---
title: "Vectorised Patterns in R Graphics"
author: "Paul Murrell"
date: 2022-06-09
categories: ["Internals"]
tags: ["graphics"]
---

```{r eval=FALSE, echo=FALSE}
knitr::opts_chunk$set(
  fig.width = 4, fig.height = 2
)
```

Support for pattern fills
was added to the R graphics engine 
[in R version 4.1.0](https://developer.r-project.org/Blog/public/2020/07/15/new-features-in-the-r-graphics-engine/), with an R interface via the
'grid' package.

```{r eval=FALSE}
library(grid)
```

For example, the following code defines a linear gradient 
that varies horizontally from red to white and 
a tiling pattern that is based on a repeating red circle.

```{r eval=FALSE}
gradcol <- c(palette()[2], "white")
grad <- linearGradient(gradcol, y1=.5, y2=.5)
patcol <- 2
pat <- pattern(circleGrob(r=unit(2, "mm"), gp=gpar(col=patcol, fill=patcol)),
               width=unit(5, "mm"), height=unit(5, "mm"),
               extend="repeat")
```

The next code calls `grid.rect()` twice, once to fill a 
rectangle with the linear gradient and a second time to fill
another rectangle with the tiling pattern.

```{r eval=FALSE, patterns}
grid.rect(1/3, width=1/4, height=1/2,
          gp=gpar(fill=grad))
grid.rect(2/3, width=1/4, height=1/2,
          gp=gpar(fill=pat))
```

<img 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" width="384">

The following code draws the two rectangles with a single call 
to `grid.rect()` and fills them both using the linear gradient.
The result is that both rectangles are filled with the same
gradient from red to white, with the gradient relative to
a bounding box around *both* rectangles (we start with red at
the left edge of the rectangle on the left and end with white at the
right edge of the rectangle on the right).

```{r eval=FALSE, grouppattern}
grid.rect(1:2/3, width=1/4, height=1/2,
          gp=gpar(fill=grad))
```

<img src="data:image/png;base64,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" width="384">

From R 4.2.0, we can produce a different result because the
`linearGradient()` function has gained a `group` argument.
If we set this to `FALSE`, then we can fill both rectangles
with the "same" gradient fill, but the gradient fill is relative
to individual rectangles, as shown below.

```{r eval=FALSE}
grad2 <- linearGradient(gradcol, y1=.5, y2=.5, 
                        group=FALSE)
```

```{r eval=FALSE, shapepattern}
grid.rect(1:2/3, width=1/4, height=1/2,
          gp=gpar(fill=grad2))
```

<img src="data:image/png;base64,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" width="384">

Another change in R 4.2.0 is that we can specify more than one pattern fill.
For example, the following code draws the two rectangles in a single
`grid.rect()` call and provides a *list* of pattern fills:
the original linear gradient and the tiling pattern.
The result is that the first rectangle is filled with the linear
gradient and the second rectangle is filled with the tiling pattern.

```{r eval=FALSE, patternlist}
grid.rect(1:2/3, width=1/4, height=1/2,
          gp=gpar(fill=list(grad, pat)))
```

<img 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" width="384">

The result is different from the very first example because 
both the linear gradient and the tiling pattern are relative to
a bounding box around both rectangles.  The following code
uses the new `group` argument to fill each rectangle with a different
pattern fill *and* have the pattern fills relative to the individual
rectangles.

```{r eval=FALSE}
pat2 <- pattern(circleGrob(r=unit(2, "mm"), gp=gpar(col=patcol, fill=patcol)),
                width=unit(5, "mm"), height=unit(5, "mm"),
                extend="repeat",
                group=FALSE)
```

```{r eval=FALSE, shapelist}
grid.rect(1:2/3, width=1/4, height=1/2,
          gp=gpar(fill=list(grad2, pat2)))
```

<img 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" width="384">

A further addition in R 4.2.0 is the ability to use pattern fills 
on "points" (data symbols).  Combining that with pattern lists
and `group=FALSE`, we can, for example, 
apply pattern fills to individual points on a scatterplot,
as shown below.  For this example, 
the pattern fill is a *radial* gradient from white to red.  

```{r eval=FALSE, ggplot, fig.width=4, fig.height=4}
library(gggrid)
grad3 <- radialGradient(rev(gradcol),
                        cx2=.8, cy2=.8, group=FALSE)
filledPoints <- function(data, coords) {
    pointsGrob(coords$x, coords$y, pch=21,
               gp=gpar(col=patcol, fill=grad3))
}
ggplot(mtcars) +
    grid_panel(filledPoints, 
               mapping=aes(x=disp, y=mpg))
```

<img 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" width="384">

Further discussion and more detail about these new facilities
can be found in the
technical report
["Vectorised Pattern Fills in R Graphics"](https://stattech.blogs.auckland.ac.nz/2022/06/01/2022-01).  The technical report 
["Constructive Geometry for Complex Grobs"](https://stattech.blogs.auckland.ac.nz/2022/06/01/2022-02-constructive-geometry-for-complex-grobs)
describes related changes to the `grobCoords()` function that is
used in the resolution of pattern fills.



