Plotting API Reference¶

Functions for visualizing complex functions in 2D, 3D, and on the Riemann sphere.

High-Level API¶

::: complexplorer.api options: show_root_heading: true show_source: true heading_level: 3 members: - show - plot - pair_plot - plot_landscape - pair_plot_landscape - riemann - publication_preset - interactive_preset - high_contrast_preset

Quick Plot Function¶

show()¶

Simplified plotting function for quick exploration.

Example:

import complexplorer as cp

# Quickest way to visualize
cp.show(lambda z: z**2)

# With custom domain
cp.show(lambda z: z**2, domain_size=6)

# With colormap
cp.show(lambda z: z**2, colormap='pastel')

Parameters: - func: Complex function z -> f(z) - domain_size: Size of square domain (default: 4) - colormap: Colormap name or object - resolution: Points per axis (default: 500) - **kwargs: Additional arguments passed to plot()

2D Plotting Functions¶

plot()¶

Main 2D visualization function.

Example:

f = lambda z: (z**2 - 1) / (z**2 + 1)
domain = cp.Rectangle(4, 4)
cmap = cp.Phase(phase_sectors=6, auto_scale_r=True)

# Basic plot
cp.plot(domain, f, cmap=cmap)

# High-resolution
cp.plot(domain, f, cmap=cmap, resolution=800)

# Save to file
cp.plot(domain, f, cmap=cmap, filename='output.png', show=False)

Parameters: - domain: Domain object (Rectangle, Disk, or Annulus) - func: Complex function z -> f(z) - cmap: Colormap object (default: Phase with 6 sectors) - resolution: Points per axis (default: 500) - figsize: Figure size in inches (default: (8, 8)) - dpi: Dots per inch (default: 100) - title: Plot title (optional) - filename: Save to file instead of displaying (optional) - show: Whether to display the plot (default: True)

Returns: matplotlib axes object

pair_plot()¶

Side-by-side visualization of domain and codomain.

Example:

# Compare input and output
cp.pair_plot(domain, f, cmap=cmap)

# Custom figure size
cp.pair_plot(domain, f, cmap=cmap, figsize=(16, 8))

# With labels
cp.pair_plot(domain, f, labels=["Domain", "Codomain"])

Parameters: - domain: Domain object - func: Complex function - cmap: Colormap (default: Phase with 6 sectors) - resolution: Points per axis (default: 500) - figsize: Figure size (default: (14, 7)) - labels: List of 2 strings for subplot titles - filename: Save to file (optional) - show: Whether to display (default: True)

Returns: matplotlib figure and axes

3D Plotting Functions (Matplotlib)¶

::: complexplorer.plotting.matplotlib.plots_3d options: show_root_heading: true show_source: true heading_level: 4 members: - plot_landscape - pair_plot_landscape

plot_landscape()¶

Create 3D surface where height represents function modulus.

Example:

# Basic 3D landscape
cp.plot_landscape(domain, f)

# With custom colormap
cmap = cp.Phase(phase_sectors=6, auto_scale_r=True)
cp.plot_landscape(domain, f, cmap=cmap)

# Adjust vertical scaling
cp.plot_landscape(domain, f, cmap=cmap, z_scale=0.5)

# Custom view angles
cp.plot_landscape(domain, f, elevation=30, azimuth=-60)

Parameters: - domain: Domain object - func: Complex function - cmap: Colormap (default: Phase) - resolution: Points per axis (default: 300) - z_scale: Vertical scale factor (default: 1.0) - modulus_mode: Height scaling mode (default: 'arctan') - modulus_params: Parameters for modulus scaling - figsize: Figure size (default: (10, 8)) - elevation: View elevation angle (default: 30) - azimuth: View azimuth angle (default: -60) - title: Plot title - filename: Save to file - show: Display plot (default: True)

Returns: matplotlib 3D axes

pair_plot_landscape()¶

Side-by-side 3D landscapes of domain and codomain.

Example:

# Compare input and output in 3D
cp.pair_plot_landscape(domain, f, cmap=cmap)

# Custom view angles
cp.pair_plot_landscape(domain, f, elevation=20, azimuth=-45)

Parameters: - Same as plot_landscape() plus: - labels: List of 2 strings for subplot titles

Returns: matplotlib figure and axes

3D Plotting Functions (PyVista)¶

::: complexplorer.plotting.pyvista.plots_3d_pv options: show_root_heading: true show_source: true heading_level: 4 members: - plot_landscape_pv - pair_plot_landscape_pv

plot_landscape_pv()¶

High-quality interactive 3D landscape (15-30x faster than matplotlib).

