Trigo

Angle constants, conversions, and wave equations, with both fast and precise sine and cosine.

Trigo.sine() and cosine() read from a lookup table across one full turn, with the phase wrapped by normalizeRadian(). Move the pointer to read its heading through arctan2().

sine() and cosine() read from a 16k-entry lookup table: fast enough to call per particle per frame, and accurate enough for motion. When you need full precision, such as building a matrix or a quaternion, use sinePrecise() and cosinePrecise(), which call Math.sin and Math.cos directly.

The constants pi, twopi, and halfpi save recomputing them, degreeToRadian() and radianToDegree() convert, and normalizeRadian() wraps an angle into (-π, π]. The *Equation helpers evaluate amplitude * f(period + shiftX) + shiftY in one call, which is the shape most oscillations take.

import { Trigo } from '@1pizzateam/spock';

const wrapped = Trigo.normalizeRadian(7.5);
const y = Trigo.sine(wrapped);
const heading = Trigo.arctan2(1, 1);

Trigo.degreeToRadian()

Degrees to radians.

Multiplies by π/180. Every angle in this library is in radians, so this is the conversion to do at the edge of degree-based input.

degreeToRadian(degree: number): number

Parameters

• degree — number.

Returns

number — the radian

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.degreeToRadian(1);

Trigo.radianToDegree()

Radians to degrees.

Converts back to degrees, mostly for display.

radianToDegree(radian: number): number

Parameters

• radian — number.

Returns

number — the degree

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.radianToDegree(Math.PI / 4);

Trigo.normalizeRadian()

Wrap radians into (-π, π].

Wraps any angle into (-π, π]. Do this before comparing or interpolating angles, otherwise a value just past π looks far from one just below it when the two are neighbours.

normalizeRadian(angle: number): number

Parameters

• angle — number.

Returns

number — the radian

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.normalizeRadian(Math.PI / 4);

Trigo.sine()

Fast sine of angle in radians.

Reads from a 16384-entry lookup table instead of calling Math.sin. Fast enough to run per particle per frame, and accurate enough for motion; use sinePrecise() when the small error would accumulate.

sine(angle: number): number

Parameters

• angle — number.

Returns

number — the sine of the angle

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.sine(Math.PI / 4);

Trigo.cosine()

Fast cosine of angle in radians.

Lookup-table cosine, with the same trade-off as sine().

cosine(angle: number): number

Parameters

• angle — number.

Returns

number — the cosine of the angle

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.cosine(Math.PI / 4);

Trigo.arctan()

Arctangent of angle (Math.atan).

Delegates to Math.atan, returning an angle in (-π/2, π/2).

arctan(angle: number): number

Parameters

• angle — number.

Returns

number — the arctan of the angle

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.arctan(Math.PI / 4);

Trigo.arctan2()

atan2(y, x), or false at the origin.

Delegates to Math.atan2(y, x) for a full-circle angle, but returns false at the origin where the angle is undefined. Note the y-then-x argument order.

arctan2(y: number, x: number): number | false

Parameters

• y — number.
• x — number.

Returns

number | false — the arctan2 of the angle or false

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.arctan2(1, 1);

Trigo.sinePrecise()

Precise sine (Math.sin).

Calls Math.sin directly, for the cases where lookup-table error matters, such as building matrices and quaternions.

sinePrecise(angle: number): number

Parameters

• angle — number.

Returns

number

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.sinePrecise(Math.PI / 4);

Trigo.cosinePrecise()

Precise cosine (Math.cos).

Calls Math.cos directly.

cosinePrecise(angle: number): number

Parameters

• angle — number.

Returns

number

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.cosinePrecise(Math.PI / 4);

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Wave equations

The ring and the wave are the same equation. Each dot sits at cosineEquation() horizontally and sineEquation() vertically, and the blue trace plots that same sine as the period advances — the height of the orange marker is shared by both.

import { Trigo } from '@1pizzateam/spock';

const slice = Trigo.twopi / 24;

// amplitude * cos(period + shiftX) + shiftY
const x = Trigo.cosineEquation(200, slice * i, 0, centerX);
const y = Trigo.sineEquation(200, slice * i, 0, centerY);

Trigo.sineEquation()

amplitude * sin(period + shiftX) + shiftY.

Evaluates amplitude * sin(period + shiftX) + shiftY in one call: amplitude is the swing, shiftX the phase offset, shiftY the centre line. It uses the fast lookup-table sine.

sineEquation(amplitude: number, period: number, shiftX: number, shiftY: number): number

Parameters

• amplitude — number.
• period — number.
• shiftX — number.
• shiftY — number.

Returns

number — the result of the equation

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.sineEquation(1, 1, 1, 1);

Trigo.cosineEquation()

amplitude * cos(period + shiftX) + shiftY.

The same wave equation as sineEquation(), a quarter turn ahead.

cosineEquation(amplitude: number, period: number, shiftX: number, shiftY: number): number

Parameters

• amplitude — number.
• period — number.
• shiftX — number.
• shiftY — number.

Returns

number — the result of the equation

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.cosineEquation(1, 1, 1, 1);

Trigo.arctanEquation()

amplitude * atan(period + shiftX) + shiftY.

Evaluates amplitude * atan(period + shiftX) + shiftY, an S-shaped curve that flattens out at both ends.

arctanEquation(amplitude: number, period: number, shiftX: number, shiftY: number): number

Parameters

• amplitude — number.
• period — number.
• shiftX — number.
• shiftY — number.

Returns

number — the result of the equation

Example

import { Trigo } from '@1pizzateam/spock';


const result = Trigo.arctanEquation(1, 1, 1, 1);