public static double AngleBetween(XVector vector1, XVector vector2)
{
double y = vector1._x * vector2._y - vector2._x * vector1._y;
double x = vector1._x * vector2._x + vector1._y * vector2._y;
return(Math.Atan2(y, x) * 57.295779513082323);
}
public static bool Equals(XVector vector1, XVector vector2)
{
if (vector1.X.Equals(vector2.X))
{
return(vector1.Y.Equals(vector2.Y));
}
return(false);
}
public static XVector Parse(string source)
{
TokenizerHelper helper = new TokenizerHelper(source, CultureInfo.InvariantCulture);
string str = helper.NextTokenRequired();
XVector vector = new XVector(Convert.ToDouble(str, CultureInfo.InvariantCulture), Convert.ToDouble(helper.NextTokenRequired(), CultureInfo.InvariantCulture));
helper.LastTokenRequired();
return(vector);
}
/// <summary>
/// Moves a rectangle by the specified amount.
/// </summary>
public void Offset(XVector offsetVector)
{
if (IsEmpty)
{
throw new InvalidOperationException("CannotCallMethod"); //SR.Get(SRID.Rect_CannotCallMethod, new object[0]));
}
_x += offsetVector.X;
_y += offsetVector.Y;
}
public static XVector Add(XVector vector1, XVector vector2)
{
return(new XVector(vector1._x + vector2._x, vector1._y + vector2._y));
}
public static double Determinant(XVector vector1, XVector vector2)
{
return(vector1._x * vector2._y - vector1._y * vector2._x);
}
public static double Multiply(XVector vector1, XVector vector2)
{
return(vector1._x * vector2._x + vector1._y * vector2._y);
}
public static XVector Multiply(XVector vector, XMatrix matrix)
{
return(matrix.Transform(vector));
}
public static XVector Divide(XVector vector, double scalar)
{
return(vector * (1.0 / scalar));
}
public static XVector Multiply(double scalar, XVector vector)
{
return(new XVector(vector._x * scalar, vector._y * scalar));
}
public static XPoint Add(XVector vector, XPoint point)
{
return(new XPoint(point.X + vector._x, point.Y + vector._y));
}
/// <summary>
/// Adds a point and a vector.
/// </summary>
public static XPoint Add(XPoint point, XVector vector)
{
return(new XPoint(point._x + vector.X, point._y + vector.Y));
}
public bool Equals(XVector value)
{
return(Equals(this, value));
}
/// <summary>
/// Subtracts a vector from a point.
/// </summary>
public static XPoint Subtract(XPoint point, XVector vector)
{
return(new XPoint(point._x - vector.X, point._y - vector.Y));
}
public static double CrossProduct(XVector vector1, XVector vector2)
{
return(vector1._x * vector2._y - vector1._y * vector2._x);
}
/// <summary>
/// Initializes a new instance of the XRect class.
/// </summary>
public XRect(XPoint point, XVector vector)
: this(point, point + vector)
{
}
/// <summary>
/// Returns a rectangle that is offset from the specified rectangle by using the specified vector.
/// </summary>
public static XRect Offset(XRect rect, XVector offsetVector)
{
rect.Offset(offsetVector.X, offsetVector.Y);
return(rect);
}
/// <summary>
/// Creates between 1 and 5 Béziers curves from parameters specified like in WPF.
/// </summary>
public static List <XPoint> BezierCurveFromArc(XPoint point1, XPoint point2, XSize size,
double rotationAngle, bool isLargeArc, bool clockwise, PathStart pathStart)
{
// See also http://www.charlespetzold.com/blog/blog.xml from January 2, 2008:
// http://www.charlespetzold.com/blog/2008/01/Mathematics-of-ArcSegment.html
double δx = size.Width;
double δy = size.Height;
Debug.Assert(δx * δy > 0);
double factor = δy / δx;
bool isCounterclockwise = !clockwise;
// Adjust for different radii and rotation angle.
XMatrix matrix = new XMatrix();
matrix.RotateAppend(-rotationAngle);
matrix.ScaleAppend(δy / δx, 1);
XPoint pt1 = matrix.Transform(point1);
XPoint pt2 = matrix.Transform(point2);
// Get info about chord that connects both points.
