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 override bool Equals(object o)
{
if ((o == null) || !(o is XVector))
{
return(false);
}
XVector vector = (XVector)o;
return(Equals(this, vector));
}
public static double Multiply(XVector vector1, XVector vector2)
{
return(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;
}
/// <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 XPoint Add(XVector vector, XPoint point)
{
return(new XPoint(point.X + vector._x, point.Y + vector._y));
}
/// <summary>
/// Transforms the specified vectors by this matrix.
/// </summary>
public void Transform(XVector[] vectors)
{
if (vectors != null)
{
int count = vectors.Length;
for (int idx = 0; idx < count; idx++)
MultiplyVector(ref vectors[idx].x, ref vectors[idx].y);
}
}
public static XVector Subtract(XVector vector1, XVector vector2)
{
return(new XVector(vector1.x - vector2.x, vector1.y - vector2.y));
}
public static XVector Multiply(XVector vector, XMatrix matrix)
{
return(matrix.Transform(vector));
}
/// <summary>
/// Initializes a new instance of the XRect class.
/// </summary>
public XRect(XPoint point, XVector vector)
: this(point, point + vector)
{ }
/// <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));
}
/// <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]));
this.x += offsetVector.x;
this.y += offsetVector.y;
}
/// <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>
/// Calculates the distance between an old anchor point and a new anchor point.
/// </summary>
/// <param name="oldType"></param>
/// <param name="newType"></param>
/// <param name="size"></param>
public static XVector CalcDistance(AnchorType oldType, AnchorType newType, XSize size)
{
if (oldType == newType)
return new XVector();
XVector result;
Delta delta = CodeBase.deltas[(int)oldType, (int)newType];
result = new XVector(size.width / 2 * delta.x, size.height / 2 * delta.y);
return result;
}
public void DrawGraph(XGraphics gfx)
{
double yOff = page_.Height * 0.11;
XRect rect = new XRect(20, yOff, page_.Width - 40, page_.Height - (yOff + 20));
DrawingUtil.DrawOutlineRect(rect, gfx, cornerRadius);
gfx.DrawRoundedRectangle(backgroundBrush, rect, cornerRadius);
XPoint center = new XPoint(page_.Width * 0.5, page_.Height * 0.45);
//Left & right boxes
XRect leftRect = new XRect(center.X - 250, yOff + 5, 160, 25);
XRect rightRect = new XRect(center.X + 90, yOff + 5, 160, 25);
DrawingUtil.DrawOutlineRect(leftRect, gfx, new XSize(10,10));
gfx.DrawRoundedRectangle(XBrushes.Yellow, leftRect, new XSize(10, 10));
DrawingUtil.DrawOutlineRect(rightRect, gfx, new XSize(10,10));
gfx.DrawRoundedRectangle(XBrushes.CornflowerBlue, rightRect, new XSize(10, 10));
gfx.DrawString("Left", new XFont("Arial", 20), XBrushes.Black, new XPoint(leftRect.X + 80, leftRect.Y + 15), XStringFormats.Center);
gfx.DrawString("Right", new XFont("Arial", 20), XBrushes.Black, new XPoint(rightRect.X + 80, rightRect.Y + 15), XStringFormats.Center);
float graphSize = (float)page_.Height * 0.175f;
XPoint[] polyPoints = DrawingUtil.Instance.GeneratePoints(center, graphSize, 7, gfx);
gfx.DrawPolygon(backgroundBrush, polyPoints, XFillMode.Winding);
XPen yellowPen = new XPen(XColors.Yellow, 2.5);
XPen greenPen = new XPen(XColors.Green, 2.5);
XPen perimeterPen = XPens.LightGray;
XPen redPen = new XPen(XColors.Red, 2.5);
GraphIcon hipFlexImg = new GraphIcon(XImage.FromFile(Directory.GetCurrentDirectory() + @"\Content\HipFlex.png"),"Hip Flexion");
GraphIcon hamStringImg = new GraphIcon(XImage.FromFile(Directory.GetCurrentDirectory() + @"\Content\HSExt.png"), "Hamstring Extension");
