Interface Vec3

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

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());

interface Vec3 {
    x: number;
    xy: { x: number; y: number };
    y: number;
    z: number;
    angle(): number;
    asArray(): [number, number, number];
    at(i: number): number;
    cross(v: Vec3): Vec3;
    distanceTo(p: Vec3): number;
    dot(v: Vec3): number;
    eq(other: Vec3, tolerance?: number): boolean;
    extend(distance: number, direction: Vec3): Vec3;
    length(): number;
    lerp(target: Vec3, fractionTo: number): Vec3;
    magnitude(): number;
    magnitudeSquared(): number;
    map(fn: (component: number, index: number) => number): Vec3;
    maximumEntryMagnitude(): number;
    minus(v: Vec3): Vec3;
    normalized(): Vec3;
    normalizedOrZero(): Vec3;
    orthog(): Vec3;
    plus(v: Vec3): Vec3;
    scale(other: number | Vec3): Vec3;
    squareDistanceTo(other: Vec3): number;
    times(c: number): Vec3;
    toString(): string;
    zip(
        other: Vec3,
        zip: (componentInThis: number, componentInOther: number) => number,
    ): Vec3;
}

Index

Properties

x xy y z

Properties

`Readonly`x

x: number

`Readonly`xy

xy: { x: number; y: number }

Returns the x, y components of this. May be implemented as a getter method.

`Readonly`y

y: number

`Readonly`z

z: number

Methods

angle

angle(): 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:

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)
Returns number
- Defined in Vec3.ts:85

asArray

asArray(): [number, number, number]
Returns [number, number, number]
- Defined in Vec3.ts:168

at

at(i: number): number
Returns the vector's idxth component. For example, Vec3.of(1, 2, 3).at(1) → 2.
Parameters
- i: number
Returns number
- Defined in Vec3.ts:32

cross

cross(v: Vec3): Vec3
Computes the cross product between this and v
Parameters
- v: Vec3
Returns Vec3
- Defined in Vec3.ts:114

distanceTo

distanceTo(p: Vec3): number
Interpreting this vector as a point in ℝ³, returns the distance to the point p.

Equivalent to .minus(p).magnitude().
Parameters
- p: Vec3
Returns number
- Defined in Vec3.ts:54

dot

dot(v: Vec3): number
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.
Parameters
- v: Vec3
Returns number
- Defined in Vec3.ts:111

eq

eq(other: Vec3, tolerance?: number): boolean

Parameters

other: Vec3
Optionaltolerance: number
The maximum difference between two components for this and [other] to be considered equal.

Returns boolean

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

extend

extend(distance: number, direction: Vec3): Vec3
Returns this plus a vector of length distance in direction.
Parameters
- distance: number
- direction: Vec3
Returns Vec3
- Defined in Vec3.ts:134

length

length(): number
Alias for .magnitude.

Returns number
- Defined in Vec3.ts:35

lerp

lerp(target: Vec3, fractionTo: number): Vec3
Returns a vector fractionTo of the way to target from this.
Parameters
- target: Vec3
- fractionTo: number
Returns Vec3
- Defined in Vec3.ts:137

magnitude

magnitude(): number
Returns the length of this vector in ℝ^3.

Returns number
- Defined in Vec3.ts:37

magnitudeSquared

magnitudeSquared(): number
Returns number
- Defined in Vec3.ts:38

map

map(fn: (component: number, index: number) => number): Vec3
Returns a vector with each component acted on by fn.
Parameters
- fn: (component: number, index: number) => number
Returns Vec3
Example
import { Vec3 } from '@js-draw/math';
console.log(Vec3.of(1, 2, 3).map(val => val + 1)); // → Vec(2, 3, 4)
- Defined in Vec3.ts:166

maximumEntryMagnitude

maximumEntryMagnitude(): 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:

import { Vec3 } from '@js-draw/math';
console.log(Vec3.of(-1, -10, 8).maximumEntryMagnitude()); // -> 10
Returns number
- Defined in Vec3.ts:68

minus

minus(v: Vec3): Vec3
Parameters
- v: Vec3
Returns Vec3
- Defined in Vec3.ts:104

normalized

normalized(): Vec3
Returns a unit vector in the same direction as this.

If this has zero length, the resultant vector has NaN components.

Returns Vec3
- Defined in Vec3.ts:92

normalizedOrZero

normalizedOrZero(): Vec3
Like normalized, except returns zero if this has zero magnitude.

Returns Vec3
- Defined in Vec3.ts:97

orthog

orthog(): Vec3
Returns a vector orthogonal to this. If this is a Vec2, returns this rotated 90 degrees counter-clockwise.

Returns Vec3
- Defined in Vec3.ts:131

plus

plus(v: Vec3): Vec3
Performs vector addition.
Parameters
- v: Vec3
Returns Vec3
- Defined in Vec3.ts:103

scale

scale(other: number | 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.
Parameters
- other: number | Vec3
Returns Vec3
Example
```
Vec3.of(1, 2, 3).scale(Vec3.of(2, 4, 6)); // → Vec3(2, 8, 18)
```
- Defined in Vec3.ts:125

squareDistanceTo

squareDistanceTo(other: Vec3): number
Interpreting this vector as a point in ℝ^3, computes the square distance to another point, p.

Equivalent to .minus(p).magnitudeSquared().
Parameters
- other: Vec3
Returns number
- Defined in Vec3.ts:46

times

times(c: number): Vec3
Parameters
- c: number
Returns Vec3
A copy of this multiplied by a scalar.
- Defined in Vec3.ts:100

toString

toString(): string
Returns string
- Defined in Vec3.ts:185

zip

zip(
other: Vec3,
zip: (componentInThis: number, componentInOther: number) => number,
): Vec3

zip Maps a component of this and a corresponding component of other to a component of the output vector.

Parameters

other: Vec3
zip: (componentInThis: number, componentInOther: number) => number

Returns Vec3

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)

Interface Vec3

Example

Index

Properties

Methods

Properties

Readonlyx

Readonlyxy

Readonlyy

Readonlyz

Methods

angle

Returns number

asArray

Returns [number, number, number]

at

Parameters

Returns number

cross

Parameters

Returns Vec3

distanceTo

Parameters

Returns number

dot

Parameters

Returns number

eq

Parameters

Returns boolean

Example

extend

Parameters

Returns Vec3

length

Returns number

lerp

Parameters

Returns Vec3

magnitude

Returns number

magnitudeSquared

Returns number

map

Parameters

Returns Vec3

Example

maximumEntryMagnitude

Returns number

minus

Parameters

Returns Vec3

normalized

Returns Vec3

normalizedOrZero

Returns Vec3

orthog

Returns Vec3

plus

Parameters

Returns Vec3

scale

Parameters

Returns Vec3

Example

squareDistanceTo

Parameters

Returns number

times

Parameters

Returns Vec3

toString

Returns string

zip

Parameters

Returns Vec3

Example

Settings

On This Page

`Readonly`x

`Readonly`xy

`Readonly`y

`Readonly`z