---
title: "Introduction to Particles"
author: "Thomas Lin Pedersen"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    fig_width: 7
    fig_height: 7
vignette: >
  %\VignetteIndexEntry{Introduction to Particles}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
set.seed(1)
```

This document provides an introduction to the use of `particles` and the 
underlying algorithm it gives the users access to. `particles` is an R 
implementation of The `d3-force` algorithm developed by Mike Bostock and can be
used to simulate many different types of interactions between particles and the 
world. While `particles` can be used as a simple physics engine it has not been
developed with this in mind and accuracy, in terms of how well it behaves like
the physical world, has not been a main priority during development.

## What is particles?
In it's essence `particles` provides a way of defining a set of spherical or 
dimensionless object, potentially connected with each other, a world 
governed by a set of rules, and then set the objects free in the world and see
how they behaves. The use cases for this are many, and include network 
visualisation, generative art, animation, and - most importantly - fun!

`particles` is build on top of `tidygraph` and uses it as the main 
representation of the particles and their relations. Even so, there is no need
to be experienced in network analysis and manipulation. `particles` can easily
be used without any of the objects being connected with each other and the 
objects can thus be thought of as stored in a simple data frame.

## Setting up a simulation
Central to the use of `particles` is the simulation, that is, setting the 
objects free in the world you've defined. There are several parts to a 
simulation:

- A description of the objects you wish to simulate
- An initialisation of the position and velocity of the objects
- A specification of how the simulation progress over time (e.g. a cooling, 
  letting the simulation slowly stabilise)
- A number of forces and constraints that governs how the objects behave in the
  system
- A specification of how many iterations the simulation should evolve

All of these steps can be specified using dedicated verbs and piped together. 
Let's look at an example:

```{r, message=FALSE}
library(particles)
library(tidygraph)

sim <- create_ring(10) %>% 
  simulate(velocity_decay = 0.6, setup = petridish_genesis(vel_max = 0)) %>% 
  wield(link_force) %>% 
  wield(manybody_force) %>% 
  impose(polygon_constraint, 
         polygon = cbind(c(-100, -100, 100, 100), c(-100, 100, 100, -100))) %>% 
  evolve(100)
```

So what's going on here? First we create a `tbl_graph` using the `create_ring()`
function from `tidygraph`, which basically creates a circular graph. Then we use
it to create a simulation using the `simulate()` function. In there we can set
how fast the velocity decays over time, as well how particles should be 
initialised. We use the `petridish_genesis()` to place the particles randomly on
a disc. Then we begin to define the forces that makes up the simulation using 
the `wield()` function. We first add a link force that makes connected particles
attract each other, and then a manybody force that pushes particles away from 
each others (unless the strength is set to a positive value in which case it
works like gravity, attracting particles to each other). We also adds a 
constraint to the system using the `impose()` function. Here we defines that 
particles must remain inside a 200x200 square. 

>The distinction between forces and constraints are a bit vague but generally 
forces will adjust the velocity of particles while constraints defines hard 
boundaries for the position and velocity of the particles.

Lastly we set the simulation to run for 100 iterations. If we did not specify a
number of iterations the simulation would run until it had cooled down (which
happens after 300 iterations using the default settings). We now have a 
simulation that has progressed a bit:

```{r}
sim
```

We could say that that was it and maybe plot it:

```{r, message=FALSE}
library(ggraph)
ggraph(as_tbl_graph(sim)) + 
  geom_edge_link() + 
  geom_node_point() + 
  theme_void()
```

(as we can see the simulation has the ring from its initial random state)

We could also change the simulation somehow and iterate some more on it:

```{r, message=FALSE}
sim <- sim %>% 
  unwield(2) %>% 
  wield(manybody_force, strength = 30) %>% 
  reheat(1) %>% 
  evolve()

ggraph(as_tbl_graph(sim)) + 
  geom_edge_link() + 
  geom_node_point() + 
  theme_void()
```

Let's unpack this. First we remove the second force (the repulsive manybody 
force) and then we add a new manybody force that attracts instead. Then we heat
up the system again (setting alpha back to the original value) and let it evolve
until it has cooled down. The result is a struggle between the link force and 
the manybody force over dominance of the system.

## Tidy eval
Many of the different forces and constraints let you set parameters on a per 
particle or per connection basis - e.g. for the link force discussed above we 
could let the strength of the force be related to the weight of the edge. 
`particles` let you reference node and edge variables directly when specifying 
the force or constraint, e.g.

