Plotting with woylier
In woylier: Alternative Tour Frame Interpolation Method

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

This vignette will demonstrate how to plot the interpolated path with the woylier package.

library(woylier)
library(geozoo)
library(ggplot2)
library(dplyr)
library(purrr)

1D example

1D projection of data in high dimension linear combination of data that is normalized. Therefore, we can plot the point on the surface of a hypersphere. The plot below the Givens interpolation steps between 2 points, 1D projection of 6D data that is.

# Generate 1D example
set.seed(2022)
p <- 6
base1 <- tourr::basis_random(p, d=1)
base2 <- tourr::basis_random(p, d=1)

# First example
frames <- givens_full_path(base1, base2, nsteps = 10)
sp <- generate_space_view(p=p)
sp_path <- add_path(sp, frames) 
point1 <- as.data.frame(t(base1)) 
point1$type <- "point1"
point2 <- as.data.frame(t(base2))
point2$type <- "point2"
sp_path <- rbind(sp_path, point1, point2) 
p
tourr::animate_xy(sp_path[,1:p], col=sp_path$type, 
                  axes="bottomleft")

2D example

In case of 2D projections, we can plot the interpolated path between 2 frames on the surface of torus. Torus can be seen as crossing of 2 circles that are orthonormal.

# Generate 2D example
set.seed(2022)
n <- 1000
p <- 3
d <- 2
base1 <- tourr::basis_random(p, d)
base2 <- tourr::basis_random(p, d)
frames_2d <- givens_full_path(base1, base2, 10)
proj_2d <- map(1:n, ~tourr::basis_random(n = p,  d=d)) %>%
  purrr::flatten_dbl() %>% 
  matrix(ncol = p*2, byrow = TRUE) %>%
  as_tibble()
# Path
path_2d <- t(apply(frames_2d, 3, c)) %>% 
  as.data.frame()
# Join
proj_2d <- proj_2d %>% 
  mutate(type="torus")
path_2d <- path_2d %>% 
  mutate(type="path")
proj_path <- bind_rows(proj_2d, path_2d)
tourr::animate_xy(proj_path[,1:6], 
                  col=proj_path$type, 
                  axes="bottomleft")