vectorialcalculus (version 1.0.5)

plot_surface_with_tangents: Surface with tangent lines at a point

Description

Draws the surface \(z = f(x, y)\) on a rectangular domain and overlays two tangent line segments at a given point \((x_0, y_0)\): one tangent in the direction of the \(x\)-axis and one tangent in the direction of the \(y\)-axis. The partial derivatives are approximated numerically by central finite differences.

Usage

plot_surface_with_tangents(
  f,
  x0,
  y0,
  xlim = c(-3, 3),
  ylim = c(-3, 3),
  n = 120,
  h = 1e-05,
  t_len = 0.75,
  title_prefix = "f"
)

Value

A plotly object representing the surface \(z = f(x, y)\) together with the point \((x_0, y_0, f(x_0, y_0))\) and the two tangent line segments. The object can be further modified with usual plotly

tools.

Arguments

f

Scalar field, given as function(x, y) returning a numeric value.

x0, y0

Numeric scalars with the coordinates of the point where the tangent lines are drawn.

xlim

Numeric vector c(x_min, x_max) giving the range of the \(x\)-axis used to draw the surface.

ylim

Numeric vector c(y_min, y_max) giving the range of the \(y\)-axis used to draw the surface.

n

Integer number of grid points per axis used to discretize the surface. Must be at least 20.

h

Numeric step used for the central finite–difference approximation of the partial derivatives \(f_x\) and \(f_y\).

t_len

Numeric scalar giving half the length of the tangent segments along the \(x\) and \(y\) directions.

title_prefix

Optional character string used as a prefix in the plot title (for example, the name of the function \(f\)).

Examples

if (interactive()) {
f <- function(x, y) sin(x) * cos(y)
p <- plot_surface_with_tangents(
  f,
  x0 = 1, y0 = 1,
  xlim = c(-3, 3),
  ylim = c(-3, 3),
  n = 80
)
# p
}