## Warning: These vignettes assume pandoc version 1.13.1; older versions may
## give poor formatting.

## Introduction

The rgl package is used to produce interactive 3-D plots. It contains high-level graphics commands modelled loosely after classic R graphics, but working in three dimensions. It also contains low level structure inspired by (but incompatible with) the grid package.

This document gives an overview. See the help pages for details.

This document was written in R Markdown, using the knitr package for production. It corresponds to rgl version 0.95.1441.

Most of the highlighted function names are HTML links. The internal links should work in any browser; the links to help topics should work if you view the vignette from within the R help system.

The document includes WebGL figures. To view these, you must have Javascript and WebGL enabled in your browser. Some older browsers may not support this – see http://get.webgl.org for tests and links to a discussion.

The WebGL figures were produced using the rglwidget package, version 0.1.1434.

## Basics and High Level Functions

The plot3d function plots points within an rgl window. It is similar to the classic plot function, but works in 3 dimensions.

For example

with(iris, plot3d(Sepal.Length, Sepal.Width, Petal.Length,
type="s", col=as.numeric(Species)))

can be used to plot three columns of the iris data.
Allowed plot types include "p", "l", "h", "s", meaning points, lines, segments from z=0, and spheres. There’s a lot of flexibility in specifying the coordinates; the xyz.coords function from the grDevices package is used for this.

You can use your mouse to manipulate the plot. The default is that if you click and hold with the left mouse button, you can rotate the plot by dragging it. The right mouse button is used to resize it, and the middle button changes the perspective in the point of view.

If you call plot3d again, it will overwrite the current plot. To open a new graphics window, use open3d.

The other high level function is persp3d to draw surfaces. It is similar to the classic persp function, but with greater flexibility. First, any of x, y or z can be specified using matrices, not just z. This allows parametric surfaces to be plotted. An even simpler specification is possible: x may be a function, in which case persp3d will work out the grid itself. See ?persp3d.function for details. For example, the MASS package estimates Gamma parameters using maximum likelihood in a ?MASS::fitdistr example. Here we show the log likelihood surface.

library(MASS)
# from the fitdistr example
set.seed(123)
x <- rgamma(100, shape = 5, rate = 0.1)
fit <- fitdistr(x, dgamma, list(shape = 1, rate = 0.1), lower = 0.001)
loglik <- function(shape, rate) sum(dgamma(x, shape=shape, rate=rate,
log=TRUE))
loglik <- Vectorize(loglik)
xlim <- fit$estimate[1]+4*fit$sd[1]*c(-1,1)
ylim <- fit$estimate[2]+4*fit$sd[2]*c(-1,1)

mfrow3d(1, 2, sharedMouse = TRUE)
persp3d(loglik,
xlim = xlim, ylim = ylim,
n = 30)
zlim <- fit\$loglik + c(-qchisq(0.99, 2)/2, 0)
next3d()
persp3d(loglik,
xlim = xlim, ylim = ylim, zlim = zlim,
n = 30)

On the left, the whole surface over a range of the parameters; on the right, only the parts of the surface with log likelihood values near the maximum.

Note: this example used the knitr hook functions (see setupKnitr) to insert the scene into this vignette; the previous example used the rglwidget function from the package of the same name. We generally recommend the newer rglwidget approach.

### Primitive shapes

Just as we have points and lines in classic graphics, there are a number of low level functions in rgl to add graphical elements to the currently active plot. The “primitive” shapes are those that are native to OpenGL:

 points3d: adds points lines3d: adds lines segments3d: adds line segments triangles3d: adds triangles quads3d: adds quadrilaterals

Each of the above functions takes arguments x, y and z, again using xyz.coords for flexibility. They group successive entries as necessary. For example, the triangles3d function takes each successive triple of points as the vertices of a triangle.

You can use these functions to annotate the current graph, or to construct a figure from scratch.

