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;
    cross(v): Vec3;
    distanceTo(p): number;
    dot(v): number;
    eq(other, tolerance?): boolean;
    extend(distance, direction): Vec3;
    length(): number;
    lerp(target, fractionTo): Vec3;
    magnitude(): number;
    magnitudeSquared(): number;
    map(fn): Vec3;
    maximumEntryMagnitude(): number;
    minus(v): Vec3;
    normalized(): Vec3;
    normalizedOrZero(): Vec3;
    orthog(): Vec3;
    plus(v): Vec3;
    scale(other): Vec3;
    squareDistanceTo(other): number;
    times(c): Vec3;
    toString(): string;
    zip(other, zip): 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.

Type declaration

x: number
y: number

`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:87

asArray

asArray(): [number, number, number]
Returns [number, number, number]
- Defined in Vec3.ts:172

at

at(i): 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:34

cross

cross(v): Vec3
Computes the cross product between this and v
Parameters
- v: Vec3
Returns Vec3
- Defined in Vec3.ts:116

distanceTo

distanceTo(p): 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:56

dot

dot(v): 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:113

eq

eq(other, tolerance?): boolean

[fuzz] The maximum difference between two components for this and [other] to be considered equal.

Parameters

other: Vec3
Optional tolerance: number

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, direction): Vec3
Returns this plus a vector of length distance in direction.
Parameters
- distance: number
- direction: Vec3
Returns Vec3
- Defined in Vec3.ts:136

length

length(): number
Alias for .magnitude.

Returns number
- Defined in Vec3.ts:37

lerp

lerp(target, fractionTo): Vec3
Returns a vector fractionTo of the way to target from this.
Parameters
- target: Vec3
- fractionTo: number
Returns Vec3
- Defined in Vec3.ts:139

magnitude

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

Returns number
- Defined in Vec3.ts:39

magnitudeSquared

magnitudeSquared(): number
Returns number
- Defined in Vec3.ts:40

map

map(fn): Vec3
Returns a vector with each component acted on by fn.
Parameters
- fn: ((component, index) => number)
  - - (component, index): number
    - Parameters
      component: number
      index: number
      Returns 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:170

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:70

minus

minus(v): Vec3
Parameters
- v: Vec3
Returns Vec3
- Defined in Vec3.ts:106

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:94

normalizedOrZero

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

Returns Vec3
- Defined in Vec3.ts:99

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:133

plus

plus(v): Vec3
Performs vector addition.
Parameters
- v: Vec3
Returns Vec3
- Defined in Vec3.ts:105

scale

scale(other): 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:127

squareDistanceTo

squareDistanceTo(other): 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:48

times

times(c): Vec3
Parameters
- c: number
Returns Vec3
A copy of this multiplied by a scalar.
- Defined in Vec3.ts:102

toString

toString(): string
Returns string
- Defined in Vec3.ts:190

zip

zip(other, zip): 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, componentInOther) => number)
  - - (componentInThis, componentInOther): number
    - Parameters
      componentInThis: number
      componentInOther: number
      Returns 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)
```
- Defined in Vec3.ts:157

Interface Vec3

Example

Index

Properties

Methods

Properties

Readonly x

Readonly xy

Type declaration

x: number

y: number

Readonly y

Readonly z

Methods

angle

Returns number

asArray

Returns [number, number, number]

at

Parameters

i: number

Returns number

cross

Parameters

v: Vec3

Returns Vec3

distanceTo

Parameters

p: Vec3

Returns number

dot

Parameters

v: Vec3

Returns number

eq

Parameters

other: Vec3

Optional tolerance: number

Returns boolean

Example

extend

Parameters

distance: number

direction: Vec3

Returns Vec3

length

Returns number

lerp

Parameters

target: Vec3

fractionTo: number

Returns Vec3

magnitude

Returns number

magnitudeSquared

Returns number

map

Parameters

fn: ((component, index) => number)

Parameters

component: number

index: number

Returns number

Returns Vec3

Example

maximumEntryMagnitude

Returns number

minus

Parameters

v: Vec3

Returns Vec3

normalized

Returns Vec3

normalizedOrZero

Returns Vec3

orthog

Returns Vec3

plus

Parameters

v: Vec3

`Readonly` x

`Readonly` xy

`Readonly` y

`Readonly` z

`Optional` tolerance: number