XPoint midPoint = new XPoint((pt1.X + pt2.X) / 2, (pt1.Y + pt2.Y) / 2);
XVector vect = pt2 - pt1;
double halfChord = vect.Length / 2;
// Get vector from chord to center.
XVector vectRotated;
// (comparing two Booleans here!)
if (isLargeArc == isCounterclockwise)
{
vectRotated = new XVector(-vect.Y, vect.X);
}
else
{
vectRotated = new XVector(vect.Y, -vect.X);
}
vectRotated.Normalize();
// Distance from chord to center.
double centerDistance = Math.Sqrt(δy * δy - halfChord * halfChord);
if (double.IsNaN(centerDistance))
{
centerDistance = 0;
}
// Calculate center point.
XPoint center = midPoint + centerDistance * vectRotated;
// Get angles from center to the two points.
double α = Math.Atan2(pt1.Y - center.Y, pt1.X - center.X);
double β = Math.Atan2(pt2.Y - center.Y, pt2.X - center.X);
// (another comparison of two Booleans!)
if (isLargeArc == (Math.Abs(β - α) < Math.PI))
{
if (α < β)
{
α += 2 * Math.PI;
}
else
{
β += 2 * Math.PI;
}
}
// Invert matrix for final point calculation.
matrix.Invert();
double sweepAngle = β - α;
// Let the algorithm of GDI+ DrawArc to Bézier curves do the rest of the job
return(BezierCurveFromArc(center.X - δx * factor, center.Y - δy, 2 * δx * factor, 2 * δy,
α / Calc.Deg2Rad, sweepAngle / Calc.Deg2Rad, pathStart, ref matrix));
}
public static XVector Subtract(XVector vector1, XVector vector2)
{
return(new XVector(vector1._x - vector2._x, vector1._y - vector2._y));
}
//+-------------------------------------------------------------------------------------------------
//
// Function: ArcToBezier
//
// Synopsis: Compute the Bezier approximation of an arc
//
// Notes: This utilitycomputes the Bezier approximation for an elliptical arc as it is defined
// in the SVG arc spec. The ellipse from which the arc is carved is axis-aligned in its
// own coordinates, and defined there by its x and y radii. The rotation angle defines
// how the ellipse's axes are rotated relative to our x axis. The start and end points
// define one of 4 possible arcs; the sweep and large-arc flags determine which one of
// these arcs will be chosen. See SVG spec for details.
//
// Returning pieces = 0 indicates a line instead of an arc
// pieces = -1 indicates that the arc degenerates to a point
//
//--------------------------------------------------------------------------------------------------
public static PointCollection ArcToBezier(double xStart, double yStart, double xRadius, double yRadius, double rotationAngle,
bool isLargeArc, bool isClockwise, double xEnd, double yEnd, out int pieces)
{
double cosArcAngle, sinArcAngle, xCenter, yCenter, r, bezDist;
XVector vecToBez1, vecToBez2;
XMatrix matToEllipse;
double fuzz2 = FUZZ * FUZZ;
bool isZeroCenter = false;
pieces = -1;
// In the following, the line segment between between the arc's start and
// end points is referred to as "the chord".
// Transform 1: Shift the origin to the chord's midpoint
double x = (xEnd - xStart) / 2;
double y = (yEnd - yStart) / 2;
double halfChord2 = x * x + y * y; // (half chord length)^2
// Degenerate case: single point
if (halfChord2 < fuzz2)
{
// The chord degeneartes to a point, the arc will be ignored
return(null);
}
// Degenerate case: straight line
if (!AcceptRadius(halfChord2, fuzz2, ref xRadius) || !AcceptRadius(halfChord2, fuzz2, ref yRadius))
{
// We have a zero radius, add a straight line segment instead of an arc
pieces = 0;
return(null);
}
if (xRadius == 0 || yRadius == 0)
{
// We have a zero radius, add a straight line segment instead of an arc
pieces = 0;
return(null);
}
// Transform 2: Rotate to the ellipse's coordinate system
rotationAngle = -rotationAngle * Calc.Deg2Rad;
double cos = Math.Cos(rotationAngle);
double sin = Math.Sin(rotationAngle);
r = x * cos - y * sin;
y = x * sin + y * cos;
x = r;
// Transform 3: Scale so that the ellipse will become a unit circle
x /= xRadius;
y /= yRadius;
// We get to the center of that circle along a verctor perpendicular to the chord
// from the origin, which is the chord's midpoint. By Pythagoras, the length of that
// vector is sqrt(1 - (half chord)^2).
