/// <summary>
/// Gets the angle in degrees for a ray that extends from the center
/// of the circle through the given point. An exception will occur,
/// however, if the point specified is the same point as the center
/// of the circle.
/// </summary>
/// <param name="pt">The point.</param>
public decimal AngleThroughPoint(Point2D pt)
{
decimal a = 0m;
// Shift point so it's relative to the origin.
pt += new Vector2D(-Center.X, -Center.Y);
// Do check here after we've translated the point
// to account for small precision rounding.
if (pt == Point2D.Origin)
{
throw new Exception("No angle through given point since point is at center of circle!");
}
// Special case for 0 and 180 where we would get
// a divide by zero below.
if (pt.Y == 0)
{
if (pt.X > 0)
{
return(0);
}
else
{
return(180);
}
}
// Special case for 90 and 270 where we can't
// determine quadrant below.
if (pt.X == 0)
{
if (pt.Y > 0)
{
return(90);
}
else
{
return(270);
}
}
a = DecimalEx.ToDeg(DecimalEx.ATan(pt.X / pt.Y));
switch (pt.Quadrant)
{
case 1:
case 2:
a = 90 - a;
break;
case 3:
case 4:
a = 270 - a;
break;
}
return(a);
}
/// <summary>
/// Gets the points of intersection between this circle and the line which
/// contains the given line segment.
/// </summary>
/// <param name="l">Line segment used to determine line equation.</param>
/// <param name="decimals">Determines rounding that should be performed when determining
/// if line intersection happens on zero, one, or two points. Default is -1 for
/// no rounding.</param>
public Point2D[] GetIntersect(LineSeg2D l, int decimals = -1)
{
LineSeg2D centToLine = default(LineSeg2D);
decimal centToLineLength = 0m;
decimal centToLineLengthForComp = 0m;
decimal radiusForComp = 0m;
if (l.IsHorizontal)
{
// The center to any horizontal line is a vertical line through
// the center of the circle.
centToLine = new LineSeg2D(this.Center, this.Center + new Vector2D(0, 1));
}
else
{
centToLine = LineSeg2D.FromPointSlope(this.Center, l.PerpendicularSlope);
}
centToLine.Pt2 = l.GetIntersect(centToLine, true).Value;
centToLineLength = centToLine.Length;
// Get numbers for comparison, rounding if necessary
centToLineLengthForComp = centToLineLength;
radiusForComp = _radius;
if (decimals >= 0)
{
centToLineLengthForComp = centToLineLengthForComp.RoundFromZero(decimals);
radiusForComp = radiusForComp.RoundFromZero(decimals);
}
// See if line is outside of circle
if (centToLineLengthForComp > radiusForComp)
{
return(new Point2D[] { });
}
// See if line is tangent to circle
if (centToLineLengthForComp == radiusForComp)
{
return(new Point2D[] { centToLine.Pt2 });
}
// Line must intersect in two places
Vector2D vCentToChord = default(Vector2D);
decimal halfChord = 0m;
// Get a vector from the center to the intersecting chord
vCentToChord = centToLine.GetVectorP1toP2();
if (vCentToChord.Magnitude == 0)
{
Vector2D offsetVector = default(Vector2D);
// Line goes through circle center
if (l.IsVertical)
{
// Slope undefined so just go up the length of the radius
offsetVector = new Vector2D(0, _radius);
}
else
{
offsetVector = new Vector2D(_radius * DecimalEx.Cos(DecimalEx.ATan(l.Slope)), _radius * DecimalEx.Sin(DecimalEx.ATan(l.Slope)));
}
return(new Point2D[] {
this.Center + offsetVector,
this.Center - offsetVector
});
}
else
{
Vector2D vChord = default(Vector2D);
// Get a vector along the chord
vChord = vCentToChord.GetPerpendicular();
// Determine the length of half the chord
halfChord = RightTriangle.GetSideFromSideHyp(centToLineLength, _radius);
// Set the magnitude of the vector along the chord
// to be half the chord length
vChord.Magnitude = halfChord;
// The two intersecting points are points translated
// from the center of the circle to the chord (+vCentToChord)
// and then translated to the ends of the chord (+-vChord)
return(new Point2D[] {
this.Center + vCentToChord + vChord,
this.Center + vCentToChord - vChord
});
}
}
/// <summary>
/// Gets angle in degrees from the two known sides.
/// </summary>
/// <param name="oppositeSide">Length of the known side opposite the angle.</param>
/// <param name="adjacentSide">Length of the known side adjacent to the angle.</param>
public static decimal GetAngleFromSides(decimal oppositeSide, decimal adjacentSide)
{
// tan(a) = opposideSide / adjacentSide
// a = atan(opposideSide / adjacentSide)
return(DecimalEx.ToDeg(DecimalEx.ATan(oppositeSide / adjacentSide)));
}