### Constructed shapes

rgl also has a number of objects which it constructs from the primitives.

 text3d, texts3d: adds text abclines3d: adds straight lines to plot (like abline) planes3d: adds planes to plot clipplanes3d: add clipping planes to plot sprites3d, particles3d: add sprites (fixed shapes or images) to plot spheres3d: adds spheres surface3d, terrain3d: a surface (as used in persp3d)

### Axes and other “decorations”

The following low-level functions control the look of the graph:

 axes3d, axis3d: add axes to plot box3d, bbox3d: add box around plot title3d: add title to plot mtext3d: add marginal text to plot decorate3d: add multiple “decorations” (scales, etc.) to plot aspect3d: set the aspect ratios for the plot bg3d, bgplot3d: set the background of the scene show2d: show a 2D plot or image in a 3D scene legend3d: set a legend for the scene grid3d: add a reference grid to a graph

For example, to plot three random triangles, one could use

triangles3d(cbind(x=rnorm(9), y=rnorm(9), z=rnorm(9)), col = "green")
decorate3d()
bg3d("lightgray")
aspect3d(1,1,1)

Besides the *3d functions mentioned above, there are even lower-level functions rgl.primitive, rgl.points, rgl.linestrips, rgl.lines, rgl.triangles, rgl.quads, rgl.texts, rgl.abclines, rgl.planes, rgl.bg, rgl.clipplanes, rgl.bbox, rgl.spheres, rgl.sprites, rgl.surface.
You should avoid using these functions, which do not work well with the higher level *3d functions. See the ?r3d help topic for details.

## Controlling the Look of the Scene

### Lighting

In most scenes, objects are “lit”, meaning that their appearance depends on their position and orientation relative to lights in the scene. The lights themselves don’t normally show up, but their effect on the objects does.

Use the light3d function to specify the position and characteristics of a light. Lights may be infinitely distant, or may be embedded within the scene. Their characteristics include ambient, diffuse, and specular components, all defaulting to white. The ambient component appears the same from any direction. The diffuse component depends on the angle between the surface and the light, while the specular component also takes the viewer’s position into account.

The rgl.light function is a lower-level function with different defaults; users should normally use light3d.

### Materials

The mental model used in rgl is that the objects being shown in scenes are physical objects in space, with material properties that affect how light reflects from them (or is emitted by them). These are mainly controlled by the material3d function, or by arguments to other functions that are passed to it.

The material properties that can be set by calls to material3d are described in detail in the ?material3d help page. Here we give an overview.

Property Default Meaning
color white vector of surface colors to apply to successive vertices for diffuse light
alpha 1 transparency: 0 is invisible, 1 is opaque
lit TRUE whether lighting calculations should be done
ambient black color in ambient light
specular white color in specular light
emission black color emitted by the surface
shininess 50 controls the specular lighting: high values look shiny
smooth TRUE whether shading should be interpolated between vertices
texture NULL optional path to a “texture” bitmap to be displayed on the surface
front, back fill should polygons be filled, or outlined?
size 3 size of points in pixels
lwd 1 width of lines in pixels

Other properties include “texmipmap”, “texmagfilter”, “texminfilter”, “texenvmap”, “fog”, “point_antialias”, “line_antialias”, “depth_mask”, and “depth_test”; see the help page for details.

There is also an rgl.material function that works at a lower level; users should normally avoid it.

### par3d: Miscellaneous graphical parameters

The par3d function, modelled after the classic graphics par function, sets or reads a variety of different rgl internal parameters. Some parameters are completely read-only; others are fixed at the time the window is opened, and others may be changed at any time.

Name Changeable? Description
antialias fixed Amount of hardware antialiasing
cex Default size for text
family Device-independent font family name; see ?text3d
font Integer font number
useFreeType Should FreeType fonts be used if available?
fontname read-only System-dependent font name set by rglFonts
FOV Field of view, in degrees. Zero means isometric perspective
ignoreExtent Should rgl ignore the size of new objects when computing the bounding box?
skipRedraw Should rgl suppress updates to the display?
maxClipPlanes read-only How many clip planes can be defined?
modelMatrix read-only The OpenGL ModelView matrix; partly set by view3d or the obsolete rgl.viewpoint
projMatrix read-only The OpenGL Projection matrix
bbox read-only Current bounding-box of the scene
viewport Dimensions in pixels of the scene within the window
windowRect Dimensions in pixels of the window on the whole screen
listeners Which subscenes respond to mouse actions in the current one
mouseMode What the mouse buttons do. See “mouseMode”
observer read-only The position of the observer; set by observer3d
scale Rescaling for each coordinate; see aspect3d
zoom Magnification of the scene

### Default settings

The r3dDefaults list and the getr3dDefaults function control defaults in new windows opened by open3d.
The function looks for the variable in the user’s global environment, and if not found there, finds the one in the rgl namespace. This allows the user to override the default settings for new windows.

