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 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 .
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 , 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 , 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 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 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 pyramid-shaped structure with a void at the center.
pyr_data <- gen_pyrfrac(n = 1000, p = 4)
langevitour(pyr_data, pointSize = 2)