# Scatterplot3d: 3D graphics - R software and data visualization

- Install and load scaterplot3d
- Prepare the data
- The function scatterplot3d()
- Basic 3D scatter plots
- Change the main title and axis labels
- Change the shape and the color of points
- Change point shapes by groups
- Change point colors by groups
- Change the global appearance of the graph
- Add bars
- Modification of scatterplot3d output
- Infos

There are many packages in R (*RGL*, *car*, *lattice*, *scatterplot3d*, …) for creating **3D graphics**.

This **tutorial** describes how to generate a scatter pot in the **3D space** using **R software** and the package **scatterplot3d**.

**scaterplot3d** is very simple to use and it can be easily extended by adding supplementary points or regression planes into an already generated graphic.

It can be easily installed, as it requires only an installed version of R.

# Install and load scaterplot3d

```
install.packages("scatterplot3d") # Install
library("scatterplot3d") # load
```

# Prepare the data

The *iris* data set will be used:

```
data(iris)
head(iris)
```

```
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 4.7 3.2 1.3 0.2 setosa
4 4.6 3.1 1.5 0.2 setosa
5 5.0 3.6 1.4 0.2 setosa
6 5.4 3.9 1.7 0.4 setosa
```

*iris* data set gives the measurements of the variables sepal length and width, petal length and width, respectively, for 50 flowers from each of 3 species of iris. The species are Iris setosa, versicolor, and virginica.

# The function scatterplot3d()

A simplified format is:

`scatterplot3d(x, y=NULL, z=NULL)`

x, y, z are the coordinates of points to be plotted. The arguments *y* and *z* can be optional depending on the structure of *x*.

In what cases, *y* and *z* are optional variables?

**Case 1 : x is a formula**of type*zvar ~ xvar + yvar*. xvar, yvar and zvar are used as x, y and z variables**Case 2 : x is a matrix**containing at least 3 columns corresponding to x, y and z variables, respectively

# Basic 3D scatter plots

```
# Basic 3d graphics
scatterplot3d(iris[,1:3])
```

```
# Change the angle of point view
scatterplot3d(iris[,1:3], angle = 55)
```

# Change the main title and axis labels

```
scatterplot3d(iris[,1:3],
main="3D Scatter Plot",
xlab = "Sepal Length (cm)",
ylab = "Sepal Width (cm)",
zlab = "Petal Length (cm)")
```

# Change the shape and the color of points

The argument *pch* and *color* can be used:

`scatterplot3d(iris[,1:3], pch = 16, color="steelblue")`

Read more on the different point shapes available in R : Point shapes in R

# Change point shapes by groups

```
shapes = c(16, 17, 18)
shapes <- shapes[as.numeric(iris$Species)]
scatterplot3d(iris[,1:3], pch = shapes)
```

Read more on the different point shapes available in R : Point shapes in R

# Change point colors by groups

```
colors <- c("#999999", "#E69F00", "#56B4E9")
colors <- colors[as.numeric(iris$Species)]
scatterplot3d(iris[,1:3], pch = 16, color=colors)
```

Read more about colors in R: colors in R

# Change the global appearance of the graph

The arguments below can be used:

**grid**: a logical value. If TRUE, a grid is drawn on the plot.**box**: a logical value. If TRUE, a box is drawn around the plot

## Remove the box around the plot

```
scatterplot3d(iris[,1:3], pch = 16, color = colors,
grid=TRUE, box=FALSE)
```

Note that, the argument **grid = TRUE** plots only the grid on the xy plane. In the next section, we’ll see how to add grids on the other facets of the 3D scatter plot.

## Add grids on scatterplot3d

This section describes how to add *xy-*, *xz-* and *yz-* to **scatterplot3d** graphics.

We’ll use a custom function named **addgrids3d()**. The source code is available here : addgrids3d.r. The function is inspired from the discussion on this forum.

A simplified format of the function is:

```
addgrids3d(x, y=NULL, z=NULL, grid = TRUE,
col.grid = "grey", lty.grid=par("lty"))
```

**x, y, and z**are numeric vectors specifying the x, y, z coordinates of points. x can be a matrix or a data frame containing 3 columns corresponding to the x, y and z coordinates. In this case the arguments y and z are optional**grid**specifies the facet(s) of the plot on which grids should be drawn. Possible values are the combination of “xy”, “xz” or “yz”. Example: grid = c(“xy”, “yz”). The default value is TRUE to add grids only on xy facet.**col.grid, lty.grid**: the color and the line type to be used for grids

**Add grids on the different factes of scatterplot3d graphics**:

```
# 1. Source the function
source('http://www.sthda.com/sthda/RDoc/functions/addgrids3d.r')
# 2. 3D scatter plot
scatterplot3d(iris[, 1:3], pch = 16, grid=FALSE, box=FALSE)
# 3. Add grids
addgrids3d(iris[, 1:3], grid = c("xy", "xz", "yz"))
```

The problem on the above plot is that the grids are drawn over the points.

The **R code** below, we’ll put the points in the foreground using the following steps:

- An empty scatterplot3 graphic is created and the result of
**scatterplot3d()**is assigned to*s3d* - The function
**addgrids3d()**is used to add grids - Finally, the function
**s3d$points3d**is used to add points on the 3D scatter plot

```
# 1. Source the function
source('~/hubiC/Documents/R/function/addgrids3d.r')
# 2. Empty 3D scatter plot using pch=""
s3d <- scatterplot3d(iris[, 1:3], pch = "", grid=FALSE, box=FALSE)
# 3. Add grids
addgrids3d(iris[, 1:3], grid = c("xy", "xz", "yz"))
# 4. Add points
s3d$points3d(iris[, 1:3], pch = 16)
```

The function **points3d()** is described in the next sections.

