EOFC.Vector2D point2)
{
m_p1 = point1;
m_p2 = point2;
m_l = (m_p2 - m_p1).Length;
}
/// <summary>
/// Returns the signed point distance from the specified point to this line.
/// </summary>
public float PointDistance(EOFC.Vector2D pt)
{
return(m_a * pt.X + m_b * pt.Y + m_c);
}
public float PointDistanceUnsigned(EOFC.Vector2D pt)
{
return(Math.Abs(A * pt.X + B * pt.Y + C) / NormalLength);
}
/// <summary>
/// Gets the point on this line segment with the specified y-value. If no such point
/// exists on the segment then false is returned. Note that if the segment is horizontal,
/// even if it has a y-value of "y", then false is returned.
/// </summary>
public bool GetPointWithYValue(float y, ref EOFC.Vector2D outPt)
{
// If this segment is horizontal, return false.
if (m_p1.Y == m_p2.Y)
{
return false;
}
NormalizedGeneralLine2D infLine = GetInfiniteLine();
float x = infLine.GetXCoord(y);
EOFC.Vector2D pt = new EOFC.Vector2D(x, y);
if (IsPointOnSegment(pt))
{
outPt.Set(pt);
return true;
}
return false;
}
public bool Intersects(GeneralLine2D line2, ref EOFC.Vector2D intersectionPt)
{
// If the two lines are parallel then they won't intersect
if (IsParallel(line2))
{
return false;
}
float x, y;
// Handle special case
if (0.0f == A)
{
y = -C / B;
x = (-line2.B * y - line2.C) / line2.A;
intersectionPt = new EOFC.Vector2D(x, y);
return true;
}
float val1 = (-line2.A * B) / A + line2.B;
y = ((line2.A * C / A) - line2.C) / val1;
x = (-B * y - C) / A;
intersectionPt = new EOFC.Vector2D(x, y);
return true;
}
public bool DoesPointProjectOnto(EOFC.Vector2D pt)
{
float p = (pt - m_p1).ScalarProjectOnto(m_p2 - m_p1);
return(p >= 0.0f && p <= m_l);
}
/// <summary>
/// Gets the point on this line segment with the specified x-value. If no such point
/// exists on the segment then false is returned. Note that if the segment is vertical,
/// even if it has a x-value of "x", then false is returned.
/// </summary>
public bool GetPointWithXValue(float x, ref EOFC.Vector2D outPt)
{
// If this segment is vertical, return false.
if (m_p1.X == m_p2.X)
{
return false;
}
NormalizedGeneralLine2D infLine = GetInfiniteLine();
float y = infLine.GetYCoord(x);
EOFC.Vector2D pt = new EOFC.Vector2D(x, y);
if (IsPointOnSegment(pt))
{
outPt.Set(pt);
return true;
}
return false;
}
