math.mcl

Euler's number.

let E = 2.7182818284590452

Pi in radians.

let PI = 3.1415926535897932

Full circle constant, equal to 2 * PI.

let TAU = 6.2831853071795864

let wave = |x| sin(x * TAU)

Origin point [0, 0, 0].

let ORIGIN = [0, 0, 0]

Zero vector [0, 0, 0].

let ZERO_V = [0, 0, 0]

Vector with all components equal to 1.

let ONE_V = [1, 1, 1]

Unit vector pointing left in scene coordinates.

let LEFT = 1l

Unit vector pointing right in scene coordinates.

let RIGHT = 1r

mesh dot = center{RIGHT * 2} Circle(0.2)

Unit vector pointing up in scene coordinates.

let UP = 1u

Unit vector pointing down in scene coordinates.

let DOWN = 1d

Unit vector pointing forward; with the default camera this is negative z.

let FORWARD = 1f

Unit vector pointing backward; with the default camera this is positive z, from the origin toward the camera.

let BACKWARD = 1b

X-axis basis vector, equal to RIGHT.

let X_HAT = RIGHT

Y-axis basis vector, equal to UP.

let Y_HAT = UP

Z-axis basis vector, equal to BACKWARD.

let Z_HAT = BACKWARD

Square root.

let sqrt = |x| ...

Cube root.

let cbrt = |x| ...

Exponential function e^x.

let exp = |x| ...

Natural logarithm.

let ln = |x| ...

Logarithm with optional base, defaulting to E.

let log = |x, base = E| ln(x) / ln(base)

Base-2 logarithm.

let log2 = |x| log(x, 2)

Base-10 logarithm.

let log10 = |x| log(x, 10)

Sine of an angle in radians.

let sin = |x| ...

Cosine of an angle in radians.

let cos = |x| ...

Tangent of an angle in radians.

let tan = |x| ...

Cotangent of an angle in radians.

let cot = |x| 1 / tan(x)

Secant of an angle in radians.

let sec = |x| 1 / cos(x)

Cosecant of an angle in radians.

let csc = |x| 1 / sin(x)

Inverse sine, returning radians.

let arcsin = |x| ...

Inverse cosine, returning radians.

let arccos = |x| ...

Inverse tangent, returning radians.

let arctan = |x| ...

Two-argument inverse tangent, returning radians.

let arctan2 = |y, x| ...

Hyperbolic sine.

let sinh = |x| ...

Hyperbolic cosine.

let cosh = |x| ...

Hyperbolic tangent.

let tanh = |x| ...

Absolute value.

let abs = |x| ...

Sign of a number: -1, 0, or 1.

let sign = |x| ...

Largest integer not greater than x.

let floor = |x| ...

Smallest integer not less than x.

let ceil = |x| ...

Round to the nearest integer.

let round = |x| ...

Truncate fractional part.

let trunc = |x| ...

Euclidean remainder of n divided by m.

The result has the sign of the divisor, so mod(-1, 4) returns 3.

let mod = |n, m| ...

Pairwise minimum of two numbers.

let min = |a, b| ...

Pairwise maximum of two numbers.

let max = |a, b| ...

Pin x to the inclusive range [low, high].

let clamp = |low, x, high| min(high, max(low, x))

let opacity = clamp(0, raw_opacity, 1)

Rectified linear unit, max(0, x).

let relu = |x| max(0, x)

Logistic sigmoid.

let sigmoid = |x| 1 / (1 + exp(-x))

Factorial of a non-negative integer.

let factorial = |n| ...

Number of ways to choose r items from n.

Returns 0 when r < 0 or r > n.

let choose = |n, r| ...

Number of ordered arrangements of r items from n.

Returns 0 when r < 0 or r > n.

let permute = |n, r| ...

Greatest common divisor.

let gcd = |n, m| ...

Least common multiple.

let lcm = |n, m| ...

Test whether n is prime.

let is_prime = |n| ...

Mean of a numeric list.

let mean = |v| ...

Variance of a numeric list.

Population variance: divides by len(v), not len(v) - 1.

let variance = |v| ...

Standard deviation of a numeric list.

let std_dev = |v| sqrt(variance(v))

Dot product of two vectors.

let dot = |u, v| ...

Cross product of two 3-D vectors.

let cross = |u, v| ...

Euclidean length of a vector.

let norm = |v| sqrt(dot(v, v))

Unit vector in the same direction as v.

Does not guard against the zero vector.

let normalize = |v| v * (1 / norm(v))

Projection of vector u onto vector v.

let proj = |u, v| v * (dot(u, v) / dot(v, v))

Angle between two vectors, in radians.

let angle_between = |u, v| arccos(dot(u, v) / (norm(u) * norm(v)))

Remap x linearly from one interval into another.

let map_range = |x, in_min, in_max, out_min, out_max| out_min + (x - in_min) / (in_max - in_min) * (out_max - out_min)

let opacity = map_range(frame, 0, 30, 0, 1)

Convert degrees to radians.

Numeric literals can use the dg suffix; use this for runtime values.

let deg_to_rad = |x| x * (PI / 180)

Convert radians to degrees.

let rad_to_deg = |x| x * (180 / PI)