align_curves function

Align two curves measured at discrete points

Finds the optimal reparametrization of the second curve (stored in data_curve2) to the first one (stored in data_curve1) with respect to the elastic distance. Constructor function for class aligned_curves.

align_curves(data_curve1, data_curve2, closed = FALSE, eps = 0.01)

Arguments

• data_curve1: data.frame with observed points in each row. Each variable is one coordinate direction. If there is a variable t, it is treated as the time parametrization, not as an additional coordinate.
• data_curve2: same as data_curve1
• closed: TRUE if the curves should be treated as closed.
• eps: convergence tolerance

Returns

an object of class aligned_curves, which is a list

with entries - data_curve1: data_curve1 with parametrization variable t

• data_curve2_aligned: data_curve2 with initial parametrization variable t and optimal parametrization t_optim

• elastic_dist: elastic distance between curve1 and curve2

• closed: TRUE if the curves should have been treated as closed.

Examples

#open curves
data_curve1 <- data.frame(x1 = c(1, 0.5, -1, -1), x2 = c(1, -0.5, -1, 1))
data_curve2 <- data.frame(x1 = c(0.1,0.7)*sin(1:6), x2 = cos(1:6))
aligned_curves <- align_curves(data_curve1, data_curve2)
plot(aligned_curves)

#different parametrization of the first curve
data_curve1$t <- 0:3/3
align_curves(data_curve1, data_curve2)

#closed curves
data_curve1 <- data.frame(x1 = sin(0:12/5), x2 = cos(0:12/5))
data_curve2 <- data.frame(x1 = c(1, 0.5, -1, -1), x2 = c(1, -0.5, -1, 1))
aligned_curves_closed <- align_curves(data_curve1, data_curve2, closed = TRUE)
plot(aligned_curves_closed, asp = 1)