Parametric Curve Fit
Polynomial fitting of parametrized points on 2D curves, also requiring to meet some points exactly.
curvefit(u, x, y, n, U = NULL, V = NULL)
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 |
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.
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.
In the same manner, derivatives/directions could be prescribed at certain points.
## 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) ## Not run: plot(x, y, col = "darkgray", pch = 19, asp = 1) xp <- cfit1$xp; yp <- cfit1$yp lines(xp, yp, col="blue") grid() ## End(Not run) ## 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) ## Not run: xp <- cfit2$xp; yp <- cfit2$yp lines(xp, yp, col="red") ## End(Not run) ## Not run: ## 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() ## End(Not run)
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