UNPKG

@js-draw/math

Version:
270 lines (269 loc) 8.81 kB
/** * A vector with three components, $\begin{pmatrix} x \\ y \\ z \end{pmatrix}$. * Can also be used to represent a two-component vector. * * A `Vec3` is immutable. * * @example * * ```ts,runnable,console * import { Vec3 } from '@js-draw/math'; * * console.log('Vector addition:', Vec3.of(1, 2, 3).plus(Vec3.of(0, 1, 0))); * console.log('Scalar multiplication:', Vec3.of(1, 2, 3).times(2)); * console.log('Cross products:', Vec3.unitX.cross(Vec3.unitY)); * console.log('Magnitude:', Vec3.of(1, 2, 3).length(), 'or', Vec3.of(1, 2, 3).magnitude()); * console.log('Square Magnitude:', Vec3.of(1, 2, 3).magnitudeSquared()); * console.log('As an array:', Vec3.unitZ.asArray()); * ``` */ export interface Vec3 { readonly x: number; readonly y: number; readonly z: number; /** * Returns the x, y components of this. * May be implemented as a getter method. */ readonly xy: { x: number; y: number; }; /** Returns the vector's `idx`th component. For example, `Vec3.of(1, 2, 3).at(1) → 2`. */ at(i: number): number; /** Alias for `.magnitude`. */ length(): number; /** Returns the length of this vector in ℝ^3. */ magnitude(): number; magnitudeSquared(): number; /** * Interpreting this vector as a point in ℝ^3, computes the square distance * to another point, `p`. * * Equivalent to `.minus(p).magnitudeSquared()`. */ squareDistanceTo(other: Vec3): number; /** * Interpreting this vector as a point in ℝ³, returns the distance to the point * `p`. * * Equivalent to `.minus(p).magnitude()`. */ distanceTo(p: Vec3): number; /** * Returns the entry of this with the greatest magnitude. * * In other words, returns $\max \{ |x| : x \in {\bf v} \}$, where ${\bf v}$ is the set of * all entries of this vector. * * **Example**: * ```ts,runnable,console * import { Vec3 } from '@js-draw/math'; * console.log(Vec3.of(-1, -10, 8).maximumEntryMagnitude()); // -> 10 * ``` */ maximumEntryMagnitude(): number; /** * Return this' angle in the XY plane (treats this as a Vec2). * * This is equivalent to `Math.atan2(vec.y, vec.x)`. * * As such, observing that `Math.atan2(-0, -1)` $\approx -\pi$ and `Math.atan2(0, -1)` $\approx \pi$ * the resultant angle is in the range $[-\pi, \pi]$. * * **Example**: * ```ts,runnable,console * import { Vec2 } from '@js-draw/math'; * console.log(Vec2.of(-1, -0).angle()); // atan2(-0, -1) * console.log(Vec2.of(-1, 0).angle()); // atan2(0, -1) * ``` */ angle(): number; /** * Returns a unit vector in the same direction as this. * * If `this` has zero length, the resultant vector has `NaN` components. */ normalized(): Vec3; /** * Like {@link normalized}, except returns zero if this has zero magnitude. */ normalizedOrZero(): Vec3; /** @returns A copy of `this` multiplied by a scalar. */ times(c: number): Vec3; /** Performs vector addition. */ plus(v: Vec3): Vec3; minus(v: Vec3): Vec3; /** * Computes the scalar product between this and `v`. * * In particular, `a.dot(b)` is equivalent to `a.x * b.x + a.y * b.y + a.z * b.z`. */ dot(v: Vec3): number; /** Computes the cross product between this and `v` */ cross(v: Vec3): Vec3; /** * If `other` is a `Vec3`, multiplies `this` component-wise by `other`. Otherwise, * if `other is a `number`, returns the result of scalar multiplication. * * @example * ``` * Vec3.of(1, 2, 3).scale(Vec3.of(2, 4, 6)); // → Vec3(2, 8, 18) * ``` */ scale(other: Vec3 | number): Vec3; /** * Returns a vector orthogonal to this. If this is a Vec2, returns `this` rotated * 90 degrees counter-clockwise. */ orthog(): Vec3; /** Returns this plus a vector of length `distance` in `direction`. */ extend(distance: number, direction: Vec3): Vec3; /** Returns a vector `fractionTo` of the way to target from this. */ lerp(target: Vec3, fractionTo: number): Vec3; /** * `zip` Maps a component of this and a corresponding component of * `other` to a component of the output