---
title: "Trajectory simulations in 2-D"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Trajectory simulations in 2-D}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
<style>
body {
text-align: justify}
</style>
```{r, echo = FALSE, eval=TRUE, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
options(knitr.table.format = "html", rmarkdown.html_vignette.check_title = FALSE)

library(eRTG3D)
library(ggplot2)
set.seed(123)
```

## 2-D simulations as special case of 3-D
Since movement in 2-D is a special case of movement in 3-D, the `eRTG3D` algorithm also supports two-dimensional simulations. The underlying data structure of the algorithm remains in three-dimensional, with the third dimension (z) being constant, as for example zero. This approach guarantees a seamless transition between 2-D and 3-D simulations. Therefore, two P and Q probabilities are be extracted from 2D and 3D trajectories, then a combined simulation can take place.

## Example trajectory
```{r }
trajectory.3D <- sim.crw.3d(nStep = 100, rTurn = 0.99, rLift = 0.99, meanStep = 0.1)
```

## Constant z-dimension
To simulate in 2-D the third dimension of the trajectory is set to zero:

```{r }
trajectory.2D <- trajectory.3D
trajectory.2D$z <- 0
head(trajectory.2D)
```

If the original trajectory is already two-dimensional, a third column `z` has to be added: `trajectory.2D$z <- 0`. 

## Simulations in 2-D
Now the workflow is the same as in 3-D, described in the standard workflow vignette:

```{r, echo = FALSE, eval=TRUE, include=FALSE}
simulation.2D <- reproduce.track.3d(trajectory.2D)
```

**Note:** Since it is not feasible to use a DEM (`DEM = demRaster`) in 2-D simualtions, the adding of a DEM in the somulations will result in dead ends. A BG layer (`BG = bgRaster`) with a binary mask or continous probabilities for the simulation area can be passed (e.g. water bodies, nutrition sources, ...).

```{r eval=FALSE}
simulation.2D <- reproduce.track.3d(trajectory.2D)
```

And plotting the results:

```{r eval=TRUE, fig.align="center"}
plot2d(trajectory.2D, simulation.2D, titleText = "2-D trajectory simulation")
```