Janhke-Emde Style Function Visualization

Demonstration

Features

• Janhke-Emde style function surface style
• Level curves and gradient flow visualization
• Critical point detection
• Customizable visualization parameters

Usage

from scipy.special import gamma
import numpy as np

from janhke_emde import (
    Bounds3D,
    VisualizationConfigBuilder,
    visualize_surface
)

def gamma2d(x, y):
    """Compute the absolute value of the gamma function for complex input x + yi."""
    return np.abs(gamma(x + y * 1j))

bounds = Bounds3D(xl=-6, xu=4, yl=-3, yu=3, zl=0, zu=5)

config = (
    VisualizationConfigBuilder()
    .with_bounds(bounds)
    .with_function(f)
    .with_mesh_points(1000)
    .with_critical_points(200)
    .with_level_params(0.2, 5.0, 0.2)
    .with_gradient_params(gamma=0.9, alpha=0.001, maxiter=10000)
    .with_gradient_points(20)
    .build()
)

visualize_surface(config)

Configuration Options

• bounds: x, y, and z bounds for visualization
• mesh_points: Number of points per side to use in the surface mesh grid
• critical_points: Number of points per side to use when searching for critical points
• randomize_critical_grid: Boolean flag to randomize the critical point search grid
• level_start: Starting value for level curves
• level_end: Ending value for level curves
• level_step: Step size between level curves
• gradient_gamma: Gradient descent momentum parameter (between 0 and 1)
• gradient_alpha: Gradient descent learning rate
• gradient_iter: Number of gradient descent iterations
• gradient_points: Number of starting points for gradient lines on each boundary
• func: Callable function to visualize, takes x,y coordinates and returns z value
• log_steps: Boolean flag to enable progress logging
• bounding_box: Boolean flag to enable bounding box visualization
• z_cap_move: Vertical offset for the z-cap

Requirements

• NumPy
• SciPy
• PyVista
• NetworkX
• Numba

Structure

See the original DOT file here