public static double GetClockwiseMostAngle(Vec2d v1, Vec2d v2)
{
// Assume v1 and v2 normalized
double dot = Vec2d.Dot(v1, v2);
// Limit dot to valid values [-1 .. 1]
dot = Math.Max(-1.0, Math.Min(1.0, dot));
double angle = Math.Acos(dot);
angle = Math.Abs(angle);
// Check clockwise / ccw
angle = (v1.X * v2.Y - v1.Y * v2.X) < 0 ? 2 * Math.PI - angle : angle;
//// Same direction (i.e. back) is to be maximum angle
//angle = angle < 0.001 && angle > -0.001 ? 2 * Math::PI : angle;
return(angle);
}
public virtual double GetCurvature(double t)
{
Vec2d der1 = this.GetFirstDerivative(t);
double speed2 = der1.Length2;
if (speed2.EpsilonEquals(0))
{
// Curvature is indeterminate, just return 0.
return(0);
}
Vec2d der2 = this.GetSecondDerivative(t);
double numer = der1.Dot(der2);
double denom = SysMath.Pow(speed2, 1.5);
return(numer / denom);
}
public static Vec2d[] LineCircleIntersection(Vec2d pointA, Vec2d pointB, Vec2d pointO, double radius)
{
Vec2d[] output = new Vec2d[2];
Vec2d v1, v2;
//Vector from point 1 to point 2
v1 = pointB - pointA;
//Vector from point 1 to the circle's center
v2 = pointO - pointA;
double dot = Vec2d.Dot(v1, v2);
Vec2d proj1 = new Vec2d(((dot / (v1.Length2)) * v1.X), ((dot / (v1.Length2)) * v1.Y));
Vec2d midpt = new Vec2d(pointA.X + proj1.X, pointA.Y + proj1.Y);
double distToCenter = (midpt.X - pointO.X) * (midpt.X - pointO.X) + (midpt.Y - pointO.Y) * (midpt.Y - pointO.Y);
if (distToCenter > radius * radius)
{
return(output);
}
if (distToCenter == radius * radius)
{
output[0] = midpt;
return(output);
}
double distToIntersection;
if (distToCenter == 0)
{
distToIntersection = radius;
}
else
{
distToCenter = Math.Sqrt(distToCenter);
distToIntersection = Math.Sqrt(radius * radius - distToCenter * distToCenter);
}
double lineSegmentLength = 1 / v1.Length;
v1 *= lineSegmentLength;
v1 *= distToIntersection;
output[0] = (midpt + v1);
output[1] = (midpt - v1);
return(output);
}
public void ValueType_Vec2d()
{
var p1 = new Vec2d(1, 0);
var p2 = new Vec2d(0, 1);
Assert.IsFalse(p1.IsEqual(p2, 0.99, 0.1));
Assert.IsTrue(p1.IsEqual(p2, 1.01, 0.1));
Assert.IsTrue(p1.IsEqual(p2, 0.99, Math.PI / 2));
Assert.IsTrue(p1.IsNormal(p2, 0.1));
Assert.IsFalse(p1.IsOpposite(p2, 0.1));
Assert.IsTrue(p1.IsOpposite(p2, Math.PI / 2));
Assert.IsFalse(p1.IsParallel(p2, 0.1));
Assert.IsTrue(p1.IsParallel(p2, Math.PI / 2));
p1 = new Vec2d(1, 2);
p2 = new Vec2d(4, 5);
Assert.AreEqual(5, p1.SquareMagnitude());
Assert.AreEqual(Math.Sqrt(5), p1.Magnitude());
p2 = p1;
p2.Add(new Vec2d(1, 2));
Assert.AreEqual(new Vec2d(2, 4), p2);
Assert.AreEqual(new Vec2d(2, 4), p1.Added(new Vec2d(1, 2)));
p2 = new Vec2d(1, 2);
p2.Subtract(new Vec2d(3, 2));
