generative art

Description Usage Arguments Details Value Note Author(s) Examples

This function takes in a single polygon and returns a function that interpolates the boundary of the polygon. This is useful for "filling in"

1	interpolate_polygon(vertex.df, method = "linear")

vertex.df

A data frame where each row corresponds to a vertex in the polygon. It must contain the columns x and y where x and y specify the coordinates of the vertex,

method

Can be either "linear" (linear interpolation) or "spline" (periodic cubic spline interpolation). When "linear" is used, the shape traced out by the interpolation function has the same shape as the original polygon, and the edges remain straight. With "spline", the interpolation function is guaranteed to go through the vertices of the original polygon, but the shape will be smooth (i.e. no straight edges and sharp corners).

When method = "linear", the interpolation function has the nice property that evenly distributed inputs will lead to vertices that are evenly distributed along the boundary of the polygon (i.e. the distance between consecutive vertices is constant). In other words: If L is the perimeter of the original polygon, then the arc length traced by the interpolation function from time 0 to t is L*t.

The return value is a function that interpolates along the boundary of the polygon. It takes in two parameters:

`time.values`	A single value or a vector of n values between 0 and 1, where 0 corresponds to the position of the first vertex, 0.5 gives the position exactly halfway around the perimeter, and 1 is the "end" of the polygon (which is back at the first vertex).
`original.vertices`	Can either be "ignore", "replace" or "add". If "ignore", the interpolation function is evaluated in the exact values given in `time.values`. If "replace", some of the values in `time.values` will be replaced so that the returned vertices are guaranteed to contain the original vertices. With "add", the original vertices are added inbetween the vertices obtained with `time.values`.

The function returns an n x 2 (plus some extra rows when original.vertices = add) data frame that contains the x- and y-coordinates of the interpolated vertices.

The results obtained with method = "spline" are generally unpredictable, such shapes that are self-intersecting, or perfect circles when the input is a regular polygon. This option should therefore be used with caution. If the goal is to get a smoothed version of the polygon, round_polygon_corners might be a better choice.

Mathias Isaksen mathiasleanderi@gmail.com

# Example: Interpolation of pentagon and comparison of original.vertices
# Create pentagon using compute_regular_polygons
vertex.df = compute_regular_polygons(center = c(0, 0), radius = 1, num.edges = 5)
# How the pentagon looks:
library(ggplot2)
ggplot()+
  geom_polygon(data = vertex.df, aes(x = x, y = y), fill = "pink")+
  geom_point(data = vertex.df, aes(x = x, y = y), color = "black")+
  coord_fixed()
# Get boundary interpolation function from interpolate_polygon
interpolation.function = interpolate_polygon(vertex.df)
# The number of vertices that we want to end up with
num.interp = 18
# Create 18 evenly distributed values between 0 and 1. Remove last element,
# as 1 leads to same position as 0
time.interp = seq(0, 1, length.out = num.interp + 1)[-(num.interp + 1)]

# One data frame per value of original.vertices
ignore.df = interpolation.function(time.interp, original.vertices = "ignore")
replace.df = interpolation.function(time.interp, original.vertices = "replace")
add.df = interpolation.function(time.interp, original.vertices = "add")

# Comparison of interpolated vertices with different original.vertices:
ggplot()+
  geom_polygon(data = ignore.df, aes(x = x, y = y, fill = "1. ignore"))+
  geom_point(data = ignore.df, aes(x = x, y = y), color = "black")+
  geom_polygon(data = replace.df, aes(x = x + 2, y = y, fill = "2. replace"))+
  geom_point(data = replace.df, aes(x = x + 2, y = y), color = "black")+
  geom_polygon(data = add.df, aes(x = x + 4, y = y, fill = "3. add"))+
  geom_point(data = add.df, aes(x = x + 4, y = y), fill = NA, color = "black")+
  scale_fill_manual("", values = c("red", "green", "blue"))+
  coord_fixed()
# When original.vertices = "ignore", the interpolated vertices contain only the
# first vertex from the original polygon, which leads to a different shape.
# The vertices are, however, evenly distributed (i.e. the distance between consecutive
# vertices is constant). With "replace", the interpolated vertices contain all
# of the original vertices, but they are not evenly distributed along
# the boundary. The same holds for "add", where the interpolated vertices
# contains both the vertices shown in "ignore" and the original vertices.
# Note: These differences are very noticeable since num.interp is small.
# Usually, we will use more than 18 interpolated vertices.