Generates a default pattern of dummy points for use in a quadrature scheme.

```
default.dummy(X, nd, random=FALSE, ntile=NULL, npix=NULL,
quasi=FALSE, …, eps=NULL, verbose=FALSE)
```

X

The observed data point pattern.
An object of class `"ppp"`

or in a format recognised by `as.ppp()`

nd

Optional. Integer, or integer vector of length 2, specifying an
`nd * nd`

or `nd[1] * nd[2]`

rectangular array of dummy points.

random

Logical value. If `TRUE`

, the dummy points are
generated randomly.

quasi

Logical value. If `TRUE`

, the dummy points are
generated by a quasirandom sequence.

ntile

Optional. Integer or pair of integers specifying the number of rows and columns of tiles used in the counting rule.

npix

Optional. Integer or pair of integers specifying the number of rows and columns of pixels used in computing approximate areas.

…

Ignored.

eps

Optional. Grid spacing.
A positive number, or a vector of two positive numbers, giving the
horizontal and vertical spacing, respectively, of the grid of
dummy points. Incompatible with `nd`

.

verbose

If `TRUE`

, information about the construction of the
quadrature scheme is printed.

A point pattern (an object of class `"ppp"`

,
see `ppp.object`

) containing the dummy points.

This function provides a sensible default for the dummy points in a quadrature scheme.

A quadrature scheme consists of
the original data point pattern, an additional pattern of dummy points,
and a vector of quadrature weights for all these points.
See `quad.object`

for further information about
quadrature schemes.

If `random`

and `quasi`

are both false (the default),
then the function creates dummy points
in a regular `nd[1]`

by `nd[1]`

rectangular grid.
If `random`

is true and `quasi`

is false,
then the frame of the window is divided into
an `nd[1]`

by `nd[1]`

array of tiles, and one dummy point
is generated at random inside each tile.
If `quasi`

is true, a quasirandom pattern of
`nd[1] * nd[2]`

points is generated.
In all cases, the four corner points of the frame of the window
are added. Then if the window is not rectangular, any dummy points
lying outside it are deleted.

If `nd`

is missing,
a default value (depending on the
data pattern `X`

) is computed by `default.ngrid`

.

Alternative functions for creating dummy patterns
include `corners`

,
`gridcentres`

,
`stratrand`

and
`spokes`

.

`quad.object`

,
`quadscheme`

,
`corners`

,
`gridcentres`

,
`stratrand`

,
`spokes`

```
# NOT RUN {
data(simdat)
P <- simdat
D <- default.dummy(P, 100)
# }
# NOT RUN {
plot(D)
# }
# NOT RUN {
Q <- quadscheme(P, D, "grid")
# }
# NOT RUN {
plot(union.quad(Q))
# }
```

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