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bezier.R
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bezier.R
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## Copyright (c) 2016, James P. Howard, II <jh@jameshoward.us>
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are
## met:
##
## Redistributions of source code must retain the above copyright
## notice, this list of conditions and the following disclaimer.
##
## Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in
## the documentation and/or other materials provided with the
## distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
## "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
## LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
## A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
## HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
## SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
## LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
## DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
## THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
## (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#' @rdname bezier
#' @name bezier
#'
#' @title Bezier curves
#'
#' @description
#' Find the quadratic and cubic Bezier curve for the given points
#'
#' @param x a vector of x values
#' @param y a vector of y values
#' @param t a vector of t values for which the curve will be computed
#'
#' @details \code{qbezier} finds the quadratic Bezier curve for the
#' given three points and \code{cbezier} finds the cubic Bezier curve
#' for the given four points. The curve will be computed at all values
#' in the vector \code{t} and a list of x and y values returned.
#'
#' @return a list composed of an x-vector and a y-vector
#'
#' @family interp
#'
#' @examples
#' x <- c(1, 2, 3)
#' y <- c(2, 3, 5)
#' f <- qbezier(x, y, seq(0, 1, 1/100))
#'
#' x <- c(-1, 1, 0, -2)
#' y <- c(-2, 2, -1, -1)
#' f <- cbezier(x, y, seq(0, 1, 1/100))
#'
#' @rdname bezier
#' @export
qbezier <- function(x, y, t) {
if(length(x) != 3 || length(y) != 3)
stop("x and y must contain exactly 3 values")
newx <- (1-t)^2 * x[1] + 2 * (1-t) * t * x[2] +
t^2 * x[3]
newy <- (1-t)^2 * y[1] + 2 * (1-t) * t * y[2] +
t^2 * y[3]
return(list(x = newx, y = newy))
}
#' @rdname bezier
#' @export
cbezier <- function(x, y, t) {
if(length(x) != 4 || length(y) != 4)
stop("x and y must contain exactly 4 values")
newx <- (1-t)^3 * x[1] + 3 * (1-t)^2 * t * x[2] +
3 * (1-t) * t^2 * x[3] + t^3 * x[4]
newy <- (1-t)^3 * y[1] + 3 * (1-t)^2 * t * y[2] +
3 * (1-t) * t^2 * y[3] + t^3 * y[4]
return(list(x = newx, y = newy))
}