Once found, the r3dDefaults list provides initial values for par3d parameters, as well as defaults for material3d and bg3d in components "material" and "bg" respectively.

## Meshes: Constructing Shapes

rgl includes a number of functions to construct and display various solid shapes. These generate objects of class "shape3d", "mesh3d" or "shapelist3d". The details of the classes are described below. We start with functions to generate them.

### Specific solids

These functions generate specific shapes. Optional arguments allow attributes such as colour or transformations to be specified.

 tetrahedron3d, cube3d, octahedron3d, dodecahedron3d, icosahedron3d: Platonic solids cuboctahedron3d, oh3d: other solids
open3d()
cols <- rainbow(7)
layout3d(matrix(1:16, 4,4), heights=c(1,3,1,3))
text3d(0,0,0,"tetrahedron3d"); next3d()
text3d(0,0,0,"cube3d"); next3d()
text3d(0,0,0,"octahedron3d"); next3d()
text3d(0,0,0,"dodecahedron3d"); next3d()
text3d(0,0,0,"icosahedron3d"); next3d()
text3d(0,0,0,"cuboctahedron3d"); next3d()
text3d(0,0,0,"oh3d"); next3d()
shade3d(oh3d(col=cols[7]))

### Generating new shapes

These functions generate new shapes:

 cylinder3d: generate a tube or cylinder polygon3d: generate a flat polygon by triangulation extrude3d: generate an “extrusion” of a polygon turn3d: generate a solid of rotation ellipse3d: generate an ellipsoid in various ways tmesh3d, qmesh3d: generate a shape from vertices and faces shapelist3d: generate a shape by combining other shapes

A related function is triangulate, which takes a two dimensional polygon and divides it up into triangles using the “ear-clipping” algorithm.

### The underlying class structure for shapes

"shape3d" is the basic abstract type. Objects of this class can be displayed by shade3d (which shades faces), wire3d (which draws edges), or dot3d (which draws points at each vertex.) Note that wire3d and dot3d only work within R; in HTML output from writeWebGL only shade3d is supported.

"mesh3d" is a descendant type. Objects of this type contain the following fields:

Field Meaning
vb A 4 by n matrix of vertices in homogeneous coordinates. Each column is a point.
it (optional) A 3 by t matrix of vertex indices. Each column is a triangle.
ib (optional) A 4 by q matrix of vertex indices. Each column is a quadrilateral.
material (optional) A list of material properties.
normals (optional) A matrix of the same shape as vb, containing normal vectors at each vertex.
texcoords (optional) A 2 by n matrix of texture coordinates corresponding to each vertex.

### Manipulating shapes

The final set of functions manipulate and modify mesh objects:

 addNormals: add normal vectors to make a shape look smooth subdivision3d: add extra vertices to make it look even smoother

## Multi-figure Layouts

rgl has several functions to support displaying multiple different “subscenes” in the same window. The high level functions are

 mfrow3d: Multiple figures (like par(“mfrow”) layout3d: Multiple figures (like layout) next3d: Move to the next figure (like plot.new or frame) subsceneList: List all the subscenes in the current layout clearSubsceneList Clear the current list and revert to the previous one

There are also lower level functions.

 newSubscene3d: Create a new subscene, with fine control over what is inherited from the parent currentSubscene3d: Report on the active subscene subsceneInfo: Get information on current subscene useSubscene3d: Make a different subscene active addToSubscene3d, delFromSubscene3d: Add objects to a subscene, or delete them gc3d: Do “garbage collection”: delete objects that are not displayed in any subscene

## Utility Functions

### User interaction

By default, rgl detects and handles mouse clicks within your scene, and uses these to control its appearance. You can find out the current handlers using the following code:

par3d("mouseMode")
##        left       right      middle       wheel
## "trackball"      "zoom"       "fov"      "pull"

The labels c("left", "right", "middle") refer to the buttons on a three button mouse, or simulations of them on other mice. "wheel" refers to the mouse wheel.

