https://github.com/damianc/math.vc
Support for vector calculus in JavaScript.
https://github.com/damianc/math.vc
Last synced: 10 days ago
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Support for vector calculus in JavaScript.
- Host: GitHub
- URL: https://github.com/damianc/math.vc
- Owner: damianc
- Created: 2025-02-15T19:19:52.000Z (3 months ago)
- Default Branch: master
- Last Pushed: 2025-02-16T02:52:05.000Z (3 months ago)
- Last Synced: 2025-05-14T10:34:12.326Z (10 days ago)
- Language: JavaScript
- Size: 19.5 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Math.vc
Support for _vector calculus_ in JavaScript.
The following methods are accessible through the `Math.vc` namespace:
- `add(A,B)`
- `sub(A,B)`
- `mul(A,k)`
- `dotProduct(A,B)`
- `crossProduct(A,B)`
- `outerProduct(A,B)`
- `kroneckerProduct(A,B)`
- `angle(A,B)`
- `projection(A,B)`
- `arePerpendicular(A,B)`
- `areParallel(A,B)`
- `length(V)`
- `normalize(V)`
Plus the following differential methods:
- `gradient(f)`
- `divergence(F)`
- `curl(F)`
- `laplacian(f)`
- `vectorLaplacian(F)`
## Overview
### `add(A,B)`
Adds two vectors.
$$
A + B
$$
### `sub(A,B)`
Subtracts two vectors.
$$
A - B
$$
### `mul(A,k)`
Multiplies a vector by a scalar value.
$$
kA
$$
### `dotProduct(A,B)`
The dot product of two vectors.
$$
A \cdot B
$$
### `crossProduct(A,B)`
The cross product of two vectors.
$$
A \times B
$$
### `outerProduct(A,B)`
The outer product of two vectors.
$$
A \otimes B = \begin{bmatrix}
a_1b_1 & a_1b_2 & \cdots
\\
a_2b_1 & a_2b_2 & \cdots
\\
\vdots & \vdots & \ddots
\end{bmatrix}
$$
### `kroneckerProduct(A,B)`
The Kronecker product of two vectors.
$$
A \otimes B = [
a_1B, ..., a_nB
]
$$
### `angle(A,B)`
Returns an angle between two vectors.
$$
\arccos\left(
\frac{A \cdot B}{|A| |B|}
\right)
$$
### `projection(A,B)`
Projects vector A on vector B.
$$
\text{proj}_B \ A = \frac{A \cdot B}{|B|^2} B
$$
### `arePerpendicular(A,B)`
Checks if two vectors are perpendicular.
$$
A \perp B \iff A \cdot B = 0
$$
### `areParallel(A,B)`
Checks if two vectors are parallel.
$$
A \parallel B \iff A \times B = [0,0,0]
$$
### `length(V)`
Returns a length of a vector.
$$
|V| = \sqrt{a_1 + \cdots + a_n}
$$
### `normalize(V)`
Performs normalization of a vector.
$$
\frac{V}{|V|}
$$
## Overview of Differential Methods
### `gradient(f)`
- input: $f: \Bbb{R}^3 \to \Bbb{R}$
- output: $\Bbb{R}^3$
$$
\text{grad} \ f = \nabla f = \left[
\frac{\partial f}{\partial x},
\frac{\partial f}{\partial y},
\frac{\partial f}{\partial z}
\right]^{\intercal}
$$
### `divergence(F)`
- input: $F: \Bbb{R}^3 \to \Bbb{R}^3$
- output: $\Bbb{R}$
$$
\text{div} \ F = \nabla \cdot F =
\frac{\partial F_x}{\partial x} +
\frac{\partial F_y}{\partial y} +
\frac{\partial F_z}{\partial z}
$$
### `curl(F)`
- input: $F: \Bbb{R}^3 \to \Bbb{R}^3$
- output: $\Bbb{R}^3$
$$
\text{curl} \ F = \nabla \times F = \begin{vmatrix}
\hat{i} & \hat{j} & \hat{k}
\\
\
\\
\frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z}
\\
\
\\
F_x & F_y & F_z
\end{vmatrix}
$$
### `laplacian(f)`
- input: $f: \Bbb{R}^3 \to \Bbb{R}$
- output: $\Bbb{R}$
$$
\Delta f = \nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}
$$
### `vectorLaplacian(F)`
- input: $F: \Bbb{R}^3 \to \Bbb{R}^3$
- output: $\Bbb{R}^3$
$$
\Delta F = \nabla^2 F = (\Delta F_1, \Delta F_2, \Delta F_3)
$$
## Input/Output
- a scalar field $f: \Bbb{R}^3 \to \Bbb{R}$ receives three arguments ($x,y,z$) and return a scalar value
- a vector field $\Bbb{R}^3$ is an object with the following three properties: `dx`, `dy` and `dz`
### Example 1
To get the following gradient:
$$
\nabla \ f, \text{ for } f(x,y,z) = x^2+y^2+z^2
$$
we shall write:
```
const f = (x,y,z) => x*x + y*y + z*z;
const grad = Math.vc.gradient(f);
grad(1,2,3)
// {dx: 2, dy: 4, dz: 6 }
```
### Example 2
To get the following curl:
$$
\text{curl} \ F, \text{ for } F(x,y,z) = (-y,x,0)
$$
we shall write:
```
const F = (x,y,z) => ({
dx: -y,
dy: x,
dz: 0
});
const curl = Math.vc.curl(F);
curl(1,1,1)
// {dx: 0, dy: 0, dz: 2}
```