---
title: "Example data structures"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Example data structures}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  message = FALSE
)
```

```{r setup}
library(cardinalR)
library(langevitour)
```

This illustrates a variety of example data structures that can be generated. These synthetic datasets represent common and challenging shapes found.

## Gaussian

A simple spherical Gaussian cluster with very small variance in $4\text{-}D$ space.

```{r}
gau_data <- gen_gaussian(n = 500, p = 4, s = diag(4) * 0.01)

langevitour(gau_data, pointSize = 2)
```

## Cube with a hole

Uniform points in a hypercube with a hollow center, useful for detecting voids or gaps.

```{r}
cube_grd_data <- gen_unifcubehole(n = 5000, p = 6)

langevitour(cube_grd_data, pointSize = 2)
```

## Circular

A curvilinear loop structure that forms a closed cycle in $4\text{-}D$.

```{r}
curvy_cyc_data <- gen_curvycycle(n = 500, p = 4) 

langevitour(curvy_cyc_data, pointSize = 2)
```

## Branching

A tree-like curvilinear structure with six branches in $6\text{-}D$, ideal for studying bifurcation patterns.

```{r}
tree_data <- gen_orgcurvybranches(n = 600, p = 5, k = 6) 

langevitour(tree_data, pointSize = 2)
```

## Cone

A pointed cone shape in $4\text{-}D$, controlled by height and radius ratio.

```{r}
cone_data <- gen_cone(n = 500, h = 5, ratio = 0.5) 

langevitour(cone_data, pointSize = 2)
```

## Conic spiral

A spiral winding around a conical surface in $5\text{-}D$ space.

```{r}
spiral_data <- gen_conicspiral(n = 500, spins = 2)

langevitour(spiral_data, pointSize = 2)
```

## Grided sphere

A regularly spaced sphere with high point density, useful for manifold learning.

```{r}
sphere_data <- gen_gridedsphere(n = 500, p = 4)

langevitour(sphere_data, pointSize = 2)
```

## S-curve with a hole

An S-shaped manifold in $8\text{-}D$ with a missing section, to evaluate resilience to structural gaps.

```{r}
scurve_data <- gen_scurvehole(n = 600) 

langevitour(scurve_data, pointSize = 2)
```

## Pyramid with a hole

A $4\text{-}D$ pyramid-shaped structure with a void at the center.

```{r}
pyr_data <- gen_pyrfrac(n = 1000, p = 4)

langevitour(pyr_data, pointSize = 2)
```