public void CreateRotation2()
{
float angle = (float)MathHelper.ToRadians(30);
Matrix22F m = Matrix22F.CreateRotation(angle);
Assert.IsTrue(Vector2F.AreNumericallyEqual(new Vector2F((float)Math.Cos(angle), (float)Math.Sin(angle)), m * Vector2F.UnitX));
}
public void Transform2D()
{
// Transform forward and inverse and compare with initial values.
var random = new Random(1234567);
var s = new Vector2F[16, 8];
var t = new Vector2F[16, 8];
for (int i = 0; i < s.GetLength(0); i++)
{
for (int j = 0; j < s.GetLength(1); j++)
{
s[i, j] = random.NextVector2F(-10, 10);
t[i, j] = s[i, j];
}
}
var fft = new FastFourierTransformF(16);
fft.Transform2D(t, true);
Assert.IsFalse(Vector2F.AreNumericallyEqual(s[0, 0], t[0, 0]));
fft.Transform2D(t, false);
for (int i = 0; i < s.GetLength(0); i++)
{
for (int j = 0; j < s.GetLength(1); j++)
{
Assert.IsTrue(Vector2F.AreNumericallyEqual(s[i, j], t[i, j]));
}
}
}
public void CreateRotation()
{
Matrix22F m = Matrix22F.CreateRotation(0.0f);
Assert.AreEqual(Matrix22F.Identity, m);
m = Matrix22F.CreateRotation((float)Math.PI / 2);
Assert.IsTrue(Vector2F.AreNumericallyEqual(Vector2F.UnitY, m * Vector2F.UnitX));
}
public void InterpolationTest()
{
var traits = Vector2Traits.Instance;
var value0 = new Vector2(2, 3);
var value1 = new Vector2(5, -6);
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)value0, (Vector2F)traits.Interpolate(value0, value1, 0.0f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)value1, (Vector2F)traits.Interpolate(value0, value1, 1.0f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(0.25f * value0 + 0.75f * value1), (Vector2F)traits.Interpolate(value0, value1, 0.75f)));
}
public void InverseWithNearSingularMatrix()
{
Matrix22F m = new Matrix22F(0.0001f, 0,
0, 0.0001f);
Vector2F v = Vector2F.One;
Vector2F w = m * v;
Assert.IsTrue(Vector2F.AreNumericallyEqual(v, m.Inverse * w));
Assert.IsTrue(Matrix22F.AreNumericallyEqual(Matrix22F.Identity, m * m.Inverse));
}
public void AreEqualWithEpsilon()
{
float epsilon = 0.001f;
Vector2F u = new Vector2F(1.0f, 2.0f);
Vector2F v = new Vector2F(1.002f, 2.002f);
Vector2F w = new Vector2F(1.0001f, 2.0001f);
Assert.IsTrue(Vector2F.AreNumericallyEqual(u, u, epsilon));
Assert.IsFalse(Vector2F.AreNumericallyEqual(u, v, epsilon));
Assert.IsTrue(Vector2F.AreNumericallyEqual(u, w, epsilon));
}
public void Inverse()
{
Assert.AreEqual(Matrix22F.Identity, Matrix22F.Identity.Inverse);
Matrix22F m = new Matrix22F(1, 2, 3, 4);
Vector2F v = Vector2F.One;
Vector2F w = m * v;
Assert.IsTrue(Vector2F.AreNumericallyEqual(v, m.Inverse * w));
Assert.IsTrue(Matrix22F.AreNumericallyEqual(Matrix22F.Identity, m * m.Inverse));
}
public void GetPoint()
{
var a = new ArcSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, -3),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(a.Point1, a.GetPoint(0), 0.001f));
Assert.IsTrue(Vector2F.AreNumericallyEqual(a.Point2, a.GetPoint(1), 0.001f));
}
public void GetTangent()
{
var s = new LineSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(-1, 9),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point2 - s.Point1, s.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point2 - s.Point1, s.GetTangent(0.3f)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Point2 - s.Point1, s.GetTangent(1)));
}
public void MultiplyTest()
{
var traits = Vector2Traits.Instance;
var value = new Vector2(-1, 2);
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)Vector2.Zero, (Vector2F)traits.Multiply(value, 0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)value, (Vector2F)traits.Multiply(value, 1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(value + value), (Vector2F)traits.Multiply(value, 2)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(value + value + value), (Vector2F)traits.Multiply(value, 3)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(-value), (Vector2F)traits.Multiply(value, -1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(-value - value), (Vector2F)traits.Multiply(value, -2)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(-value - value - value), (Vector2F)traits.Multiply(value, -3)));
}
public void GetTangent()
{
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(10, 3),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(3 * (b.ControlPoint1 - b.Point1), b.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(3 * (b.Point2 - b.ControlPoint2), b.GetTangent(1)));
}
public void MultiplyVector()
{
Vector2F v = new Vector2F(2.34f, 3.45f);
Assert.AreEqual(v, Matrix22F.Multiply(Matrix22F.Identity, v));
Assert.AreEqual(Vector2F.Zero, Matrix22F.Multiply(Matrix22F.Zero, v));
Matrix22F m = new Matrix22F(12, 23, 45, 67);
Assert.IsTrue(Vector2F.AreNumericallyEqual(v, Matrix22F.Multiply(m * m.Inverse, v)));
for (int i = 0; i < 2; i++)
{
Assert.AreEqual(Vector2F.Dot(m.GetRow(i), v), Matrix22F.Multiply(m, v)[i]);
}
}
public void FromByTest()
{
// IAnimationValueTraits<T> is used in a from-by animation to a add a relative offset to
// the start value.
