R help - Dec 2011 - How to scale arrows to approximately fill a plot region?

In a variety of graphic applications, I plot some data, together with 
arrows representing variables
or linear transformations of variables as vectors in the same space, as 
in a biplot.

In my applications, the scale of the arrows is arbitrary -- all that 
matters is relative length.
I'd like to blow them up or shrink them to fit the available space in 
the plot.
The origin is typically at some mean for (x,y), but that is not 
necessarily so.
There must be some general, perhaps approximate solution for this problem,
but I can't see it.

Below is a simple test case.  I found the approximate solution, scale <- 
14 by trial and error.
[I'm ignoring aspect ratio, because that determines the bbox I calculate 
from the plot.]


set.seed(123135251)
x <- 2 + 5* rnorm(50)
y <- 5 + 2* rnorm(50)
plot(x,y)

# get bounding box of plot region, in data coordinates
bbox <- matrix(par("usr"), 2, 2, dimnames=list(c("min",
"max"),c("x", "y")))
# center vectors here
origin <- colMeans(bbox)
points(origin[1], origin[2], pch=16, cex=2)

# vectors to be displayed in this space
vectors <- cbind( runif(5), (runif(5)-.5))

# draw arrows, given origin and length in xy
Arrows <- function(xy, lenxy, length=.1, angle=10, ...) {
         arrows(xy[1], xy[2], xy[1]+lenxy[,1], xy[2]+lenxy[,2], 
length=length, angle=angle, ...)
     }

## How to determine scale so that vectors ~ fill the bounding box???
scale <- 14
Arrows(origin, scale*vectors)


-- 
Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept.
York University      Voice: 416 736-5115 x66249 Fax: 416 736-5814
4700 Keele Street    Web:   http://www.datavis.ca
Toronto, ONT  M3J 1P3 CANADA

On 07.12.2011 18:52, Michael Friendly wrote:
> In a variety of graphic applications, I plot some data, together with
> arrows representing variables
> or linear transformations of variables as vectors in the same space, as
> in a biplot.
>
> In my applications, the scale of the arrows is arbitrary -- all that
> matters is relative length.
> I'd like to blow them up or shrink them to fit the available space in
> the plot.
> The origin is typically at some mean for (x,y), but that is not
> necessarily so.
> There must be some general, perhaps approximate solution for this problem,
> but I can't see it.
>
> Below is a simple test case. I found the approximate solution, scale <-
> 14 by trial and error.
> [I'm ignoring aspect ratio, because that determines the bbox I
calculate
> from the plot.]
>
>
> set.seed(123135251)
> x <- 2 + 5* rnorm(50)
> y <- 5 + 2* rnorm(50)
> plot(x,y)
>
> # get bounding box of plot region, in data coordinates
> bbox <- matrix(par("usr"), 2, 2,
dimnames=list(c("min", "max"),c("x",
> "y")))
> # center vectors here
> origin <- colMeans(bbox)
> points(origin[1], origin[2], pch=16, cex=2)
>
> # vectors to be displayed in this space
> vectors <- cbind( runif(5), (runif(5)-.5))
>
> # draw arrows, given origin and length in xy
> Arrows <- function(xy, lenxy, length=.1, angle=10, ...) {
> arrows(xy[1], xy[2], xy[1]+lenxy[,1], xy[2]+lenxy[,2], length=length,
> angle=angle, ...)
> }
>
> ## How to determine scale so that vectors ~ fill the bounding box???
> scale <- 14
> Arrows(origin, scale*vectors)
>
>
Michael, you know it. Go and grab a coffee, this is school maths:

If you have a starting point and a direction as well as the plotting 
region, you can simply calculate a (positive ?) scale so that an arrow 
crosses the border. Now do this for all arrows and all borders and take 
the minimal positive value. Should be few lines of code only.

Therefore:

scale <- c(sapply(bbox[,"x"] - origin["x"], function(i)
i/vectors[,1]),
            sapply(bbox[,"y"] - origin["y"], function(i)
i/vectors[,2]))
scale <- min(scale[scale > 0])


Best wishes,
Uwe

On 12/08/2011 04:52 AM, Michael Friendly wrote:
> In a variety of graphic applications, I plot some data, together with
> arrows representing variables
> or linear transformations of variables as vectors in the same space, as
> in a biplot.
>
> In my applications, the scale of the arrows is arbitrary -- all that
> matters is relative length.
> I'd like to blow them up or shrink them to fit the available space in
> the plot.
> The origin is typically at some mean for (x,y), but that is not
> necessarily so.
> There must be some general, perhaps approximate solution for this problem,
> but I can't see it.
>
> Below is a simple test case. I found the approximate solution, scale <-
> 14 by trial and error.
> [I'm ignoring aspect ratio, because that determines the bbox I
calculate
> from the plot.]
>
>
> set.seed(123135251)
> x <- 2 + 5* rnorm(50)
> y <- 5 + 2* rnorm(50)
> plot(x,y)
>
> # get bounding box of plot region, in data coordinates
> bbox <- matrix(par("usr"), 2, 2,
dimnames=list(c("min", "max"),c("x",
> "y")))
> # center vectors here
> origin <- colMeans(bbox)
> points(origin[1], origin[2], pch=16, cex=2)
>
> # vectors to be displayed in this space
> vectors <- cbind( runif(5), (runif(5)-.5))
>
> # draw arrows, given origin and length in xy
> Arrows <- function(xy, lenxy, length=.1, angle=10, ...) {
> arrows(xy[1], xy[2], xy[1]+lenxy[,1], xy[2]+lenxy[,2], length=length,
> angle=angle, ...)
> }
>
> ## How to determine scale so that vectors ~ fill the bounding box???
> scale <- 14
> Arrows(origin, scale*vectors)
>
>
Hi Michael,
Have a look at the vectorField (plotrix) function. This scales the 
arrows to the unit cells in the plot, so it's trivial to change the code 
in the bottom half of the function to scale to the entire plot.

Jim