In MrMallIronmaker/dddr: Three-Dimensional Spatial Operations in R

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width=8,
  fig.height=5
)

library(dplyr)
library(ggplot2)
library(dddr)

The R package dddr works well with three-diensional spatial data. It gives three-dimensional objects like points, velocities, and rotations first-class vector status in R, enabling usage as column types within data.frame and tibble.

Vector Mathematics

Vectors have addition and subtraction operations, as well as scalar multiplication.

spiral <- data.frame(i = seq(0, 10*pi, by=0.05)) %>%
  mutate(
    # vector3s are created using three numeric vector arguments,
    # and thanks to dplyr, can refer to other columns in the dataframe
    circular_part = vector3(x=cos(i), y=sin(i), z=0),
    forward_part = vector3(x=0, y=0, z=i/15),
    # vector3s can be added together and multiplied by numerics 
    spiral_part = circular_part * i / 30 + forward_part
  )

ggplot(spiral, aes(x=spiral_part$x, y=spiral_part$y)) +
  geom_point() +
  geom_path() +
  coord_equal()

spiral %>%
  mutate(addition_example = spiral_part + vector3(1, 1, 0)) %>%
  ggplot() +
  geom_point(aes(x=spiral_part$x, y=spiral_part$y), color="black") +
  geom_path(aes(x=spiral_part$x, y=spiral_part$y), color="black") +
  geom_point(aes(x=addition_example$x, y=addition_example$y), color="blue") +
  geom_path(aes(x=addition_example$x, y=addition_example$y), color="blue") +
  coord_equal()

spiral %>%
  mutate(multiplication_example = spiral_part * 1.5) %>%
  ggplot() +
  geom_point(aes(x=spiral_part$x, y=spiral_part$y), color="black") +
  geom_path(aes(x=spiral_part$x, y=spiral_part$y), color="black") +
  geom_point(aes(x=multiplication_example$x, y=multiplication_example$y), color="blue") +
  geom_path(aes(x=multiplication_example$x, y=multiplication_example$y), color="blue") +
  coord_equal()

Rotations

Vectors can be rotated using the rotate function in many different ways. One approach is a very simple axis-angle.

spiral %>%
  mutate(axis_angle_rotation = rotate(spiral_part, axis=vector3(0, 1, 0), angle=pi/4)) %>%
  ggplot() +
  geom_point(aes(x=spiral_part$x, y=spiral_part$y), color="black") +
  geom_path(aes(x=spiral_part$x, y=spiral_part$y), color="black") +
  geom_point(aes(x=axis_angle_rotation$x, y=axis_angle_rotation$y), color="blue") +
  geom_path(aes(x=axis_angle_rotation$x, y=axis_angle_rotation$y), color="blue") +
  coord_equal()

Another approach uses from/to specific vectors.

spiral %>%
  mutate(from_to_rotation = rotate(spiral_part, from=vector3(0, 0, 1), to=vector3(-1, -1, -1))) %>%
  ggplot() +
  geom_point(aes(x=spiral_part$x, y=spiral_part$y), color="black") +
  geom_path(aes(x=spiral_part$x, y=spiral_part$y), color="black") +
  geom_point(aes(x=from_to_rotation$x, y=from_to_rotation$y), color="blue") +
  geom_path(aes(x=from_to_rotation$x, y=from_to_rotation$y), color="blue") +
  coord_equal()

Spatial Functions

There are a handful of other useful functions, including angle_between, and vector projection and rejection.

spiral %>%
  mutate(angle = angle_between(spiral_part, vector3(0, 0, 0), origin=vector3(0, -2, 0))) %>%
  ggplot() +
  geom_point(aes(x=i, y=angle)) +
  geom_line(aes(x=i, y=angle))