# linequad: Quadrature Scheme on a Linear Network In spatstat.linnet: Linear Networks Functionality of the 'spatstat' Family

## Quadrature Scheme on a Linear Network

### Description

Generates a quadrature scheme (an object of class `"quad"`) on a linear network.

### Usage

```linequad(X, Y, ..., eps = NULL, nd = 1000, random = FALSE)
```

### Arguments

 `X` Data points. An object of class `"lpp"` or `"ppp"`. `Y` Line segments on which the points of `X` lie. An object of class `"psp"`. Required only when `X` is a `"ppp"` object. `...` Ignored. `eps` Optional. Spacing between successive dummy points along each segment. (This is the maximum spacing; some spacings will be shorter.) `nd` Optional. Total number of dummy points to be generated. (Actual number may be larger.) `random` Logical value indicating whether the sequence of dummy points should start at a randomly-chosen position along each segment.

### Details

This command generates a quadrature scheme (object of class `"quad"`) from a pattern of points on a linear network.

Normally the user does not need to call `linequad` explicitly. It is invoked by spatstat functions when needed. A quadrature scheme is required by `lppm` in order to fit point process models to point pattern data on a linear network. A quadrature scheme is also used by `rhohat.lpp` and other functions.

In order to create the quadrature scheme, dummy points are placed along each line segment of the network. The dummy points are evenly-spaced with spacing `eps`. The default is `eps = totlen/nd` where `totlen` is the total length of all line segments in the network.

Every line segment of the network will contain at least one dummy point. Consequently the actual number of dummy points generated will typically be greater than `nd`, especially when `nd` is small. If `eps` is specified, the number of dummy points will be greater than `totlen/eps`, especially when `eps` is large.

### Value

A quadrature scheme (object of class `"quad"`).

`lppm`