pracma (version 1.7.3)

curvefit: Parametric Curve Fit

Description

Polynomial fitting of parametrized points on 2D curves, also requiring to meet some points exactly.

Usage

curvefit(u, x, y, n, U = NULL, V = NULL)

Arguments

u

the parameter vector.

x, y

x-, y-coordinates for each parameter value.

n

order of the polynomials, the same in x- and y-dirction.

U

parameter values where points will be fixed.

V

matrix with two columns and lemgth(U) rows; first column contains the x-, the second the y-values of those points kept fixed.

Value

• Returns a list with 4 components, xp and yp coordinates of the fitted points, and px and py the coefficients of the fitting polynomials in x- and y-direction.

Details

This function will attempt to fit two polynomials to parametrized curve points using the linear least squares approach with linear equality constraints in lsqlin. The requirement to meet exactly some fixed points is interpreted as a linear equality constraint.

See Also

circlefit, lsqlin

Examples

##  Approximating half circle arc with small perturbations
N <- 50
u <- linspace(0, pi, N)
x <- cos(u) + 0.05 * randn(1, N)
y <- sin(u) + 0.05 * randn(1, N)
n <- 8
cfit1 <- curvefit(u, x, y, n)
plot(x, y, col = "darkgray", pch = 19, asp = 1)
xp <- cfit1$xp; yp <- cfit1$yp
lines(xp, yp, col="blue")
grid()

##  Fix the end points at t = 0 and t = pi
U <- c(0, pi)
V <- matrix(c(1, 0, -1, 0), 2, 2, byrow = TRUE)
cfit2 <- curvefit(u, x, y, n, U, V)
xp <- cfit2$xp; yp <- cfit2$yp
lines(xp, yp, col="red")

##  Archimedian spiral
n <- 8
u <- linspace(0, 3*pi, 50)
a <- 1.0
x <- as.matrix(a*u*cos(u))
y <- as.matrix(a*u*sin(u))
plot(x, y, type = "p", pch = 19, col = "darkgray", asp = 1)
lines(x, y, col = "darkgray", lwd = 3)
cfit <- curvefit(u, x, y, n)
px <- c(cfit$px); py <- c(cfit$py)
v <- linspace(0, 3*pi, 200)
xs <- polyval(px, v)
ys <- polyval(py, v)
lines(xs, ys, col = "navy")
grid()