# mba.surf {MBA}

### Description

The function `mba.surf`

returns a surface approximated from a bivariate scatter of data points using multilevel B-splines.

### Usage

mba.surf(xyz, no.X, no.Y, n = 1, m = 1, h = 8, extend=FALSE, sp=FALSE, ...)

### Arguments

- xyz
- a n x 3 matrix or data frame, where n is the number of observed points. The three columns correspond to point x, y, and z coordinates. The z value is the response at the given x, y coordinates.
- no.X
- resolution of the approximated surface along the x axis.
- no.Y
- resolution of the approximated surface along the y axis.
- n
- initial size of the spline space in the hierarchical construction along the x axis. If the rectangular domain is a square, n = m = 1 is recommended. If the x axis is k times the length of the y axis, n = 1, m = k is recommended. The default is n = 1.
- m
- initial size of the spline space in the hierarchical construction along the y axis. If the y axis is k times the length of the x axis, m = 1, n = k is recommended. The default is m = 1.
- h
- Number of levels in the hierarchical construction. If, e.g., n = m = 1 and h = 8, the resulting spline surface has a coefficient grid of size 2^h + 3 = 259 in each direction of the spline surface. See references for additional information.
- extend
- if FALSE, a convex hull is computed for the input points and all matrix elements in z that have centers outside of this polygon are set to
`NA`

; otherwise, all elements in z are given an estimated z value. - sp
- if TRUE, the resulting surface is returned as a
`SpatialPixelsDataFrame`

object; otherwise, the surface is in`image`

format. - ...
`b.box`

is an optional vector to sets the bounding box. The vector's elements are minimum x, maximum x, minimum y, and maximum y, respectively.

### Values

List with 8 component:

- xyz.est
- a list that contains vectors x, y and the no.X x no.Y matrix z of estimated z-values.
- no.X
`no.X`

from arguments.- no.Y
`no.Y`

from arguments.- n
`n`

from arguments.- m
`m`

from arguments.- h
`h`

from arguments.- extend
`extend`

from arguments.- sp
`sp`

from arguments.- b.box
`b.box`

defines the bounding box over which z is estimated.

### Note

If `no.X != no.Y`

then use `sp=TRUE`

for compatibility with the `image`

function. The function `mba.surf`

relies on the Multilevel B-spline Approximation (MBA) algorithm. The underlying code was developed at SINTEF Applied Mathematics by Dr. Oyvind Hjelle. Dr. Oyvind Hjelle based the algorithm on the paper by the originators of Multilevel B-splines:

S. Lee, G. Wolberg, and S. Y. Shin. Scattered data interpolation with multilevel B-splines. IEEE Transactions on Visualization and Computer Graphics, 3(3):229--244, 1997.

For additional documentation and references please see:

www.sintef.no/upload/IKT/9011/geometri/MBA/mba_doc/index.html.

This minor portion of the MBA codebase was ported by Andrew O. Finley finleya@msu.edu.

### See Also

`mba.points`

### Examples

data(LIDAR) mba.int <- mba.surf(LIDAR, 300, 300, extend=TRUE)$xyz.est ## Not run: ##Image plot image(mba.int, xaxs="r", yaxs="r") ##Perspective plot persp(mba.int, theta = 135, phi = 30, col = "green3", scale = FALSE, ltheta = -120, shade = 0.75, expand = 10, border = NA, box = FALSE) ##For a good time I recommend using rgl library(rgl) ex <- 10 x <- mba.int[[1]] y <- mba.int[[2]] z <- ex*mba.int[[3]] zlim <- range(z) zlen <- zlim[2] - zlim[1] + 1 colorlut <- heat.colors(as.integer(zlen)) col <- colorlut[ z-zlim[1]+1 ] open3d() surface3d(x, y, z, color=col, back="lines") ## End(Not run)

Documentation reproduced from package MBA, version 0.0-7. License: GPL (>= 2)