The button actions generally correspond to click and drag operations. Possible values for “mouseMode” for buttons or the wheel are as follows:

 "none" No action "trackball" The mouse acts as a virtual trackball. Clicking and dragging rotates the scene "xAxis", "yAxis", "zAxis" Like "trackball", but restricted to rotation about one axis "polar" The mouse affects rotations by controlling polar coordinates directly "selecting" The mouse is being used by the select3d function "zoom" The mouse zooms the display "fov" The mouse affects perspective by changing the field of view "pull" Rotating the mouse wheel towards the user “pulls the scene closer” "push" The same rotation “pushes the scene away” "user" A user action set by rgl.setMouseCallbacks, rgl.setWheelCallback. Use rgl.getMouseCallbacks and rgl.getWheelCallback to retrieve

The following functions make use of the mouse for selection within a scene.

 identify3d like the classic graphics identify function select3d returns a function that tests whether a coordinate was selected selectpoints3d selects from specific objects

The rgl.select3d function is an obsolete version of select3d, and rgl.select is a low-level support function.

### Animations

rgl has several functions that can be used to construct animations. These are based on functions that update the scene according to the current real-world time, and repeated calls to those. The functions are:

 play3d Repeatedly call the update function spin3d Update the display by rotating at a constant rate par3dinterp Compute new values of some par3d parameters by interpolation over time

See the movie3d function for a way to output an animation to a file on disk.
Animations are not currently supported in the HTML written by writeWebGL, though the rglwidget::playwidget function provides equivalent functionality.

### Exporting and importing scenes

rgl contains several functions to write scenes to disk for use by other software, or to read them in.

In order from highest fidelity to lowest, the functions are:

 scene3d Save a scene to an R variable, which can be saved and reloaded writeWebGL Write HTML and Javascript to display a scene in a web browser. (See also User Interaction in WebGL.) writePLY Write PLY files (commonly used in 3D printing) readOBJ, writeOBJ Read or write OBJ files (commonly used in 3D graphics) readSTL, writeSTL Read or write STL files (also common in 3D printing) rgl.useNULL A helper function for setting a NULL device

See the help page rgl.useNULL for instructions on how to use rgl on a “headless” system.

There are also functions to save snapshots or other recordings of a scene, without any 3D information being saved:

 snapshot3d Save a PNG file bitmap of the scene rgl.postscript Save a Postscript, LaTeX, PDF, SVG or PGF vector rendering of the scene movie3d Save a series of bitmaps to be assembled into a movie rgl.pixels Obtain pixel-level information about the scene in an R variable rgl.Sweave Driver function for inserting a snapshot into a Sweave document. hook_rgl, hook_webgl knitr hook functions for inserting images into a document. setupKnitr Function to set up knitr hooks

The rgl.snapshot function is identical to snapshot3d. The functions rgl.Sweave.off, Sweave.snapshot are involved in Sweave processing and not normally called by users.

### Working with WebGL scenes

There are currently two schemes for exporting a scene to a web page. Both require the rglwidget package and use the same underlying code.

The recommended approach works with the htmlwidgets framework (see http://www.htmlwidgets.org/). In an R Markdown document in knitr, use the chunk option webgl=TRUE, or the rglwidget::rglwidget() function. More details are given in the vignette User Interaction in WebGL.

The older approach uses the writeWebGL function to export a scene to HTML and Javascript code.
The functions below write HTML and Javascript for working with the exported scene.

 propertySlider insert a slider to make changes to a scene clipplaneSlider insert a slider to control a clipping plane subsetSlider insert a slider to control which objects are displayed toggleButton insert a button to toggle some items propertySetter function to modify properties subsetSetter function to choose subsets ageSetter function to “age” vertices par3dinterpSetter function like par3dinterp vertexSetter function to modify individual vertices matrixSetter function to modify matrices

### Working with the scene

rgl maintains internal structures for all the scenes it displays. The following functions allow users to find information about them and manipulate them.

 open3d open a new window rgl.close close the current window rgl.bringtotop bring the current window to the top rgl.cur id of the active device rgl.dev.list ids of all active devices rgl.set set a particular device to be active rgl.ids ids and types of all current objects rgl.attrib, rgl.attrib.count: attributes of objects in the scene pop3d, rgl.pop delete an object from the scene clear3d, rgl.clear delete all objects of certain classes rgl.projection return information about the current projection rgl.user2window, rgl.window2user convert between coordinates in the current projection

In addition to these, there are some other related functions which should rarely be called by users: rgl.init, rgl.open, rgl.quit.

