public static Rectangle2D EllipticalArc0(
double cX, double cY,
double r1, double r2,
double angle,
double startAngle, double sweepAngle)
{
// Get the ellipse rotation transform.
var cosT = Cos(angle);
var sinT = Sin(angle);
var i = (r1 - r2) * (r1 + r2) * sinT * cosT;
// Find the angles of the Cartesian extremes.
var angles = new double[4] {
Atan2(i, (r2 * r2 * sinT * sinT) + (r1 * r1 * cosT * cosT)),
Atan2((r1 * r1 * sinT * sinT) + (r2 * r2 * cosT * cosT), i),
Atan2(i, (r2 * r2 * sinT * sinT) + (r1 * r1 * cosT * cosT)) + PI,
Atan2((r1 * r1 * sinT * sinT) + (r2 * r2 * cosT * cosT), i) + PI
};
// Sort the angles so that like sides are consistently at the same index.
Array.Sort(angles);
// Get the start and end angles adjusted to polar coordinates.
var t0 = EllipticalPolarAngleTests.EllipticalPolarAngle(startAngle, r1, r2);
var t1 = EllipticalPolarAngleTests.EllipticalPolarAngle(startAngle + sweepAngle, r1, r2);
// Interpolate the ratios of height and width of the chord.
var sinT0 = Sin(t0);
var cosT0 = Cos(t0);
var sinT1 = Sin(t1);
var cosT1 = Cos(t1);
// Get the end points of the chord.
var bounds = new Rectangle2D(
// Apply the rotation transformation and translate to new center.
new Point2D(
cX + ((r1 * cosT0 * cosT) - (r2 * sinT0 * sinT)),
cY + ((r1 * cosT0 * sinT) + (r2 * sinT0 * cosT))),
// Apply the rotation transformation and translate to new center.
new Point2D(
cX + ((r1 * cosT1 * cosT) - (r2 * sinT1 * sinT)),
cY + ((r1 * cosT1 * sinT) + (r2 * sinT1 * cosT))));
// Find the parent ellipse's horizontal and vertical radii extremes.
var halfWidth = Sqrt((r1 * r1 * cosT * cosT) + (r2 * r2 * sinT * sinT));
var halfHeight = Sqrt((r1 * r1 * sinT * sinT) + (r2 * r2 * cosT * cosT));
// Expand the elliptical boundaries if any of the extreme angles fall within the sweep angle.
if (AngleWithinAngleTests.Within(angles[0], angle + startAngle, sweepAngle))
{
bounds.Right = cX + halfWidth;
}
if (AngleWithinAngleTests.Within(angles[1], angle + startAngle, sweepAngle))
{
bounds.Bottom = cY + halfHeight;
}
if (AngleWithinAngleTests.Within(angles[2], angle + startAngle, sweepAngle))
{
bounds.Left = cX - halfWidth;
}
if (AngleWithinAngleTests.Within(angles[3], angle + startAngle, sweepAngle))
{
bounds.Top = cY - halfHeight;
}
// Return the points of the Cartesian extremes of the rotated elliptical arc.
return(bounds);
}
public static (double X, double Y) RectangleCenter(Rectangle2D rectangle) => Center0(rectangle);
public static Rectangle2D EllipticalArc3(
double cX, double cY,
double r1, double r2,
double angle,
double startAngle, double sweepAngle)
{
// Get the ellipse rotation transform.
var cosT = Cos(angle);
var sinT = Sin(angle);
// Calculate the radii of the angle of rotation.
var a = r1 * cosT;
var b = r2 * sinT;
var c = r1 * sinT;
var d = r2 * cosT;
// Calculate the vectors of the Cartesian extremes.
var u1 = r1 * Cos(Atan2(d, c));
var v1 = -(r2 * Sin(Atan2(d, c)));
var u2 = r1 * Cos(Atan2(-b, a));
var v2 = -(r2 * Sin(Atan2(-b, a)));
// Find the angles of the Cartesian extremes.
var angles = new List <double>(4)
{
Atan2((u1 * sinT) - (v1 * cosT), (u1 * cosT) + (v1 * sinT)),
Atan2((u2 * sinT) - (v2 * cosT), (u2 * cosT) + (v2 * sinT)),
Atan2((u1 * sinT) - (v1 * cosT), (u1 * cosT) + (v1 * sinT)) + PI,
Atan2((u2 * sinT) - (v2 * cosT), (u2 * cosT) + (v2 * sinT)) + PI
};
// Sort the angles so that like sides are consistently at the same index.
angles.Sort();
// Find the parent ellipse's horizontal and vertical radii extremes.
var halfWidth = Sqrt((a * a) + (b * b));
var halfHeight = Sqrt((c * c) + (d * d));
// Get the end points of the chord.
var bounds = new Rectangle2D(
InterpolateRotatedEllipticalArcTests.EllipticalArc(0, cX, cY, r1, r2, angle, startAngle, sweepAngle),
InterpolateRotatedEllipticalArcTests.EllipticalArc(1, cX, cY, r1, r2, angle, startAngle, sweepAngle));
// Expand the elliptical boundaries if any of the extreme angles fall within the sweep angle.
if (AngleWithinAngleTests.Within(angles[0], angle + startAngle, sweepAngle))
{
bounds.Right = cX + halfWidth;
}
if (AngleWithinAngleTests.Within(angles[1], angle + startAngle, sweepAngle))
{
bounds.Bottom = cY + halfHeight;
}
if (AngleWithinAngleTests.Within(angles[2], angle + startAngle, sweepAngle))
{
bounds.Left = cX - halfWidth;
}
if (AngleWithinAngleTests.Within(angles[3], angle + startAngle, sweepAngle))
{
bounds.Top = cY - halfHeight;
}
// Return the points of the Cartesian extremes of the rotated elliptical arc.
return(bounds);
}
