MathUtil

π.

2π — a full turn.

π/2 — a quarter turn.

π/4 — an eighth of a turn.

The default tolerance for "close enough": about 8 significant decimal digits of headroom below Single's ~7. Small enough that it does not hide a real error, large enough to absorb the rounding of a few chained operations.

The slack a predicate needs when it compares two quantities that were rounded independently: eight times Single's unit roundoff of 2⁻²⁴, which is about the loss of a chain of half a dozen operations with room to spare.

Converts degrees to radians.

Converts radians to degrees.

Whether a value is within ZeroTolerance of zero.

Whether a value is within ZeroTolerance of one.

Whether two values are close enough to be treated as equal. The tolerance is scaled by the larger magnitude, so it behaves absolutely near zero and relatively out where Single steps in units of thousands — a fixed epsilon is wrong at one end or the other and there is no single value that is right at both.

Constrains a value to an interval.

Constrains a value to [0, 1].

Linearly interpolates between two values.

Finds the interpolant that Lerp would need.

Interpolates with a curve that is flat at both ends (3t² − 2t³).

Interpolates with a curve whose first and second derivatives vanish at both ends (6t⁵ − 15t⁴ + 10t³). Worth the extra multiplies wherever the result drives acceleration, because SmoothStep has a visible jerk at its endpoints.

Wraps an angle into (−π, π].

The shortest signed angle from one angle to another, in (−π, π]. Interpolating a heading without this goes the long way round whenever the pair straddles ±π.

Whether a value is a power of two. Zero is not.

The smallest power of two that is at least .

Rounds up to a multiple of .

Wraps a value into [0, length), unlike %, which reflects around zero for negative input and is almost never what a looping animation or a tiled coordinate wants.

Bounces a value back and forth within [0, length].