Plot Morse-Smale Trajectories from Point

Visualizes gradient flow trajectories (both ascending and descending) from a specific starting point. Shows the trajectories on a contour plot background, marks the starting point and endpoints (critical points), and optionally adds directional arrows along the trajectories.

Usage

# S3 method for class 'morse.smale.trajectories.from.point'
plot(
  x,
  y,
  mixture,
  grid,
  step = 0.01,
  show.arrows = TRUE,
  use.custom.legend = FALSE,
  ...
)

Arguments

x

Starting x coordinate

y

Starting y coordinate

mixture

Object containing:

• f: Function taking (x, y) and returning scalar value

• gradient: Function taking (x, y) and returning gradient vector c(dx, dy)

grid

Grid object created by create.grid for contour plot background

step

Step size for gradient flow integration (default 0.01)

show.arrows

Logical, whether to show directional arrows on trajectories

use.custom.legend

Logical, whether to use custom legend.

...

Additional arguments passed to function.contours.plot

Value

Invisible list containing:

ascending

Matrix of points along ascending trajectory

descending

Matrix of points along descending trajectory

Examples

if (FALSE) { # \dontrun{
grid <- create.grid(50)
mixture <- list(
  f = function(x, y) -((x-0.3)^2 + (y-0.7)^2) - 2*((x-0.7)^2 + (y-0.3)^2),
  gradient = function(x, y) {
    c(-2*(x-0.3) - 4*(x-0.7), -2*(y-0.7) - 4*(y-0.3))
  }
)
# Plot trajectories from a point
result <- plot.morse.smale.trajectories.from.point(0.5, 0.5, mixture, grid)
} # }