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https://github.com/CAIMEOX/VoxelGeometry
Voxel geometry structure generator
https://github.com/CAIMEOX/VoxelGeometry
canvas chaos-game diffusion-limited-aggregation fractal function-programming geometry iterated-function-system lsystem turtle-graphics voxel voxel-generator
Last synced: 3 months ago
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Voxel geometry structure generator
- Host: GitHub
- URL: https://github.com/CAIMEOX/VoxelGeometry
- Owner: CAIMEOX
- License: agpl-3.0
- Created: 2022-07-31T03:18:53.000Z (over 2 years ago)
- Default Branch: core
- Last Pushed: 2024-04-04T14:55:54.000Z (7 months ago)
- Last Synced: 2024-07-28T13:25:19.338Z (3 months ago)
- Topics: canvas, chaos-game, diffusion-limited-aggregation, fractal, function-programming, geometry, iterated-function-system, lsystem, turtle-graphics, voxel, voxel-generator
- Language: TypeScript
- Homepage:
- Size: 3.09 MB
- Stars: 18
- Watchers: 3
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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- awesome-minecraft-bedrock - VoxelGeometry - Gametest based Minecraft geometry structure generator. (Tool (Create) / World)
README
# Voxel Geometry
Voxel Geometry is voxel geometry library which is used to construct **Space** (A collection of 3-dimension Vectors) and perform **transformation** between Spaces.
A voxel represents a value on a regular grid in three-dimensional space. Geometry means this software is very **mathematically** and owns more features as follows for generating awesome structures.
- **Basic Geometry** : Sphere, circle, cylinder, torus, line and more.
- **Lindenmayer system** (**L-System**) : A parallel rewriting system. The recursive nature of the L-system rules leads to self-similarity and thereby, fractal-like forms are easy to describe with an L-system.
- **Turtle Graphic** : Full features and extensions of turtle graphics.
- **Transformer** : Transforming space into another by pipe, compose, scale, diffusion and more.
- **Expression drawing** : Constructing from math expression or parametric equation.
- **Canvas API** : Javascript browser graphics API support.
- **Linear and Nonlinear Transform** : Mapping space into another one.
- **Diffusion Limited Aggression** : Simulating particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles.
- **Chaos Theory** : Iterated Function System which uses Chaos Game.
## Application
You can check the branches for the Application of this library in Minecraft.
- **core** : Voxel Geometry core
- **ws** : Voxel Geometry for Minecraft Bedrock (Based on Websocket server)
- **gt** : Voxel Geometry for Minecraft Bedrock (Based on Gametest framework)
- **webviewer** : Voxel Geometry Web Viewer
## Screenshots
Check the [gallery folder](https://github.com/CAIMEOX/VoxelGeometry/tree/webviewer/gallery#readme) for more information.
## Installation
```bash
npm i @pureeval/voxel-geometry
```
## Basic Concepts
### Vector
A vector represent a voxel in the Space, which has 3 components.
```js
// Create a unit vector
const vec: Vec3 = vec3(1, 1, 1);
```
### Space
Many Voxel Geometry functions will return a **Space** (A array of 3D vectors).
```ts
const ball: Space = sphere(5, 4);
```
## Basic Geometry
### Sphere
Create a sphere with radius.
```haskell
sphere :: (radius, inner_radius) -> Space
sphere(5,4)
```
### Circle
Create a circle with radius.
```haskell
circle :: (radius, inner_radius) -> Space
circle(5, 4)
```
### Torus
Create a torus.
```haskell
torus :: (radius, ring_radius) -> Space
torus(10,8)
```
## Transformer
### scale
Scale up a Space
```haskell
scale :: (Space, size) -> Space
```
### swap
Change the direction of a space.
```haskell
swap :: (Space, number, number) -> Space
```
### pipe
Take the point of the previous space as the origin of the next space.
```haskell
pipe :: (Space_1, Space_2, ...) -> Space
```
### diffusion
Spread out points of a space by a factor.
```haskell
diffusion :: (Space, factor) -> Space
```
### move
Move a space into a specific point.
```haskell
move :: (Space, x, y, z) -> Space
```
### embed
Embed a space into another space
```haskell
embed :: (Space, Space) -> Space
```
### Array Generator
Construct a discrete set of points.
