/// <summary>
/// Gets hypotenuse from a known side and the angle adjacent to that side.
/// </summary>
/// <param name="side">Length of the known side.</param>
/// <param name="angleAdjacentToSide">The angle adjacent to the known side in degrees.</param>
public static decimal GetHypFromSideAdjAngle(decimal side, decimal angleAdjacentToSide)
{
// cos(a) = s / h
// h * cos(a) = s
// h = s / cos(a)
return(side / DecimalEx.Cos(DecimalEx.ToRad(angleAdjacentToSide)));
}
/// <summary>
/// Gets a line segment of length 1 starting at the point on the circle
/// and extending either clockwise or counterclockwise.
/// </summary>
/// <param name="degrees">An angle.</param>
public LineSeg2D TangentAt(decimal degrees, decimal length, bool clockwise)
{
var r = RightTriangleAbstract.FromTwoSides(_radius, length);
decimal rad = DecimalEx.ToRad(degrees + r.AngleA);
LineSeg2D ret = default(LineSeg2D);
Debug.Assert(r.AngleA == RightTriangle.GetAngleFromSides(length, _radius));
Debug.Assert(r.Hypotenuse == RightTriangle.GetHypFromSides(length, _radius));
ret.Pt1 = PointAt(degrees);
if (!clockwise)
{
ret.Pt2 = new Point2D(_center.X + r.Hypotenuse * DecimalEx.Cos(rad), _center.Y + r.Hypotenuse * DecimalEx.Sin(rad));
}
else
{
ret.Pt2 = new Point2D(ret.Pt1.X - (_center.X + r.Hypotenuse * DecimalEx.Cos(rad) - ret.Pt1.X), ret.Pt1.Y - (_center.Y + r.Hypotenuse * DecimalEx.Sin(rad) - ret.Pt1.Y));
}
return(ret);
}
/// <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 the coordinates of the point on the circle at the given angle.
/// </summary>
/// <param name="degrees">The angle in degrees.</param>
public Point2D PointAt(decimal degrees)
{
decimal rad = DecimalEx.ToRad(degrees);
return(new Point2D(_center.X + _radius * DecimalEx.Cos(rad), _center.Y + _radius * DecimalEx.Sin(rad)));
}
/// <summary>
/// Gets a side from the adjacent angle and the length of the hypotenuse.
/// </summary>
/// <param name="adjacentAngle">Angle adjacent to the side to calculate in degrees.</param>
/// <param name="hypotenuse">Length of the hypotenuse.</param>
public static decimal GetSideFromAdjAngleHyp(decimal adjacentAngle, decimal hypotenuse)
{
// cos(adjacentAngle) = x / hypotenuse
// x = hypotenuse * cos(adjacentAngle)
return(hypotenuse * Convert.ToDecimal(DecimalEx.Cos(DecimalEx.ToRad(adjacentAngle))));
}