GraphIcon hipAbdImg = new GraphIcon(XImage.FromFile(Directory.GetCurrentDirectory() + @"\Content\HipAbd.png"), "Hip Abduction");
GraphIcon hipIntImg = new GraphIcon(XImage.FromFile(Directory.GetCurrentDirectory() + @"\Content\HipInt.png"), "Hip Internal Rotation");
GraphIcon hipExtImg = new GraphIcon(XImage.FromFile(Directory.GetCurrentDirectory() + @"\Content\HipExt.png"), "Hip External Rotation");
GraphIcon kneeFlexImg = new GraphIcon(XImage.FromFile(Directory.GetCurrentDirectory() + @"\Content\KneeFlex.png"), "Knee Flexion");
GraphIcon AnkleFlexImg = new GraphIcon(XImage.FromFile(Directory.GetCurrentDirectory() + @"\Content\AnkleFlex.png"), "Ankle Flexion");
GraphIcon[] icons = new GraphIcon[] { hipFlexImg, hamStringImg, hipAbdImg, hipIntImg, hipExtImg, kneeFlexImg, AnkleFlexImg };
//center out
for (int l = 0; l < polyPoints.Length - 1; l++)
gfx.DrawLine(greenPen, center, polyPoints[l]);
//percentage Lines & icons
gfx.DrawString(0 + "%", new XFont("Arial", 10), XBrushes.Black, center + new XPoint(5, 0));
for (int j = 0; j < polyPoints.Length - 1; j++)
{
XPoint pt1 = polyPoints[j];
XPoint pt2 = polyPoints[j + 1];
for (int i = 10; i > 0; i--)
{
float increment = -i * 0.1f;
if (j < 1)
gfx.DrawString((i * 10).ToString() + '%', new XFont("Arial", 8), XBrushes.Black, DrawingUtil.Instance.Interpolate(center, polyPoints[0], increment) + new XPoint(5, 0));
gfx.DrawLine(perimeterPen,
DrawingUtil.Instance.Interpolate(center, pt1, increment),
DrawingUtil.Instance.Interpolate(center, pt2, increment));
}
XVector vec = new XVector(pt1.X, pt1.Y);
XVector vec2 = new XVector(center.X, center.Y);
XImage img = icons[j].img;
double wRatio = (double)img.PixelWidth / (double)img.PixelHeight;
XVector dir = vec2 - vec;
dir.Normalize();
double txtOffset = dir.X * -10;
XPoint halfmg = new XPoint(-20, -20);
XPoint imgpos = new XPoint(dir.X * (-graphSize - 50), dir.Y * (-graphSize - 50)) + center + halfmg;
gfx.DrawImage(img, new XRect(imgpos, new XSize(wRatio * 60, 60)));
gfx.DrawString(icons[j].txt, arialSmall, XBrushes.Black, imgpos + new XPoint(txtOffset, -10), XStringFormats.Center);
}
//leftSide
XPoint[] percentagePoints = new XPoint[polyPoints.Length - 1];
for (int k = 0; k < polyPoints.Length - 1; k++)
{
Parameter kv = userParameters_.ElementAt(k);
percentagePoints[k] = DrawingUtil.Instance.Interpolate(center, polyPoints[k], -kv.Percentage);
gfx.DrawLine(yellowPen, center, DrawingUtil.Instance.Interpolate(center, polyPoints[k], -kv.AmberVal));
gfx.DrawLine(redPen, center, DrawingUtil.Instance.Interpolate(center, polyPoints[k], -kv.RedVal));
}
gfx.DrawPolygon(new XPen(XColor.FromArgb(1, 0, 255, 255)),
new XSolidBrush(XColor.FromArgb(100, 255, 255, 0)),
percentagePoints,
XFillMode.Alternate);
XPoint[] linePoints = new XPoint[percentagePoints.Length + 1];
for (int i = 0; i < percentagePoints.Length; i++)
{
linePoints[i] = percentagePoints[i];
}
linePoints[linePoints.Length - 1] = percentagePoints[0];
gfx.DrawLines(new XPen(XColor.FromArgb(255, 255, 255, 0), 2), linePoints);
//right side
for (int k = 10; k < polyPoints.Length + 9; k++)
{
Parameter kv = userParameters_.ElementAt(k);
percentagePoints[k - 10] = DrawingUtil.Instance.Interpolate(center, polyPoints[k - 10], -kv.Percentage);
gfx.DrawLine(yellowPen, center, DrawingUtil.Instance.Interpolate(center, polyPoints[k -10], -kv.AmberVal));
gfx.DrawLine(redPen, center, DrawingUtil.Instance.Interpolate(center, polyPoints[k - 10], -kv.RedVal));
}
gfx.DrawPolygon(new XPen(XColor.FromArgb(1, 0, 255, 255)),
new XSolidBrush(XColor.FromArgb(100, 54, 127, 180)),
