Package 'Dcurvature'

Discrete Curvature for an Ordered 2D Curve

Description

Compute pointwise discrete curvature from an ordered sequence of 2D points using circumcenter-based geometry on consecutive triplets.

Usage

curvature(data)

Arguments

data	A numeric matrix/data frame with at least two columns representing ordered x and y coordinates. Additional columns are ignored.

Value

A numeric vector of curvature values with one value per input row. Boundary points are set to 0.

Examples

pts <- cbind(
  x = seq(0, 1, length.out = 8),
  y = sin(seq(0, pi, length.out = 8))
)
curvature(pts)

---

Load the bundled example data as a data frame

Description

Reads ‘data.xlsx’ from the package via read_excel.

Usage

load_example_data(sheet = NULL, ...)

Arguments

sheet	Sheet to read; passed to read_excel. Default is the first sheet.
...	Optional arguments passed to read_excel.

Value

A data frame.

Examples

x <- load_example_data()
head(x)

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Run the curvature Shiny app

Description

Launches the discrete-curvature criterion app. You can start from an explained-variance table (upload CSV/Excel or use the bundled example), or from raw variables (Excel, then PCA). Elbow detection uses curvature on the variance curves, with optional KMO in PCA mode.

Usage

run_curvature_app(..., .runApp = shiny::runApp)

Arguments

...	Optional arguments passed to runApp (e.g. port, launch.browser, host).
.runApp	Internal app runner used for testing. Defaults to runApp.

Value

Invisibly returns the result of shiny::runApp. Called for its side effect of starting a Shiny app.

Examples

if (interactive()) {
  run_curvature_app()
}

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Discrete-curvature selection of the number of components

Description

Applies the discrete-curvature elbow criterion to an explained-variance sequence and returns the adaptive selection $m^*$ (first/second-order difference operators). When a minimum cumulative-variance threshold tau is supplied, it also returns the extended selection $m^{**} = \max(m^*, \min\{i : V_i \ge \tau\})$.

Usage

select_components(
  variance,
  type = c("cumulative", "individual"),
  axis_range = c("0p", "01"),
  tau = NULL
)

Arguments

variance	Numeric vector of individual explained variance per component (percent or proportion), ordered from the first component.
type	Curve the criterion is applied to: "cumulative" (default) or "individual".
axis_range	Axis normalization: "0p" (default, x in [0, p]) or "01" (both axes scaled to [0, 1]).
tau	Optional minimum cumulative-variance threshold (same units as variance). If supplied, mstar_ext is computed.

Details

This exposes, as a single reproducible call, the same logic used by the interactive application run_curvature_app.

Value

A list with mstar, order_used (1 or 2), mstar_ext (NA when tau is NULL), type, axis_range, tau, and table: a data frame with per-component individual/cumulative variance, normalized curvature (kappa_norm) and normalized second differences (d2_norm).

See Also

curvature, run_curvature_app

Examples

v <- c(35.2, 22.8, 15.1, 9.5, 6.2, 4.1, 2.8, 1.9, 1.3, 1.1)
select_components(v, type = "cumulative", tau = 90)

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