var traits = Vector2Traits.Instance;
var from = new Vector2(-1, -2);
var by = new Vector2(4, -5);
var to = traits.Add(from, by);
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(by + from), (Vector2F)to));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)from, (Vector2F)traits.Add(to, traits.Inverse(by))));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)by, (Vector2F)traits.Add(traits.Inverse(from), to)));
}
public void AreEqual()
{
float originalEpsilon = Numeric.EpsilonF;
Numeric.EpsilonF = 1e-8f;
Vector2F u = new Vector2F(1.0f, 2.0f);
Vector2F v = new Vector2F(1.000001f, 2.000001f);
Vector2F w = new Vector2F(1.00000001f, 2.00000001f);
Assert.IsTrue(Vector2F.AreNumericallyEqual(u, u));
Assert.IsFalse(Vector2F.AreNumericallyEqual(u, v));
Assert.IsTrue(Vector2F.AreNumericallyEqual(u, w));
Numeric.EpsilonF = originalEpsilon;
}
public void Flatten()
{
var s = new ArcSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, -3),
};
var points = new List <Vector2F>();
var tolerance = 1f;
s.Flatten(points, 10, tolerance);
Assert.IsTrue(Vector2F.AreNumericallyEqual(points[0], s.Point1));
Assert.IsTrue(Vector2F.AreNumericallyEqual(points.Last(), s.Point2));
var curveLength = s.GetLength(0, 1, 10, tolerance);
Assert.IsTrue(CurveHelper.GetLength(points) >= curveLength - tolerance * points.Count / 2);
Assert.IsTrue(CurveHelper.GetLength(points) <= curveLength);
}
public void CycleOffsetTest()
{
// IAnimationValueTraits<T> is used in a cyclic animation to a add the cycle offset in
// each iteration.
var traits = Vector2Traits.Instance;
var first = new Vector2(1, 2); // Animation value of first key frame.
var last = new Vector2(-4, 5); // Animation value of last key frame.
var cycleOffset = traits.Add(traits.Inverse(first), last);
// Cycle offset should be the difference between last and first key frame.
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)last, (Vector2F)traits.Add(first, cycleOffset)));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)last, (Vector2F)(cycleOffset + first)));
// Check multiple cycles (post-loop).
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)last, (Vector2F)traits.Add(first, traits.Multiply(cycleOffset, 1))));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(cycleOffset + cycleOffset + last), (Vector2F)traits.Add(first, traits.Multiply(cycleOffset, 3))));
// Check multiple cycles (pre-loop).
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)first, (Vector2F)traits.Add(last, traits.Multiply(cycleOffset, -1))));
Assert.IsTrue(Vector2F.AreNumericallyEqual((Vector2F)(first - cycleOffset - cycleOffset), (Vector2F)traits.Add(last, traits.Multiply(cycleOffset, -3))));
}
public void Transform1DComparedWithDft()
{
// Transform forward and inverse and compare with initial values.
var random = new Random(1234567);
var s = new Vector2F[16];
var t = new Vector2F[16];
for (int i = 0; i < s.Length; i++)
{
s[i] = random.NextVector2F(-10, 10);
t[i] = s[i];
}
FastFourierTransformF.DFT(s, true);
FastFourierTransformF.Transform1D(t, true);
for (int i = 0; i < s.Length; i++)
{
Assert.IsTrue(Vector2F.AreNumericallyEqual(s[i], t[i]));
}
}
public void GetTangent()
{
CatmullRomSegment2F c = new CatmullRomSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, 3),
Point3 = new Vector2F(7, 8),
Point4 = new Vector2F(10, 2),
};
HermiteSegment2F h = new HermiteSegment2F
{
Point1 = c.Point2,
Tangent1 = (c.Point3 - c.Point1) * 0.5f,
Tangent2 = (c.Point4 - c.Point2) * 0.5f,
Point2 = c.Point3,
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(h.Tangent1, c.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(h.Tangent2, c.GetTangent(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(h.GetTangent(0.7f), c.GetTangent(0.7f)));
}
public void GetTangent()
{
HermiteSegment2F s = new HermiteSegment2F
{
Point1 = new Vector2F(1, 2),
Tangent1 = (new Vector2F(10, 3) - new Vector2F(1, 2)) * 3,
Tangent2 = (new Vector2F(10, 2) - new Vector2F(7, 8)) * 3,
Point2 = new Vector2F(10, 2),
};
BezierSegment2F b = new BezierSegment2F
{
Point1 = new Vector2F(1, 2),
ControlPoint1 = new Vector2F(10, 3),
ControlPoint2 = new Vector2F(7, 8),
Point2 = new Vector2F(10, 2),
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Tangent1, s.GetTangent(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(s.Tangent2, s.GetTangent(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(b.GetTangent(0.7f), s.GetTangent(0.7f)));
}
public void GetPoint()
{
CardinalSegment2F c = new CardinalSegment2F
{
Point1 = new Vector2F(1, 2),
Point2 = new Vector2F(10, 3),
Point3 = new Vector2F(7, 8),
Point4 = new Vector2F(10, 2),
Tension = 0.3f
};
HermiteSegment2F h = new HermiteSegment2F
{
Point1 = c.Point2,
Tangent1 = (1 - c.Tension) * (c.Point3 - c.Point1) * 0.5f,
Tangent2 = (1 - c.Tension) * (c.Point4 - c.Point2) * 0.5f,
Point2 = c.Point3,
};
Assert.IsTrue(Vector2F.AreNumericallyEqual(c.Point2, c.GetPoint(0)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(c.Point3, c.GetPoint(1)));
Assert.IsTrue(Vector2F.AreNumericallyEqual(h.GetPoint(0.33f), c.GetPoint(0.33f)));
}
