get_srv_from_points function

Helper functions for curve data measured at discrete points

Compute the square-root-velocity transformation or the parametrization with respect to arc length for a curve observed at discrete points.

get_srv_from_points(data_curve)

get_points_from_srv(srv_data)

get_arc_length_param(data_curve)

Arguments

• data_curve: A data.frame with observed points on a curve. Each row is one point, each variable one coordinate direction. If there is a variable t, it is treated as the time parametrization, not as an additional coordinate.
• srv_data: A data.frame with first column t corresponding to the parametrization and square-root-velocity vectors in the remaining columns.

Returns

get_srv_from_points returns a data.frame with first column t corresponding to the parametrization and square-root-velocity vectors in the remaining columns. If no parametrization is given, the curve will be parametrized with respect to arc length. This parametrization will be computed by a call to get_arc_length_param as well.

Functions

• get_srv_from_points(): Compute square-root-velocity transformation for curve data measured at discrete points. The inverse transformation can be computed with get_points_from_s
• get_points_from_srv(): The inverse transformation to get_srv_from_points. Transforms square-root-velocity data to points representing a curve (with no parametrization).
• get_arc_length_param(): Compute arc length parametrization.

Examples

data_curve1 <- data.frame(x1 = 1:6*sin(1:6), x2 = cos(1:6))
get_arc_length_param(data_curve1) #same parametrization as in
get_srv_from_points(data_curve1)

data_curve2 <- data.frame(t = seq(0,1, length = 6), data_curve1)
plot(data_curve2[,2:3], type = "l", xlim = c(-6, 2), ylim = c(-2, 1))
srv_data <- get_srv_from_points(data_curve2)
#back transformed curve starts at (0,0)
lines(get_points_from_srv(srv_data), col = "red")