Surface approximation from bivariate scattered data using multilevel B-splines

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 \(n \times 3\) 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.

Value

List with 8 component:

xyz.est

a list that contains vectors x, y and the \(no.X \times no.Y\) 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. Øyvind Hjelle. Dr. Øyvind Hjelle based the algorithm on the paper by the originators of Multilevel B-splines:

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

For additional documentation and references see:

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

See also

mba.points

Examples

if (FALSE) { # \dontrun{
data(LIDAR)

mba.int <- mba.surf(LIDAR, 300, 300, extend=TRUE)$xyz.est

# Image plot of the surface.
image(mba.int, xaxs = "r", yaxs = "r")

# Perspective plot of the surface.
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)

# Exaggerate z a bit for effect.
mba.int$z <- 10*mba.int$z

# Make nice colors for the rgl surface.
zlim <- range(mba.int$z)
zlen <- zlim[2] - zlim[1] + 1

colorlut <- terrain.colors(zlen) # Height color lookup table.

col <- colorlut[mba.int$z - zlim[1] + 1 ] # Assign colors to heights for each point.

open3d()
surface3d(mba.int$x, mba.int$y, mba.int$z, color = col)

} # }