public void Invert(ref Matrix3 minv)
{
//Credit: https://stackoverflow.com/a/18504573
var d = Determinant;
if (FloatMath.CloseTo(d, 0))
{
throw new InvalidOperationException("Matrix is singular and cannot be inverted.");
}
var m = this;
// computes the inverse of a matrix m
double det = m.R0C0 * (m.R1C1 * m.R2C2 - m.R2C1 * m.R1C2) -
m.R0C1 * (m.R1C0 * m.R2C2 - m.R1C2 * m.R2C0) +
m.R0C2 * (m.R1C0 * m.R2C1 - m.R1C1 * m.R2C0);
var invdet = 1 / det;
minv.R0C0 = (float)((m.R1C1 * m.R2C2 - m.R2C1 * m.R1C2) * invdet);
minv.R0C1 = (float)((m.R0C2 * m.R2C1 - m.R0C1 * m.R2C2) * invdet);
minv.R0C2 = (float)((m.R0C1 * m.R1C2 - m.R0C2 * m.R1C1) * invdet);
minv.R1C0 = (float)((m.R1C2 * m.R2C0 - m.R1C0 * m.R2C2) * invdet);
minv.R1C1 = (float)((m.R0C0 * m.R2C2 - m.R0C2 * m.R2C0) * invdet);
minv.R1C2 = (float)((m.R1C0 * m.R0C2 - m.R0C0 * m.R1C2) * invdet);
minv.R2C0 = (float)((m.R1C0 * m.R2C1 - m.R2C0 * m.R1C1) * invdet);
minv.R2C1 = (float)((m.R2C0 * m.R0C1 - m.R0C0 * m.R2C1) * invdet);
minv.R2C2 = (float)((m.R0C0 * m.R1C1 - m.R1C0 * m.R0C1) * invdet);
}
/// <summary>
/// Compares two objects for equality by value.
/// </summary>
public static bool operator ==(UIBox2 a, UIBox2 b)
{
return(FloatMath.CloseTo(a.Bottom, b.Bottom) &&
FloatMath.CloseTo(a.Right, b.Right) &&
FloatMath.CloseTo(a.Top, b.Top) &&
FloatMath.CloseTo(a.Left, b.Left));
}
/// <summary>
/// Creates a new instance of a Ray.
/// </summary>
/// <param name="position">Starting position of the ray.</param>
/// <param name="direction">Unit direction vector that the ray is pointing.</param>
public Ray(Vector2 position, Vector2 direction)
{
_position = position;
_direction = direction;
DebugTools.Assert(FloatMath.CloseTo(_direction.LengthSquared, 1));
}
/// <summary>
/// Creates a new instance of a Ray.
/// </summary>
/// <param name="position">Starting position of the ray.</param>
/// <param name="direction">Unit direction vector that the ray is pointing.</param>
public Ray(Vector2 position, Vector2 direction, int collisionMask)
{
_position = position;
_direction = direction;
_collisionMask = collisionMask;
DebugTools.Assert(FloatMath.CloseTo(_direction.LengthSquared, 1));
}
private bool Contains(float x, float y)
{
var dx = Position.X - x;
var dy = Position.Y - y;
var d2 = dx * dx + dy * dy;
var r2 = Radius * Radius;
// Instead of d2 <= r2, use FloatMath.CloseTo to allow for some tolerance.
return((d2 < r2) || FloatMath.CloseTo(d2, r2));
}
private static bool EqualsApprox(Angle a, Angle b)
{
// reduce both angles
var aReduced = Reduce(a.Theta);
var bReduced = Reduce(b.Theta);
var aPositive = FlipPositive(aReduced);
var bPositive = FlipPositive(bReduced);
// The second two expressions cover an edge case where one number is barely non-negative while the other number is negative.
// In this case, the negative number will get FlipPositived to ~2pi and the comparison will give a false negative.
return(FloatMath.CloseTo(aPositive, bPositive) ||
FloatMath.CloseTo(aPositive + MathHelper.TwoPi, bPositive) ||
FloatMath.CloseTo(aPositive, bPositive + MathHelper.TwoPi));
}
public bool IsEmpty()
{
return(FloatMath.CloseTo(Width, 0.0f) && FloatMath.CloseTo(Height, 0.0f));
}