Assert.AreEqual(new Vec2d(-2, 0), p2);
Assert.AreEqual(new Vec2d(-2, 0), p1.Subtracted(new Vec2d(3, 2)));
p2 = new Vec2d(1, 2);
Assert.AreEqual(-4, p1.Crossed(new Vec2d(3, 2)));
Assert.AreEqual(Math.Sqrt(16), p1.CrossMagnitude(new Vec2d(3, 2)));
Assert.AreEqual(16, p1.CrossSquareMagnitude(new Vec2d(3, 2)));
p2 = new Vec2d(1, 2);
p2.Divide(2);
Assert.AreEqual(new Vec2d(0.5, 1), p2);
Assert.AreEqual(new Vec2d(0.5, 1), p1.Divided(2));
Assert.AreEqual(5, p1.Dot(new Vec2d(1, 2)));
p2 = new Vec2d(1, 2);
p2.Multiply(2);
Assert.AreEqual(new Vec2d(2, 4), p2);
Assert.AreEqual(new Vec2d(2, 4), p1.Multiplied(2));
p2 = new Vec2d(1, 2);
p2.Scale(2);
Assert.AreEqual(new Vec2d(2, 4), p2);
Assert.AreEqual(new Vec2d(2, 4), p1.Scaled(2));
p2 = new Vec2d(1, 23);
Assert.AreEqual("0.0434372242763069,0.99905615835506", p2.Normalized().ToString());
p2.Normalize();
Assert.AreEqual("0.0434372242763069,0.99905615835506", p2.ToString());
p2 = new Vec2d(1, 2);
p2.Reverse();
Assert.AreEqual(new Vec2d(-1, -2), p2);
Assert.AreEqual(new Vec2d(-1, -2), p1.Reversed());
p2.SetLinearForm(new Vec2d(1, 2), new Vec2d(4, 5));
Assert.AreEqual(new Vec2d(5, 7), p2);
p2.SetLinearForm(2, new Vec2d(1, 2), new Vec2d(4, 5));
Assert.AreEqual(new Vec2d(6, 9), p2);
p2.SetLinearForm(2, new Vec2d(1, 2), 3, new Vec2d(4, 5));
Assert.AreEqual(new Vec2d(14, 19), p2);
p2.SetLinearForm(2, new Vec2d(1, 2), 3, new Vec2d(4, 5), new Vec2d(7, 8));
Assert.AreEqual(new Vec2d(21, 27), p2);
p2 = new Vec2d(2, 1);
Assert.AreEqual(new Vec2d(1, 0), p2.Mirrored(new Vec2d(1, 0)));
p2.Mirror(new Vec2d(1, 0));
Assert.AreEqual(new Vec2d(1, 0), p2);
var m2 = new Ax2d(new Pnt2d(-1, 2), new Dir2d(-1, 0));
p2 = new Vec2d(2, 1);
Assert.AreEqual(new Vec2d(2, -1), p2.Mirrored(m2));
p2.Mirror(m2);
Assert.AreEqual(new Vec2d(2, -1), p2);
p2 = new Vec2d(2, 1);
Assert.AreEqual("-1,2", p2.Rotated(Math.PI / 2).ToString());
p2.Rotate(Math.PI / 2);
Assert.AreEqual("-1,2", p2.ToString());
//TestContext.WriteLine(string.Format(CultureInfo.InvariantCulture, "{0},{1},{2}", gp2.x, gp2.y, gp2.z));
Trsf2d t1 = new Trsf2d();
t1.SetRotation(new Pnt2d(1, 2), Math.PI / 2);
p2 = new Vec2d(2, 1);
Assert.AreEqual("-1,2", p2.Transformed(t1).ToString());
p2.Transform(t1);
Assert.AreEqual("-1,2", p2.ToString());
}
/// <summary>
/// Returns a signed angle in radians between vector u and v.
/// </summary>
/// <param name="u">first (normalized!) vector</param>
/// <param name="v">second (normalized!) vector</param>
/// <returns></returns>
public static double GetAngle(Vec2d u, Vec2d v)
{
return(Math.Atan2(Vec2d.Dot(new Vec2d(-u.Y, u.X), v), Vec2d.Dot(u, v)));
}
public void Dot()
{
var p1 = new Vec2d(1, 2);
Assert.AreEqual(5, p1.Dot(new Vec2d(1, 2)));
}