### Working with 3-D vectors

Most rgl functions work internally with “homogeneous” coordinates. In this system, 3-D points are represented with 4 coordinates, generally called (x, y, z, w). The corresponding Euclidean point is (x/w, y/w, z/w), if w is nonzero; zero values of w correspond to “points at infinity”. The advantage of this system is that affine transformations including translations and perspective shifts become linear transformations, with multiplication by a 4 by 4 matrix.

rgl has the following functions to work with homogeneous coordinates:

 asEuclidean, asHomogeneous: convert between homogeneous and Euclidean coordinates rotate3d, scale3d, translate3d: apply a transformation transform3d: apply a general transformation rotationMatrix, scaleMatrix, translationMatrix: compute the transformation matrix identityMatrix return a 4 x 4 identity matrix

There is also a function GramSchmidt, mainly for internal use: it does a Gram-Schmidt orthogonalization of a 3x3 matrix, with some specializations for its use in cylinder3d.

## Warning: Work in Progress!

This vignette is in a preliminary form. Many aspects of the rgl package are not described, or do not have examples. There may even be functions that are missed completely, if the following list is not empty:

## character(0)

## Index of Functions

The following functions and constants are described in this document:

 GramSchmidt hook_webgl qmesh3d rgl.projection spin3d Sweave.snapshot icosahedron3d quads3d rgl.quads sprites3d abclines3d identify3d r3dDefaults rgl.quit subdivision3d addNormals identityMatrix readOBJ rgl.select subsceneInfo addToSubscene3d layout3d readSTL rgl.select3d subsceneList ageSetter legend3d rgl.Sweave rgl.set subsetSetter asEuclidean light3d rgl.Sweave.off rgl.setMouseCallbacks subsetSlider asHomogeneous lines3d rgl.abclines rgl.setWheelCallback surface3d aspect3d material3d rgl.attrib rgl.snapshot terrain3d axes3d matrixSetter rgl.attrib.count rgl.spheres tetrahedron3d axis3d mfrow3d rgl.bbox rgl.sprites text3d bbox3d mouseMode rgl.bg rgl.surface texts3d bg3d movie3d rgl.bringtotop rgl.texts title3d bgplot3d mtext3d rgl.clear rgl.triangles tmesh3d box3d newSubscene3d rgl.clipplanes rgl.useNULL toggleButton clear3d next3d rgl.close rgl.user2window transform3d clearSubsceneList observer3d rgl.cur rgl.viewpoint translate3d clipplaneSlider octahedron3d rgl.dev.list rgl.window2user translationMatrix clipplanes3d oh3d rgl.getMouseCallbacks rglFonts triangles3d cube3d open3d rgl.getWheelCallback rotate3d triangulate cuboctahedron3d par3d rgl.ids rotationMatrix turn3d currentSubscene3d par3dinterp rgl.init scale3d useSubscene3d cylinder3d par3dinterpSetter rgl.light scaleMatrix vertexSetter decorate3d particles3d rgl.lines scene3d view3d delFromSubscene3d persp3d rgl.linestrips segments3d wire3d dodecahedron3d planes3d rgl.material select3d writeOBJ dot3d play3d rgl.open selectpoints3d writePLY ellipse3d plot3d rgl.pixels setupKnitr writeSTL extrude3d points3d rgl.planes shade3d writeWebGL gc3d polygon3d rgl.points shapelist3d getr3dDefaults pop3d rgl.pop show2d grid3d propertySetter rgl.postscript snapshot3d hook_rgl propertySlider rgl.primitive spheres3d