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math

The math module provides utilities for performing mathematical calculations.

It contains the following classes:

• Elegant
• Math
• Vector

Elegant

The Elegant class supplies a useful utility for combining pairs of signed integers, based on “An Elegant Pairing Method” by Matthew Szudzik

Static Methods

pair(vec: Vector): Number

Pairs the x and y of vec into a single result.

pair(x: Number, y: Number): Number

Pairs the x and y into a single result.

unpair(z: Number): Vector

Reverses the value z into a vector (x, y).

unpairAsList(z: Number): List<Number>

Reverses the value z into a list [ x, y ].

Math

The Math class provides various common mathematical functions. For convenience, you can also import this class M, like so:

import "math" for M, Math
System.print(M.min(21, 42))
System.print(Math.max(21, 42))

Static Methods

abs(n: Number): Number

Returns the absolute magnitude of n.

acos(n: Number): Number

Returns the arccosine of n.

asin(n: Number): Number

Returns the arcsine of n.

atan(n: Number): Number

atan(n1: Number, n2: Number): Number

Returns the arctan of n.

ceil(n: Number): Number

Rounds n up to the next largest integer value.

clamp(number : Number, min : Number, max : Number) : Number

Clamps number between min and max.

cos(n: Number): Number

Returns the cosine of n.

floor(n: Number): Number

Rounds n down to the next smallest integer value.

lerp(low: Number, value: Number, high: Number): Number

This performs a linear interpolation between low and high, based on the value of value, which will be clamped to a range of [0..1].

log(n: Number): Number

Returns the natural logarithm of n.

max(n1: Number, n2: Number): Number

Returns the larger of n1 and n2.

mid(n1: Number, n2: Number, n3: Number): Number

Returns the number which is in the middle of the others. This can be used as an inclusive clamping function.

min(n1: Number, n2: Number): Number

Returns the smaller of n1 and n2.

round(n: Number): Number

Rounds n to the nearest integer value.

sign(n: Number): Number

If n is negative, this returns -1. If n is positive, this returns 1. If n is equal to zero, it returns 0.

sin(n: Number): Number

Returns the sine of n.

tan(n: Number): Number

Returns the tan of n.

Vector

The Vector class works as a vector of up to 4 dimensions. You can also refer to it as a Point or Vec. This class also implements DOME’s Hashable interface, allowing it to be used with our collections.

Constructor

Vector.new(): Vector

Vector.new(x, y): Vector

Vector.new(x, y, z): Vector

Vector.new(x, y, z, w): Vector

Create a vector. If a value isn’t provided, it is set to (0, 0, 0, 0). Unless you specifically need 3 or 4-dimensional vectors, you can ignore z and w.

Vector.fromPair(z: Number): Vector

Reverses an Elegant pairing to produce the corresponding vector.

Instance Fields

x: Number

y: Number

z: Number

w: Number

manhattan: Number

This returns the “taxicab length” of the vector, easily calculated as x + y + z + w.

length: Number

This returns the Euclidean magnitude of the vector.

perp: Vector

Returns the 2D vector perpendicular to the current vector. This doesn’t work for vectors with 3 or more dimensions.

unit: Vector

Returns a copy of the current vector, where it’s arguments have been scaled such that it’s length is 1.

pair: Number

Uses the Elegant algorithm to pair the x and y coordinates. This can be reversed with Elegant.unpair(_).

Instance Methods

dot(vec: Vector): Num

This returns the dot-product of the vector with another vector.

cross(vec: Vector): Num

This returns the cross-product of the vector with another vector, resulting in a new vector that is perpendicular to the other two. This only works for 3-dimensional vectors. The w component will be discarded.

Operators

-Vector: Vector

Returns the vector, but it’s elements are multiplied by -1.

Vector + Vector: Vector

Returns an element-wise addition of the two Vectors. This will error if you try to add a Vector to something other than a Vector.

Vector - Vector: Vector

Returns an element-wise subtraction of the two Vectors. This will error if you try to subtract a Vector from something other than a Vector, or vice versa.

Vector * Number: Vector

Returns the given vector, where it’s elements have been multipled by the scalar. This will error if the multiplier is not a number.

Vector / Number: Vector

Returns the given vector, where it’s elements have been divided by the scalar. This will error if the divisor is not a Number.