This is a simple but very generalizable method I just decided to call the "Warped Circular Motion" algorithm. It lets you parametrically generate abstract geometric stimuli based on tracing lines between points of a circle with an angle-varying radius. Useful for conditioning experiments for instance. The implementation is in R and also plots the figure using the ggplot2 library. The uploaded R script generates frames of an animation where random shapes, defined by the parameters, smoothly morph into each other; anim.mp4 is an example of what you get as output.
The function requires: library(ggplot2).
The parameters are: save-name, base-angle [in proportion of PI], and number of vertices, and then two subsets of parameters: base-radius, and amplitude, frequency, and phase [in proportion of 2 PI] of radius oscillations.
geomaker <- function(savename, angle_offset, nPoints, xrparams, yrparams) {
angle = seq(0.5 * angle_offset * 2 * pi, (1 + 0.5 * angle_offset) * 2 * pi, length.out = nPoints + 1);
r = xrparams[1] + xrparams[2] * cos(xrparams[3] * (angle + xrparams[4] * 2 * pi))
r2 = yrparams[1] + yrparams[2] * cos(yrparams[3] * (angle + yrparams[4] * 2 * pi))
x = r * cos(angle);
y = r2 * sin(angle);
D <- data.frame(x, y);
p0 <- ggplot(D, aes(x = x, y = y)) + geom_polygon(fill="white", colour="black", size=5)
p0 <- p0 + theme_void() + theme(legend.position="none") + theme(aspect.ratio=1)
ggsave(savename, plot = p0)
print(p0)
}
So it's all based on warped circles, but that encompasses triangles and squares (just specify fewer points to draw lines between) through very squiggly shapes.
Some examples are:
Basic shapes:
Triangle upright: geomaker('test.png', 1/2, 3, c(1, 0, 0, 0), c(1, 0, 0, 0))
Triangle pointing left: geomaker('test.png', 1, 3, c(1, 0, 0, 0.5), c(1, 0, 0, 0.25))
Square: geomaker('test.png', 1/4, 4, c(1, 0, 0, 0.5), c(1, 0, 0, 0.25))
Diamond: geomaker('test.png', 0, 4, c(1, 0, 0, 0.5), c(1, 0, 0, 0.25))
Circle: geomaker('test.png', 0, 200, c(1, 0, 0, 0), c(1, 0, 0, 0))
Complex shapes:
Wobbly circle: geomaker('test.png', 0, 200, c(0.9, 0.1, 16, 0.5), c(0.9, 0.1, 16, 0.5))
Soft cross: geomaker('test.png', 0, 200, c(0.7, 0.3, 4, 0), c(0.7, 0.3, 4, 0))
Goat head: geomaker('test.png', 0, 200, c(1.5, 0.5, 5, -0.25), c(0.5, 1.5, 3, 0.25))
Frog: geomaker('test.png', 0, 200, c(0.5, 0.5, 5, 0), c(1.5, 0.5, 3, 0))
Shark attack: geomaker('test.png', 0, 200, c(1, 0, 2, 0), c(0.5, 0.35, 20, 0))
Seemingly random squiggles: geomaker('test.png', 0, 400, c(5, 30, 4, 0.15), c(10.5, 10.35, 20, 0))
And so on!
Please cite as: Thomas Edward Gladwin. (2017, October 25). thomasgladwin/geomaker: v1. Zenodo. http://doi.org/10.5281/zenodo.1036613