public static Pnt2d FindEllipseCenterFromEndpoints(Pnt2d startPnt, Pnt2d endPnt, double rX, double rY, double angle, bool sense)
{
// https://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
// F.6.5.1
var matRotation = new Mat2d();
matRotation.SetRotation(-angle);
var v1 = new XY(startPnt.X - endPnt.X, startPnt.Y - endPnt.Y)
.Multiplied(0.5)
.Multiplied(matRotation);
// F.6.5.2
var denom = rX.Sqr() * v1.Y.Sqr() + rY.Sqr() * v1.X.Sqr();
var numer = rX.Sqr() * rY.Sqr() - denom;
var root = Math.Sqrt(Math.Abs(numer / denom)) * (sense ? -1 : 1);
var c1 = new XY(rX * v1.Y / rY, -(rY * v1.X / rX)).Multiplied(root);
// F.6.5.3
matRotation.SetRotation(angle);
var c = new XY(startPnt.X + endPnt.X, startPnt.Y + endPnt.Y)
.Multiplied(0.5)
.Added(c1.Multiplied(matRotation));
return(c.ToPnt());
}
public void Rotate()
{
Mat2d m1 = new Mat2d();
m1.SetRotation(Math.PI / 2);
var p2 = new XY(4, 5);
Assert.That(new XY(-5, 4).IsEqual(p2.Multiplied(m1), 0.0000001));
Assert.That(new XY(-5, 4).IsEqual(p2 * m1, 0.0000001));
p2.Multiply(m1);
Assert.That(new XY(-5, 4).IsEqual(p2, 0.0000001));
}
public static Pnt2d FindEllipseCenterFromEndpoints(Pnt2d startPnt, Pnt2d endPnt, double rX, double rY, double angle, bool sense)
{
// https://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
// F.6.5.1
var matRotation = new Mat2d();
matRotation.SetRotation(-angle);
var v1 = new XY(startPnt.X - endPnt.X, startPnt.Y - endPnt.Y)
.Multiplied(0.5)
.Multiplied(matRotation);
// F.6.5.2
var denom = rX.Sqr() * v1.Y.Sqr() + rY.Sqr() * v1.X.Sqr();
var numer = rX.Sqr() * rY.Sqr() - denom;
// This correction is used in SvgNet, no idea what it is doing.
//double root = 0;
//if (numer < 0)
//{
// var s = (float)Math.Sqrt(1.0 - numer / (rX.Sqr() * rY.Sqr()));
// rX *= s;
// rY *= s;
// root = 0.0;
//}
//else
//{
// root = Math.Sqrt(numer / denom) * (sense ? -1 : 1);
//}
var root = Math.Sqrt(Math.Abs(numer / denom)) * (sense ? -1 : 1);
var c1 = new XY(rX * v1.Y / rY, -(rY * v1.X / rX)).Multiplied(root);
// F.6.5.3
matRotation.SetRotation(angle);
var c = new XY(startPnt.X + endPnt.X, startPnt.Y + endPnt.Y)
.Multiplied(0.5)
.Added(c1.Multiplied(matRotation));
return(c.ToPnt());
}
public void ValueType_XY()
{
var p1 = new XY(1, 2);
var p2 = new XY(4, 5);
Assert.AreEqual(5, p1.SquareModulus());
Assert.AreEqual(Math.Sqrt(5), p1.Modulus());
Assert.IsTrue(p1.IsEqual(p2, 3));
Assert.IsFalse(p1.IsEqual(p2, 2.99));
p2 = p1;
p2.Add(new XY(1, 2));
Assert.AreEqual(new XY(2, 4), p2);
Assert.AreEqual(new XY(2, 4), p1.Added(new XY(1, 2)));
p2 += new XY(1, 2);
Assert.AreEqual(new XY(3, 6), p2);
Assert.AreEqual(-4, p1.Crossed(new XY(3, 2)));
Assert.AreEqual(Math.Sqrt(16), p1.CrossMagnitude(new XY(3, 2)));
Assert.AreEqual(16, p1.CrossSquareMagnitude(new XY(3, 2)));
p2 = new XY(1, 2);
p2.Divide(2);
Assert.AreEqual(new XY(0.5, 1), p2);
Assert.AreEqual(new XY(0.5, 1), p1.Divided(2));
Assert.AreEqual(5, p1.Dot(new XY(1, 2)));
p2 = new XY(1, 2);
p2.Multiply(2);
Assert.AreEqual(new XY(2, 4), p2);
Assert.AreEqual(new XY(2, 4), p1.Multiplied(2));
Assert.AreEqual(new XY(2, 4), p1 * 2);
p2 = new XY(1, 2);
p2.Multiply(new XY(1, 2));
Assert.AreEqual(new XY(1, 4), p2);
Assert.AreEqual(new XY(1, 4), p1.Multiplied(new XY(1, 2)));
Assert.AreEqual(new XY(1, 4), p1 * new XY(1, 2));
Mat2d m1 = new Mat2d();
m1.SetRotation(Math.PI / 2);
p2 = new XY(4, 5);
Assert.AreEqual("-5,4", p2.Multiplied(m1).ToString());
Assert.AreEqual("-5,4", (p2 * m1).ToString());
p2.Multiply(m1);
Assert.AreEqual("-5,4", p2.ToString());
p2 = new XY(1, 23);
Assert.AreEqual("0.0434372242763069,0.99905615835506", p2.Normalized().ToString());
p2.Normalize();
Assert.AreEqual("0.0434372242763069,0.99905615835506", p2.ToString());
p2 = new XY(1, 2);
p2.Reverse();
Assert.AreEqual(new XY(-1, -2), p2);
Assert.AreEqual(new XY(-1, -2), p1.Reversed());
p2 = new XY(1, 2);
p2.Subtract(new XY(3, 2));
Assert.AreEqual(new XY(-2, 0), p2);
Assert.AreEqual(new XY(-2, 0), p1.Subtracted(new XY(3, 2)));
Assert.AreEqual(new XY(-2, 0), p1 - new XY(3, 2));
p2.SetLinearForm(new XY(1, 2), new XY(4, 5));
Assert.AreEqual(new XY(5, 7), p2);
p2.SetLinearForm(2, new XY(1, 2), new XY(4, 5));
Assert.AreEqual(new XY(6, 9), p2);
p2.SetLinearForm(2, new XY(1, 2), 3, new XY(4, 5));
Assert.AreEqual(new XY(14, 19), p2);
p2.SetLinearForm(2, new XY(1, 2), 3, new XY(4, 5), new XY(7, 8));
Assert.AreEqual(new XY(21, 27), p2);
//TestContext.WriteLine(string.Format(CultureInfo.InvariantCulture, "{0},{1}", gp2.x, gp2.y));
//TestContext.WriteLine(string.Format(CultureInfo.InvariantCulture, "{0},{1}", new gp_XY(1, 23).Normalized().X(), new gp_XY(1, 23).Normalized().Y()));
}