vector. * * @example * ``` * const a = Vec3.of(1, 2, 3); * const b = Vec3.of(0.5, 2.1, 2.9); * * const zipped = a.zip(b, (aComponent, bComponent) => { * return Math.min(aComponent, bComponent); * }); * * console.log(zipped.toString()); // → Vec(0.5, 2, 2.9) * ``` */ zip(other: Vec3, zip: (componentInThis: number, componentInOther: number) => number): Vec3; /** * Returns a vector with each component acted on by `fn`. * * @example * ```ts,runnable,console * import { Vec3 } from '@js-draw/math'; * console.log(Vec3.of(1, 2, 3).map(val => val + 1)); // → Vec(2, 3, 4) * ``` */ map(fn: (component: number, index: number) => number): Vec3; asArray(): [number, number, number]; /** * @param tolerance The maximum difference between two components for this and [other] * to be considered equal. * * @example * ``` * Vec3.of(1, 2, 3).eq(Vec3.of(4, 5, 6), 100); // → true * Vec3.of(1, 2, 3).eq(Vec3.of(4, 5, 6), 0.1); // → false * Vec3.of(1, 2, 3).eq(Vec3.of(4, 5, 6), 3); // → true * Vec3.of(1, 2, 3).eq(Vec3.of(4, 5, 6), 3.01); // → true * Vec3.of(1, 2, 3).eq(Vec3.of(4, 5, 6), 2.99); // → false * ``` */ eq(other: Vec3, tolerance?: number): boolean; toString(): string; } declare class Vec2Impl implements Vec3 { readonly x: number; readonly y: number; constructor(x: number, y: number); get z(): number; get xy(): { x: number; y: number; }; at(idx: number): number; length(): number; magnitude(): number; magnitudeSquared(): number; squareDistanceTo(p: Vec3): number; distanceTo(p: Vec3): number; maximumEntryMagnitude(): number; angle(): number; normalized(): Vec3; normalizedOrZero(): Vec3; times(c: number): Vec3; plus(v: Vec3): Vec3; minus(v: Vec3): Vec3; dot(other: Vec3): number; cross(other: Vec3): Vec3; scale(other: Vec3 | number): Vec3; orthog(): Vec3; extend(distance: number, direction: Vec3): Vec3; lerp(target: Vec3, fractionTo: number): Vec3; zip(other: Vec3, zip: (componentInThis: number, componentInOther: number) => number): Vec3; map(fn: (component: number, index: number) => number): Vec3; asArray(): [number, number, number]; eq(other: Vec3, fuzz?: number): boolean; toString(): string; } /** * A `Vec2` is a {@link Vec3} optimized for working in a plane. `Vec2`s have an * always-zero `z` component. * * ```ts,runnable,console * import { Vec2 } from '@js-draw/math'; * * const v = Vec2.of(1, 2); * console.log('a Vec2:', v); * console.log('x component:', v.x); * console.log('z component:', v.z); * ``` */ export declare namespace Vec2 { /** * Creates a `Vec2` from an x and y coordinate. * * @example * ```ts,runnable,console * import { Vec2 } from '@js-draw/math'; * const v = Vec2.of(3, 4); // x=3, y=4. * ``` */ const of: (x: number, y: number) => Vec2Impl; /** * Creates a `Vec2` from an object containing `x` and `y` coordinates. * * @example * ```ts,runnable,console * import { Vec2 } from '@js-draw/math'; * const v1 = Vec2.ofXY({ x: 3, y: 4.5 }); * const v2 = Vec2.ofXY({ x: -123.4, y: 1 }); * ``` */ const ofXY: ({ x, y }: { x: number; y: number; }) => Vec2Impl; /** A vector of length 1 in the X direction (→). */ const unitX: Vec2Impl; /** A vector of length 1 in the Y direction (↑). */ const unitY: Vec2Impl; /** The zero vector: A vector with x=0, y=0. */ const zero: Vec2Impl; } /** Contains static methods for constructing a {@link Vec3}. */ export declare namespace Vec3 { /** * Construct a vector from three components. * * @example * ```ts,runnable,console * import { Vec3 } from '@js-draw/math'; * const v1 = Vec3.of(1, 2, 3); * console.log(v1.plus(Vec3.of(0, 100, 0))); * ``` */ const of: (x: number, y: number, z: number) => Vec3; /** A unit vector in the x direction (`[1, 0, 0]`). */ const unitX: Vec2Impl; /** A unit vector in the y direction (`[0, 1, 0]`). */ const unitY: Vec2Impl; /** The zero vector (`[0, 0, 0]`). */ const zero: Vec2Impl; /** A vector of length 1 in the z direction. */ const unitZ: Vec3; } export default Vec3;