dscurve: Parametric curves or a graph of functions

In dsmodels: A Language to Facilitate Simulation and Visualization of Two-Dimensional Dynamical Systems

Description

This function takes a description of a curve and creates an object displaying the curve, and optionally it's behavior throughout iterations of the system. Functions can be provided as expressions of x, for graphing curves, or t, for parametric curves. The curve is defined either by the graph of a single function or a pair of parametric equations. By default, rendered with the lines function.

Usage

dscurve(fun, yfun = NULL, col = "black", image = NULL, lwd = 3,
  n = NULL, iters = 0, crop = TRUE, tstart = 0, tend = 1,
  discretize = FALSE, xlim = NULL, ...)

Arguments

fun	A function. If yfun is provided, this is the x-equation of the parametric equations. If not, the function's graph is rendered. See sections describing graphs and parameteric equations for more info.
yfun	The y-equation of the parameteric equations. See sections describing parametric equations for more info.
col	The color of the original curve, as a string.
image	A single color as a string, or a vector of colors as a string. See details for more information.
lwd	Line width expressed as a double. Only used if discretize is not set.
n	The number of points that will be calculated. Defaults to the dsrange's renderCount. n is used to interact with discretize.
iters	Determines the number of iterations of the function when making a color gradient. Use col = color1, image = color2, iters = n to create a gradient of colors between color1 and color2. See details for more information.
crop	If crop==TRUE, the original curve and all iterations are cropped to the range.
tstart	Only used for parametric curves. The minimum input for both functions. Default 0.
tend	Only used for parametric curves. The maximum input for the functions. Default 1.
discretize	Set discretize=TRUE to display the calculated points, instead of connecting them as a curve: the curve is displayed with points instead of lines.
xlim	Only used for the graph of a function. Determines the range of x values for which the function is plotted. Defaults to the x limits of the model's dsrange.
...	Further graphical parameters passed to lines or points.

The graph of a function

If the parameter yfun is not provided, then dscurve contains the curve of points (x,fun(x)). The inputs to fun are n points between the maximum dsrange's x limits, but can be overwritten with the xlim parameter. fun can either be any function of a single parameter, or an expression with exactly x as the free variable.

Parametric equations

If the parameter fun and yfun are both provided, dscurve contains the parametric curve described by the functions. The function is calculated at n points ranging from tmin to tmax. fun and yfun can either be any function of a single parameter, or an expression with exactly t as the free variable.

Images of curves

The dscurve object begins with an initial curve. Images of the curve may be displayed in three ways. If the image parameter is a single color and iters is not set, then dscurve will calculate and display the image of the curve under the model's function in that color.

If the image parameter is a vector of k colors, then dscurve calculates and displays k successive images of the curve using those colors. The string "NA" may be used to avoid displaying an iteration.

If the image parameter is a single color and iters is defined, then iters successive images are displayed, using a gradient between col and image.

In most cases, rather than specifying col and image separately, they may be combined into a single vector.

See Also

dspoint

Examples

library(dsmodels)

fun <- function(X,Y) {
  list(
    X/exp(Y),
    Y/exp(X)
  )
}

model <- dsmodel(fun, title = "Points on a One-Dimensional Curve")
range <- dsrange(-2:2,-2:2, discretize = 0.5)

# Add the graph of a function and its image in blue.
graphcrv <- dscurve(function(x) x^2,
                    col = "orange",
                    image = "blue",
                    discretize = TRUE,
                    xlim = c(-2,2))
model + range +	graphcrv
# Add the graph of expression of x.
model + dscurve(x^2+1, col="yellow")

# Create a parametric curve with image iterations red then green.
paramcrv <- dscurve(function(t) t^2, function(t) t,
                    image = c("red", "green"),
                    tstart = -2, tend = 2)
dsmodel(fun, "A Parametric Curve and Iterations of that Curve") +
  dsrange(-2:2, -2:2, discretize = 0.5) +
# A parametic curve defined by expressions of t.
  paramcrv + dscurve(4*t-2,4*t-2,col="blue")

dsmodels documentation built on May 2, 2019, 8:35 a.m.