Control Polygons

Generate the control polygon for a uni-variable B-spline

Usage

cp(x, ...)

# S3 method for class 'cpr_bs'
cp(x, theta, ...)

# S3 method for class 'formula'
cp(
  formula,
  data,
  method = stats::lm,
  method.args = list(),
  keep_fit = TRUE,
  check_rank = TRUE,
  ...
)

Arguments

x

a cpr_bs object

...

pass through

theta

a vector of (regression) coefficients, the ordinates of the control polygon.

formula

a formula that is appropriate for regression method being used.

data

a required data.frame

method

the regression method such as lm, glm, lmer, etc.

method.args

a list of additional arguments to pass to the regression method.

keep_fit

(logical, default value is TRUE). If TRUE the regression model fit is retained and returned in as the fit element. If FALSE the fit element with be NA.

check_rank

(logical, defaults to TRUE) if TRUE check that the design matrix is full rank.

Value

a cpr_cp object, this is a list with the element cp, a data.frame reporting the x and y coordinates of the control polygon. Additional elements include the knot sequence, polynomial order, and other meta data regarding the construction of the control polygon.

Details

cp generates the control polygon for the given B-spline function.

Examples

# Support
xvec <- runif(n = 500, min = 0, max = 6)
bknots <- c(0, 6)

# Define the basis matrix
bmat1 <- bsplines(x = xvec, iknots = c(1, 1.5, 2.3, 4, 4.5), bknots = bknots)
bmat2 <- bsplines(x = xvec, bknots = bknots)

# Define the control vertices ordinates
theta1 <- c(1, 0, 3.5, 4.2, 3.7, -0.5, -0.7, 2, 1.5)
theta2 <- c(1, 3.4, -2, 1.7)

# build the two control polygons
cp1 <- cp(bmat1, theta1)
cp2 <- cp(bmat2, theta2)

# black and white plot
plot(cp1)

plot(cp1, show_spline = TRUE)


# multiple control polygons
plot(cp1, cp2, show_spline = TRUE)

plot(cp1, cp2, color = TRUE)

plot(cp1, cp2, show_spline = TRUE, color = TRUE)


# via formula
DF  <- data.frame(x = xvec, y = sin((xvec - 2)/pi) + 1.4 * cos(xvec/pi))
cp3 <- cp(y ~ bsplines(x, bknots = bknots), data = DF)

# plot the spline and target data.
plot(cp3, show_cp = FALSE, show_spline = TRUE) +
  ggplot2::geom_line(mapping = ggplot2::aes(x = x, y = y, color = "Target"),
                     data = DF, linetype = 2)