rcsr: Compute the Details of a 3D Spline for a Hive Plot Edge

In HiveR: 2D and 3D Hive Plots for R

Description

This is a wild bit of trigonometry! Three points in 3D space, two ends and an control point, are rotated into 2D space. Then a spline curve is computed. This is necessary because spline curves are only defined in R as 2D objects. The new collection of points, which is the complete spline curve and when drawn will be the edge of a hive plot, is rotated back into the original 3D space. rcsr stands for rotate, compute spline, rotate back.

Usage

rcsr(p0, cp, p1)

Arguments

p0	A triple representing one end of the final curve (x, y, z).
cp	A triple representing the control point used to compute the final curve (x, y, z).
p1	A triple representing the other end of the final curve (x, y, z).

Details

See the code for exactly how the function works. Based upon the process described at http://www.fundza.com/mel/axis_to_vector/index.html Timing tests show this function is fast and scales linearly (i.e. 10x more splines to draw takes 10x more time). Roughly 3 seconds were required to draw 1,000 spline curves in my testing.

Value

A 3 column matrix with the x, y and z coordinates to be plotted to create a hive plot edge.

Author(s)

Bryan A. Hanson, DePauw University. [e-mail]

Examples

# This is a lengthy example to prove it works.
# Read it and then copy the whole thing to a blank script.
# Parts of it require rgl and are interactive.
# So none of the below is run during package build/check.

### First, a helper function
## Not run: 

drawUnitCoord <- function() {

  # Simple function to draw a unit 3D coordinate system

  # Draw a Coordinate System

  r <- c(0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1) # in polar coordinates
  theta <- c(0, 0, 0, 90, 0, 180, 0, 270, 0, 0, 0, 0) # start, end, start, end
  phi <- c(0, 90, 0, 90, 0, 90, 0, 90, 0, 0, 0, 180)
  cs <- data.frame(radius = r, theta, phi)
  ax.coord <- sph2cart(cs)

  segments3d(ax.coord, col = "gray", line_antialias = TRUE)
  points3d(
    x = 0, y = 0, z = 0, color = "black", size = 4,
    point_antialias = TRUE
  ) # plot origin

  # Label the axes

  r <- c(1.1, 1.1, 1.1, 1.1, 1.1, 1.1) # in polar coordinates
  theta <- c(0, 90, 180, 270, 0, 0)
  phi <- c(90, 90, 90, 90, 0, 180)
  l <- data.frame(radius = r, theta, phi)
  lab.coord <- sph2cart(l)
  text3d(lab.coord, texts = c("+x", "+y", "-x", "-y", "+z", "-z"))
}

###  Now, draw a reference coordinate system and demo the function in it.

drawUnitCoord()

### Draw a bounding box

box <- data.frame(
  x = c(1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1),
  y = c(1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1),
  z = c(1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1)
)

segments3d(box$x, box$y, box$z, line_antialias = TRUE, col = "red")

### Draw the midlines defining planes

mid <- data.frame(
  x = c(0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1),
  y = c(-1, -1, -1, 1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 1, 1, 1, 1, -1),
  z = c(-1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0)
)

segments3d(mid$x, mid$y, mid$z, line_antialias = TRUE, col = "blue")

### Generate two random points

p <- runif(6, -1, 1)

# Special case where p1 is on z axis
# Uncomment line below to demo
# p[4:5] <- 0

p0 <- c(p[1], p[2], p[3])
p1 <- c(p[4], p[5], p[6])

### Draw the pts, label them, draw vectors to those pts from origin

segments3d(
  x = c(0, p[1], 0, p[4]),
  y = c(0, p[2], 0, p[5]),
  z = c(0, p[3], 0, p[6]),
  line_antialias = TRUE, col = "black", lwd = 3
)

points3d(
  x = c(p[1], p[4]),
  y = c(p[2], p[5]),
  z = c(p[3], p[6]),
  point_antialias = TRUE, col = "black", size = 8
)

text3d(
  x = c(p[1], p[4]),
  y = c(p[2], p[5]),
  z = c(p[3], p[6]),
  col = "black", texts = c("p0", "p1"), adj = c(1, 1)
)

### Locate control point
### Compute and draw net vector from origin thru cp
### Connect p0 and p1

s <- p0 + p1
segments3d(
  x = c(0, s[1]), y = c(0, s[2]), z = c(0, s[3]),
  line_antialias = TRUE, col = "grey", lwd = 3
)

segments3d(
  x = c(p[1], p[4]), # connect p0 & p1
  y = c(p[2], p[5]),
  z = c(p[3], p[6]),
  line_antialias = TRUE, col = "grey", lwd = 3
)

cp <- 0.6 * s # Now for the control point

points3d(
  x = cp[1], # Plot the control point
  y = cp[2],
  z = cp[3],
  point_antialias = TRUE, col = "black", size = 8
)

text3d(
  x = cp[1], # Label the control point
  y = cp[2],
  z = cp[3],
  texts = c("cp"), col = "black", adj = c(1, 1)
)

### Now ready to work on the spline curve

n2 <- rcsr(p0, cp, p1) # Compute the spline

lines3d(
  x = n2[, 1], y = n2[, 2], z = n2[, 3],
  line_antialias = TRUE, col = "blue", lwd = 3
)

### Ta-Da!!!!!

## End(Not run)

HiveR documentation built on July 1, 2020, 7:04 p.m.