# Add bars

The argument **type = “h”** is used. This is useful to see very clearly the x-y location of points.

```
scatterplot3d(iris[,1:3], pch = 16, type="h",
color=colors)
```

# Modification of scatterplot3d output

**scatterplot3d** returns a list of function closures which can be used to add elements on a existing plot.

The returned functions are :

**xyz.convert()**: to convert 3D coordinates to the 2D parallel projection of the existing scatterplot3d. It can be used to add arbitrary elements, such as legend, into the plot.**points3d()**: to add*points*or*lines*into the existing plot**plane3d()**: to add a*plane*into the existing plot**box3d()**: to add or refresh a*box*around the plot

## Add legends

### Specify the legend position using xyz.convert()

- The result of
**scatterplot3d()**is assigned to*s3d* - The function
**s3d$xyz.convert()**is used to specify the coordinates for legends - the function
**legend()**is used to add legends to plots

```
s3d <- scatterplot3d(iris[,1:3], pch = 16, color=colors)
legend(s3d$xyz.convert(7.5, 3, 4.5), legend = levels(iris$Species),
col = c("#999999", "#E69F00", "#56B4E9"), pch = 16)
```

It’s also possible to specify the **position of legends** using the following keywords: “bottomright”, “bottom”, “bottomleft”, “left”, “topleft”, “top”, “topright”, “right” and “center”.

**legend**in R: legend in R.

### Specify the legend position using keywords

```
# "right" position
s3d <- scatterplot3d(iris[,1:3], pch = 16, color=colors)
legend("right", legend = levels(iris$Species),
col = c("#999999", "#E69F00", "#56B4E9"), pch = 16)
```

```
# Use the argument inset
s3d <- scatterplot3d(iris[,1:3], pch = 16, color=colors)
legend("right", legend = levels(iris$Species),
col = c("#999999", "#E69F00", "#56B4E9"), pch = 16, inset = 0.1)
```

What means the argument **inset** in the R code above?

The argument **inset** is used to inset distance(s) from the margins as a fraction of the plot region when legend is positioned by keyword. ( see ?legend from R). You can play with *inset* argument using negative or positive values.

```
# "bottom" position
s3d <- scatterplot3d(iris[,1:3], pch = 16, color=colors)
legend("bottom", legend = levels(iris$Species),
col = c("#999999", "#E69F00", "#56B4E9"), pch = 16)
```

Using *keywords* to specify the *legend position* is very simple. However, sometimes, there is an overlap between some points and the legend box or between the axis and legend box.

Is there any solution to avoid this overlap?

Yes, there are several solutions using the combination of the following arguments for the function **legend()**:

**bty = “n”**: to**remove the box around the legend**. In this case the background color of the legend becomes transparent and the overlapping points become visible.**bg = “transparent”**: to change the background color of the legend box to*transparent*color (this is only possible when bty != “n”).**inset**: to modify the distance(s) between plot margins and the legend box.**horiz**: a logical value; if TRUE, set the legend horizontally rather than vertically**xpd**: a logical value; if TRUE, it enables the legend items to be drawn outside the plot.

### Customize the legend position

```
# Custom point shapes
s3d <- scatterplot3d(iris[,1:3], pch = shapes)
legend("bottom", legend = levels(iris$Species),
pch = c(16, 17, 18),
inset = -0.25, xpd = TRUE, horiz = TRUE)
```

```
# Custom colors
s3d <- scatterplot3d(iris[,1:3], pch = 16, color=colors)
legend("bottom", legend = levels(iris$Species),
col = c("#999999", "#E69F00", "#56B4E9"), pch = 16,
inset = -0.25, xpd = TRUE, horiz = TRUE)
```

```
# Custom shapes/colors
s3d <- scatterplot3d(iris[,1:3], pch = shapes, color=colors)
legend("bottom", legend = levels(iris$Species),
col = c("#999999", "#E69F00", "#56B4E9"),
pch = c(16, 17, 18),
inset = -0.25, xpd = TRUE, horiz = TRUE)
```

In the R code above, you can play with the arguments *inset*, *xpd* and *horiz* to see the effects on the appearance of the legend box.

## Add point labels

The function **text()** is used as follow:

```
scatterplot3d(iris[,1:3], pch = 16, color=colors)
text(s3d$xyz.convert(iris[, 1:3]), labels = rownames(iris),
cex= 0.7, col = "steelblue")
```

## Add regression plane and supplementary points

- The result of
**scatterplot3d()**is assigned to*s3d* - A linear model is calculated as follow : lm(zvar ~ xvar + yvar). Assumption : zvar depends on xvar and yvar
- The function
**s3d$plane3d()**is used to add the regression plane - Supplementary points are added using the function
**s3d$points3d()**

The data sets *trees* will be used:

```
data(trees)
head(trees)
```

```
Girth Height Volume
1 8.3 70 10.3
2 8.6 65 10.3
3 8.8 63 10.2
4 10.5 72 16.4
5 10.7 81 18.8
6 10.8 83 19.7
```

This data set provides measurements of the girth, height and volume for black cherry trees.

**3D scatter plot with the regression plane**:

```
# 3D scatter plot
s3d <- scatterplot3d(trees, type = "h", color = "blue",
angle=55, pch = 16)
# Add regression plane
my.lm <- lm(trees$Volume ~ trees$Girth + trees$Height)
s3d$plane3d(my.lm)
# Add supplementary points
s3d$points3d(seq(10, 20, 2), seq(85, 60, -5), seq(60, 10, -10),
col = "red", type = "h", pch = 8)
```

# Infos

This analysis has been performed using **R software** (ver. 3.1.2) and **scatterplot3d** (ver. 0.3-35)

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