```haskell
array_gen :: (xn, yn, zn, dx, dy, dz) -> Space
```
- \_n : Count
- d\_ : Interval
With step function:
```haskell
array_gen_fn :: (xn, yn, zn, num -> num, num -> num, num -> num) -> Space
```
## Turtle
### Turtle2D
Turtle graphics are vector graphics using a relative cursor (the "turtle") upon a Cartesian plane (x and y axis).
Voxel Geometry supports basic functions of turtle graphics:
```javascript
// Draw a straight with length 10
const t = new Turtle2D();
t.forward(10);
plot(t.getTrack());
```
### Turtle3D
Same as Turtle2D but lives in 3D space.
## L-System
An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar.It consists of an **alphabet**, a collection of **production rules** that expand each symbol into some larger string of symbols, an initial "**axiom**" string from which to begin construction, and a **mechanism** (Such as Turtle Graphics) for translating the generated strings into geometric structures.
In Voxel Geometry, you can use this function to create a Bracketed L-system:
```haskell
lsystem :: (axiom, Rules, generation) -> Space
```
For instance, we can create Peano curve by using l-system.
```javascript
lsystem(
'X',
{
X: 'XFYFX+F+YFXFY-F-XFYFX',
Y: 'YFXFY-F-XFYFX+F+YFXFY'
},
5
);
```
Voxel Geometry uses Turtle Graphics as default mechanism.
## Canvas
Voxel geometry supports a part of Canvas API in browser.
## Math Interpreter
### Parametric Equation
Parametric equations are commonly used to express the coordinates of the points that make up a geometric object such as a curve or surface. It includes group of quantities as functions of one or more independent variables called **parameters**.
For instance, we could write down the Parametric equations of ellipse. (t is the parameter, which varies from 0 to 2\*Pi)
```javascript
// a and b are constants
x = a * cos(t);
y = b * sin(t);
```
Express this in Voxel Geometry (step represent the changing value of the parameter):
```javascript
let step = 0.1;
plot(simple_parametric('5*Math.cos(t)', '0', '10*Math.sin(t)', ['t', 0, Math.PI * 2, step]));
```
### Expression
Takes a math expression (Such as inequality) as a condition and intervals, construct a space satisfies this:
```haskell
simple_equation :: (Expr, start, end, step) -> Space
```
For instance we can construct a sphere:
```javascript
plot(simple_equation('x*x+y*y+z*z<=5', -5, 5, 1));
```
## Diffusion Limited Aggression
Simulating particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles.
### DLA2D
```haskell
DLA2D :: (width, maxWalk, iterations, stepLength, temperature, stuckSpace = centerPoint) -> Space
```
- width : Width of operation space.
- maxWalk : Maximum number of particles that can exist simultaneously.
- iterations : Determine how many times before each particle supplement.
- stepLength : Step size of particles.
- temperature : The temperature of the iterative system will gradually decrease, which is related to the number of subsequent replenishment points.
- stuckSpace : A collection of particles that have been fixed at the beginning.
### DLA3D
Same as DLA2D but lives in 3D space.
```haskell
DLA3D :: (width, maxWalk, iterations, stepLength, temperature, stuckSpace = centerPoint) -> Space
```
## Iterated Function System
An iterated function system is a finite set of mappings on a complete metric space. Iterated function systems (IFSs) are a method of constructing **fractals**.
Voxel Geometry uses the classic algorithm named **Chaos Game** to compute IFS fractals.
Voxel Geometry uses the representation introduced in [this website](https://cs.lmu.edu/~ray/notes/ifs/)
By convention an IFS is written in rows of numbers in the form :
```
a b c d e f p
```
which describes the transform `λ(x,y).(ax+by+e,cx+dy+f)`. The value p represents the percentage of the fractal's area generated by the transform. Theoretically it is not required but if you select it well, the fractal is drawn much more efficiently.
```haskell
create_IFS :: (form, width, height) -> IFS
```
Here is a classic to try:
```javascript
// Create an IFS with Fractals.angle, 100000 iteration
plot(create_IFS(Fractals.angle, 100, 100).run(100000));
```