halfChord2 = x * x + y * y; // now in the circle coordinates
if (halfChord2 > 1)
{
// The chord is longer than the circle's diameter; we scale the radii uniformly so
// that the chord will be a diameter. The center will then be the chord's midpoint,
// which is now the origin.
r = Math.Sqrt(halfChord2);
xRadius *= r;
yRadius *= r;
xCenter = yCenter = 0;
isZeroCenter = true;
// Adjust the unit-circle coordinates x and y
x /= r;
y /= r;
}
else
{
// The length of (-y,x) or (x,-y) is sqrt(rHalfChord2), and we want a vector
// of length sqrt(1 - rHalfChord2), so we'll multiply it by:
r = Math.Sqrt((1 - halfChord2) / halfChord2);
//if (isLargeArc != (eSweepDirection == SweepDirection.Clockwise))
if (isLargeArc != isClockwise)
// Going to the center from the origin=chord-midpoint
{
// in the direction of (-y, x)
xCenter = -r * y;
yCenter = r * x;
}
else
{
// in the direction of (y, -x)
xCenter = r * y;
yCenter = -r * x;
}
}
// Transformation 4: shift the origin to the center of the circle, which then becomes
// the unit circle. Since the chord's midpoint is the origin, the start point is (-x, -y)
// and the endpoint is (x, y).
XPoint ptStart = new XPoint(-x - xCenter, -y - yCenter);
XPoint ptEnd = new XPoint(x - xCenter, y - yCenter);
// Set up the matrix that will take us back to our coordinate system. This matrix is
// the inverse of the combination of transformation 1 thru 4.
matToEllipse = new XMatrix(cos * xRadius, -sin * xRadius,
sin * yRadius, cos * yRadius,
(xEnd + xStart) / 2, (yEnd + yStart) / 2);
if (!isZeroCenter)
{
// Prepend the translation that will take the origin to the circle's center
matToEllipse.OffsetX += (matToEllipse.M11 * xCenter + matToEllipse.M21 * yCenter);
matToEllipse.OffsetY += (matToEllipse.M12 * xCenter + matToEllipse.M22 * yCenter);
}
// Get the sine & cosine of the angle that will generate the arc pieces
GetArcAngle(ptStart, ptEnd, isLargeArc, isClockwise, out cosArcAngle, out sinArcAngle, out pieces);
// Get the vector to the first Bezier control point
bezDist = GetBezierDistance(cosArcAngle, 1);
//if (eSweepDirection == SweepDirection.Counterclockwise)
if (!isClockwise)
{
bezDist = -bezDist;
}
vecToBez1 = new XVector(-bezDist * ptStart.Y, bezDist * ptStart.X);
PointCollection result = new PointCollection();
// Add the arc pieces, except for the last
for (int idx = 1; idx < pieces; idx++)
{
// Get the arc piece's endpoint
XPoint ptPieceEnd = new XPoint(ptStart.X * cosArcAngle - ptStart.Y * sinArcAngle, ptStart.X * sinArcAngle + ptStart.Y * cosArcAngle);
vecToBez2 = new XVector(-bezDist * ptPieceEnd.Y, bezDist * ptPieceEnd.X);
result.Add(matToEllipse.Transform(ptStart + vecToBez1));
result.Add(matToEllipse.Transform(ptPieceEnd - vecToBez2));
result.Add(matToEllipse.Transform(ptPieceEnd));
// Move on to the next arc
ptStart = ptPieceEnd;
vecToBez1 = vecToBez2;
}
// Last arc - we know the endpoint
vecToBez2 = new XVector(-bezDist * ptEnd.Y, bezDist * ptEnd.X);
result.Add(matToEllipse.Transform(ptStart + vecToBez1));
result.Add(matToEllipse.Transform(ptEnd - vecToBez2));
result.Add(new XPoint(xEnd, yEnd));
return(result);
}
