Bezier function

Compute the Bezier function of a collection of polynomials. By Bezier function we mean the Bezier curve function, a parametric map running from t = 0, the first point, to t = 1, the last point, where the coordinate mappings are linear combinations of Bernstein polynomials.

bezier_function(points, weights = rep(1L, nrow(points)))

bezierFunction(...)

Arguments

points	a matrix or data frame of numerics. the rows represent points.
weights	the weights in a weighted Bezier curve
...	...; used internally

Value

function of a single parameter

Details

The function returned is vectorized and evaluates the Bezier curve in a numerically stable way with de Castlejau's algorithm (implemented in R).

References

http://en.wikipedia.org/wiki/Bezier_curve, http://en.wikipedia.org/wiki/De_Casteljau's_algorithm

See also

bezier()

Examples

library(ggplot2); theme_set(theme_bw())


t <- seq(0, 1, length.out = 201)
points <- data.frame(x = 0:3, y = c(0,1,-1,0))


f <- bezier_function(points)
df <- as.data.frame(f(t))

ggplot(aes(x = x, y = y), data = df) +
  geom_point(data = points, color = "red", size = 8) +
  geom_path(data = points, color = "red") +
  geom_path()




f <- bezier_function(points, weights = c(1,5,5,1))
df <- as.data.frame(f(t))

ggplot(aes(x = x, y = y), data = df) +
  geom_point(data = points, color = "red", size = 8) +
  geom_path(data = points, color = "red") +
  geom_path()




f <- bezier_function(points, weights = c(1,10,10,1))
df <- as.data.frame(f(t))

ggplot(aes(x = x, y = y), data = df) +
  geom_point(data = points, color = "red", size = 8) +
  geom_path(data = points, color = "red") +
  geom_path()