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Interactive 3D plotly visualisation of a simplicial cone

Source: R/plot_cone_3d.R
plot_cone_3d.Rd

Builds an interactive plotly widget showing a simplicial cone in \(\mathbb{R}^3\): the three generator rays, the planar faces, and the spherical triangle traced by the cone on the unit sphere. The widget is suitable for embedding in pkgdown articles and Shiny apps.

Usage

plot_cone_3d(
  V,
  ray_colors = NULL,
  surface_color = "orange",
  opacity = 0.5,
  show_sphere = TRUE,
  resolution = 60,
  show_legend = TRUE
)

Arguments

V

A 3x3 matrix where columns are the generating vectors of the cone.

ray_colors

Vector of 3 colors for the generator rays. If NULL, defaults to "red", "green", "blue".

surface_color

Color for the cone surface (default: "orange").

opacity

Opacity of the cone surface (default: 0.3).

show_sphere

Logical; whether to show a reference unit sphere (default: TRUE).

resolution

Integer; resolution for the arcs and surface mesh (default: 60).

show_legend

Logical; whether to show the legend (default: TRUE).

Value

A plotly object containing the visualization.

Details

The visualization includes generator rays (unit vectors extending from the origin, each clickable to trigger JavaScript console logs and Shiny events), spherical arcs (geodesic arcs connecting the tips of the vectors, perfectly aligned with the surface mesh), and the spherical triangle (the region on the unit sphere enclosed by the cone, constructed using barycentric subdivision and spherical projection). Each ray displays tooltips with vector coordinates.

The plot title includes the calculated normalized solid angle measure.

References

Sievert, C. (2020). Interactive Web-Based Data Visualization with R, plotly, and Shiny. Chapman and Hall/CRC. ISBN 978-1138331457.

Mazonka, O. (2012). Solid angle of conical surfaces, polyhedral cones, and intersecting spherical caps. arXiv:1205.1396 (math.MG). doi:10.48550/arXiv.1205.1396

See also

plotIntersectingCones for the visualisation of two intersecting circular cones; plot.cone_diagnosis for the diagnostic eigenvalue plot; compute_solid_angle for the scalar measure shown in the title; shinySolidAngleR for the dashboard that embeds these plots.

Examples

if (FALSE) { # \dontrun{
# Octant in R^3
plot_cone_3d(diag(3), ray_colors = c("orange", "purple", "blue"))

# Narrow cone with custom rays
V2 <- matrix(c(1, 0,   0,
               1, 0.2, 0,
               1, 0,   0.2), nrow = 3, byrow = FALSE)
plot_cone_3d(V2, ray_colors = c("green", "red", "blue"), opacity = 0.5)
} # }