Example data structures
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.
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.
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 \(4\text{-}D\).
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.
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.
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.
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.
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.
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.
pyr_data <- gen_pyrfrac(n = 1000, p = 4)
langevitour(pyr_data, pointSize = 2)