```{r, message=FALSE}
sim <- play_islands(3, 10, 0.6, 3) %>% 
  mutate(group = group_infomap()) %>% 
  activate(edges) %>% 
  mutate(weight = ifelse(.N()$group[to] == .N()$group[from], 1, 0.25)) %>% 
  simulate() %>% 
  wield(link_force, strength = weight, distance = 10/weight) %>% 
  evolve()

ggraph(as_tbl_graph(sim)) + 
  geom_edge_link(aes(width = weight), alpha = 0.3, lineend = 'round') + 
  geom_node_point() + 
  theme_void() + 
  theme(legend.position = 'none')
```

The nice thing about using node and edge variables is that `particles` keeps
track of them and if you change them the force will get retrained:

```{r, message=FALSE}
sim <- sim %>% 
  activate(edges) %>% 
  mutate(weight = 1) %>% 
  reheat(1) %>% 
  evolve()

ggraph(as_tbl_graph(sim)) + 
  geom_edge_link(aes(width = weight), alpha = 0.3, lineend = 'round') + 
  geom_node_point() + 
  theme_void() + 
  theme(legend.position = 'none')
```

Consult the documentation of each force and constraint to see which parameters
that are tidy evaled.

## Iteration callback
Sometimes you are more interested in the process than the end point. In that
case you might want to look at the state of the simulation at each step it goes
through. Luckily, the `evolve()` function comes with a powerful callback 
mechanism that allows you to do all sorts of things. If the callback function
returns a simulation object it will replace the current simulation, otherwise
the return value will be discarded and the side-effects, such as plots, will be
the only effect of it. As you can imagine you can do many things with this 
capability, such as removing or adding new particles and connections, or 
changing forces midway. If the callback plots the current state it can be used
directly with the `animation` package to produce animated views of your 
simulation. Lastly, it can be used to record the state so the it can easily be
retrieved later on. For this you can use the predefined `record()` function:

```{r}
volcano_field <- (volcano - min(volcano)) / diff(range(volcano)) * 2 * pi
sim <- create_empty(1000) %>% 
  simulate(alpha_decay = 0, setup = aquarium_genesis(vel_max = 0)) %>% 
  wield(reset_force, xvel = 0, yvel = 0) %>% 
  wield(field_force, angle = volcano_field, vel = 0.1, xlim = c(-5, 5), ylim = c(-5, 5)) %>% 
  evolve(100, record)

traces <- data.frame(do.call(rbind, lapply(sim$history, position)))
names(traces) <- c('x', 'y')
traces$particle <- rep(1:1000, 100)

ggplot(traces) +
  geom_path(aes(x, y, group = particle), size = 0.1) + 
  theme_void() + 
  theme(legend.position = 'none')
```

In this example we define a field force based on our beloved volcano data set. 
The field force applies a velocity based on a given vector field. We define that
the simulation has no cooling (`alpha_decay = 0`) and that the particles should 
be placed randomly in a rectangle. Besides the field force we also add a reset
force that sets the velocity to zero in each iteration so that the vector field
does not accumulate. When all this is done we run the simulation for 100 
iterations and saves each state with the `record()` function.

To get the plot we extract the positions from each iteration and simply plots
the trajectory of each particle.

## Summing up
Hopefully you have gotten a taste of what is possible with `particles`, but 
there are many more options and possibilities. The package is developed both
for practical use and for having fun — with luck you can do both simultaneously.