percentagePoints,
XFillMode.Alternate);
for (int i = 0; i < percentagePoints.Length; i++)
{
linePoints[i] = percentagePoints[i];
}
linePoints[linePoints.Length - 1] = percentagePoints[0];
gfx.DrawLines(new XPen(XColor.FromArgb(255, 54, 127, 180), 2), linePoints);
XRect leftRectLSI = new XRect(center.X - 250, page_.Height * 0.725, 120, 25);
XRect rightRectLSI = new XRect(center.X + 70, page_.Height * 0.725, 120, 25);
XRect LSIRect = new XRect(page_.Width - 100, page_.Height * 0.725, 35, 25);
XSize rad = new XSize(10, 10);
DrawingUtil.DrawOutlineRect(leftRectLSI, gfx, rad);
DrawingUtil.DrawOutlineRect(rightRectLSI, gfx, rad);
DrawingUtil.DrawOutlineRect(LSIRect, gfx, rad);
gfx.DrawRoundedRectangle(XBrushes.Yellow, leftRectLSI,rad);
gfx.DrawRoundedRectangle(XBrushes.CornflowerBlue, rightRectLSI, rad);
gfx.DrawRoundedRectangle(XBrushes.LightGray, LSIRect, rad);
gfx.DrawString("Left", new XFont("Arial", 14), XBrushes.Black, new XPoint(leftRectLSI.X + 60, leftRectLSI.Y + 12.5), XStringFormats.Center);
gfx.DrawString("Right", new XFont("Arial", 14), XBrushes.Black, new XPoint(rightRectLSI.X + 60, rightRectLSI.Y + 12.5), XStringFormats.Center);
gfx.DrawString("LSI", new XFont("Arial", 14), XBrushes.Black, new XPoint(LSIRect.X + 17.5, LSIRect.Y + 10), XStringFormats.Center);
for (int l = 0; l < polyPoints.Length - 1; l++)
{
XBrush leftParamCol = XBrushes.Green;
XBrush rightParamCol = XBrushes.Green;
XBrush lsiParamCol = XBrushes.Green;
XFont arial = new XFont("Arial", 13,XFontStyle.Bold);
Parameter leftParam = userParameters_.ElementAt(l);
Parameter rightParam = userParameters_.ElementAt(l + 10);;
leftParamCol = DrawingUtil.Instance.ChooseBrushColor(leftParam.Color);
rightParamCol = DrawingUtil.Instance.ChooseBrushColor(rightParam.Color);
char degree = Convert.ToChar('\u00b0');
double increment = l * page_.Height * 0.025;
double y = page_.Height * 0.775 + increment;
XRect rl = new XRect(leftRectLSI.X + (leftRectLSI.Width * 0.5) - 25, y, 50, 15);
DrawingUtil.DrawOutlineRect(rl, gfx, rad);
gfx.DrawRoundedRectangle(leftParamCol, rl, rad);
gfx.DrawString(leftParam.Value.ToString() + degree, arial, XBrushes.Black, new XPoint(rl.X + 25, rl.Y + 7.5), XStringFormats.Center);
XRect rr = new XRect(rightRectLSI.X + (rightRectLSI.Width * 0.5) - 25, y, 50, 15);
DrawingUtil.DrawOutlineRect(rr, gfx, rad);
gfx.DrawRoundedRectangle(rightParamCol, rr, rad);
gfx.DrawString(rightParam.Value.ToString() + degree, arial, XBrushes.Black, new XPoint(rr.X + 25, rr.Y + 7.5), XStringFormats.Center);
XRect rlsi = new XRect(LSIRect.X + (LSIRect.Width * 0.5) - 17.5, y, 35, 15);
DrawingUtil.DrawOutlineRect(rlsi, gfx, rad);
lsiParamCol = DrawingUtil.Instance.ChooseBrushColor(leftParam.LSI, 49, 74);
gfx.DrawRoundedRectangle(lsiParamCol, rlsi, rad);
gfx.DrawString(leftParam.LSI.ToString("0") + "%", arial, XBrushes.Black, new XPoint(rlsi.X + 17.5, rlsi.Y + 7.5), XStringFormats.Center);
gfx.DrawString(leftParam.Name.Substring(4,leftParam.Name.Length - 4), new XFont("Arial", 10), XBrushes.Black,
DrawingUtil.Instance.Interpolate(new XPoint(rl.X + rl.Width, y + 7.5), new XPoint(rr.X, y), -0.5), XStringFormats.TopCenter);
gfx.DrawLine(XPens.DarkSlateGray, new XPoint(leftRectLSI.X, rl.Y + 17.5), new XPoint(rlsi.X + 35, rl.Y + 17.5));
}
}
public static double Determinant(XVector vector1, XVector vector2)
{
return(vector1._x * vector2._y - vector1._y * vector2._x);
}
//+-------------------------------------------------------------------------------------------------
//
// 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);
}
public static bool Equals(XVector vector1, XVector vector2)
{
return vector1.x == vector2.x && vector1.y == vector2.y;
}
public static XVector Add(XVector vector1, XVector vector2)
{
return(new XVector(vector1._x + vector2._x, vector1._y + vector2._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 static XVector Multiply(double scalar, XVector vector)
{
return(new XVector(vector.x * scalar, vector.y * scalar));
}
/// <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 Determinant(XVector vector1, XVector vector2)
{
return(vector1.x * vector2.y - vector1.y * vector2.x);
}
public static double CrossProduct(XVector vector1, XVector vector2)
{
return vector1.x * vector2.y - vector1.y * vector2.x;
}
/// <summary>
/// Transforms the specified vector by this Matrix and returns the result.
/// </summary>
public XVector Transform(XVector vector)
{
XVector vector2 = vector;
MultiplyVector(ref vector2.x, ref vector2.y);
return vector2;
}
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);
}
/// <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);
}
/// <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>
/// 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);
}
/// <summary>
/// Initializes a new instance of the XRect class.
/// </summary>
public XRect(XPoint point, XVector vector)
: this(point, point + vector)
{
}
public static XVector Add(XVector vector1, XVector vector2)
{
return new XVector(vector1.x + vector2.x, vector1.y + vector2.y);
}
public static XVector Multiply(XVector vector, double scalar)
{
return(new XVector(vector._x * scalar, vector._y * scalar));
}
/// <summary>
/// Indicates whether the values are so close that they can be considered as equal.
/// </summary>
public static bool AreClose(XVector vector1, XVector vector2)
{
return AreClose(vector1.X, vector2.X) && AreClose(vector1.Y, vector2.Y);
}
public static XVector Subtract(XVector vector1, XVector vector2)
{
return new XVector(vector1.x - vector2.x, vector1.y - vector2.y);
}
/// <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 Multiply(double scalar, XVector vector)
{
return new XVector(vector.x * scalar, vector.y * scalar);
}
public static double CrossProduct(XVector vector1, XVector vector2)
{
return(vector1.x * vector2.y - vector1.y * vector2.x);
}
public static XVector Divide(XVector vector, double scalar)
{
return vector * (1.0 / scalar);
}
public static XVector Add(XVector vector1, XVector vector2)
{
return(new XVector(vector1.x + vector2.x, vector1.y + vector2.y));
}
public static XVector Multiply(XVector vector, XMatrix matrix)
{
return matrix.Transform(vector);
}
public static XPoint Add(XVector vector, XPoint point)
{
return(new XPoint(point.x + vector.x, point.y + vector.y));
}
public static double Multiply(XVector vector1, XVector vector2)
{
return vector1.x * vector2.x + vector1.y * vector2.y;
}
public static XVector Divide(XVector vector, double scalar)
{
return(vector * (1.0 / scalar));
}
public static double CrossProduct(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 bool Equals(XVector value)
{
return Equals(this, value);
}
public static double Determinant(XVector vector1, XVector vector2)
{
return vector1.x * vector2.y - vector1.y * vector2.x;
}
public static XVector Subtract(XVector vector1, XVector vector2)
{
return(new XVector(vector1._x - vector2._x, vector1._y - vector2._y));
}
public bool Equals(XVector value)
{
return(Equals(this, value));
}
public static bool Equals(XVector vector1, XVector vector2)
{
if (vector1.X.Equals(vector2.X))
return vector1.Y.Equals(vector2.Y);
return false;
}