Example:

# Basic PyVista landscape
cp.plot_landscape_pv(domain, f)

# High resolution with custom colormap
cmap = cp.Phase(phase_sectors=6, auto_scale_r=True)
cp.plot_landscape_pv(domain, f, cmap=cmap, resolution=400)

# Save screenshot
cp.plot_landscape_pv(domain, f, cmap=cmap,
                      filename='landscape.png', show=False)

# Interactive mode
cp.plot_landscape_pv(domain, f, cmap=cmap, window_size=(1200, 900))

Parameters: - domain: Domain object - func: Complex function - cmap: Colormap - resolution: Points per axis (default: 300) - modulus_mode: Height scaling mode (default: 'arctan') - modulus_params: Parameters for scaling - window_size: Window dimensions (default: (1024, 768)) - title: Plot title - filename: Save screenshot - show: Display interactive window (default: True) - notebook: Use notebook backend (default: False)

Returns: PyVista plotter object (if show=False)

Interactive Controls: - Left mouse: Rotate view - Middle mouse: Pan - Right mouse: Zoom - Scroll wheel: Zoom in/out - 'r': Reset camera - 's': Save screenshot - 'q': Quit

pair_plot_landscape_pv()¶

Side-by-side PyVista landscapes.

Example:

# High-quality comparison
cp.pair_plot_landscape_pv(domain, f, cmap=cmap)

# Wide window for side-by-side
cp.pair_plot_landscape_pv(domain, f, window_size=(1600, 800))

Parameters: - Same as plot_landscape_pv() plus: - labels: List of 2 strings for subplot titles - window_size: Default (1400, 700) for side-by-side

Returns: PyVista plotter object

Riemann Sphere Functions (Matplotlib)¶

::: complexplorer.plotting.matplotlib.riemann options: show_root_heading: true show_source: true heading_level: 4 members: - riemann

riemann()¶

Create Riemann sphere visualization using matplotlib 3D.

Example:

f = lambda z: z**2 / (z**2 + 1)

# Basic Riemann sphere
cp.riemann(f)

# With custom colormap
cmap = cp.Phase(phase_sectors=6, auto_scale_r=True)
cp.riemann(f, cmap=cmap)

# High resolution
cp.riemann(f, cmap=cmap, resolution=400)

# Adjust view angle
cp.riemann(f, cmap=cmap, elevation=20, azimuth=45)

Parameters: - func: Complex function - cmap: Colormap (default: Phase) - resolution: Points per dimension (default: 300) - n_theta: Latitudinal divisions (default: 50) - phase_sectors: Longitudinal divisions (default: 50) - modulus_mode: Height scaling (default: 'arctan') - figsize: Figure size (default: (10, 10)) - elevation, azimuth: View angles - title: Plot title - filename: Save to file - show: Display plot (default: True)

Returns: matplotlib 3D axes

Riemann Sphere Functions (PyVista)¶

::: complexplorer.plotting.pyvista.riemann_pv options: show_root_heading: true show_source: true heading_level: 4 members: - riemann_pv

riemann_pv()¶

High-quality interactive Riemann sphere with relief mapping.

Example:

# Basic Riemann relief map
cp.riemann_pv(f)

# With custom colormap
cmap = cp.Phase(phase_sectors=6, auto_scale_r=True)
cp.riemann_pv(f, cmap=cmap)

# Smooth bounded relief (recommended)
cp.riemann_pv(f, modulus_mode='arctan')

# High resolution
cp.riemann_pv(f, cmap=cmap, modulus_mode='arctan',
             n_theta=100, phase_sectors=60, resolution=600)

# Domain restriction for stability
domain = cp.Annulus(inner_radius=0.1, outer_radius=10)
cp.riemann_pv(f, domain=domain, modulus_mode='logarithmic')

Parameters: - func: Complex function - cmap: Colormap - domain: Optional domain restriction - modulus_mode: Height scaling mode (default: 'arctan') - modulus_params: Parameters for modulus scaling - n_theta: Latitudinal resolution (default: 50) - phase_sectors: Longitudinal resolution (default: 50) - resolution: Function sampling resolution (default: 400) - window_size: Window dimensions (default: (1024, 768)) - title: Plot title - filename: Save screenshot - show: Display window (default: True) - project_from_north: Projection pole (default: True)

Returns: PyVista plotter (if show=False)

Modulus Modes for Riemann Sphere: - constant: Flat sphere (no relief) - arctan: Smooth bounded relief (recommended) - logarithmic: Emphasize poles/zeros - adaptive: Auto-adjust to function behavior - sigmoid: S-curve mapping - linear: Direct mapping (can be unstable)

Preset Configurations¶

publication_preset()¶

High-resolution settings for publication-quality figures.

Example:

settings = cp.publication_preset()
# Returns: {'resolution': 1200, 'dpi': 300, 'figsize': (4, 4)}

cp.plot(domain, f, **settings, filename='publication.pdf')

Returns: dict with resolution, dpi, figsize

interactive_preset()¶

Fast settings for interactive exploration.

Example:

settings = cp.interactive_preset()
# Returns: {'resolution': 300, 'dpi': 100, 'figsize': (8, 8)}

cp.plot(domain, f, **settings)

Returns: dict with resolution, dpi, figsize

high_contrast_preset()¶

Maximum contrast colormap settings.

Example:

cmap = cp.high_contrast_preset()
# Returns: Phase(phase_sectors=6, auto_scale_r=True, v_base=0.3)

cp.plot(domain, f, cmap=cmap)

Returns: Phase colormap with high contrast

Modulus Scaling Modes¶

All 3D and Riemann sphere functions support multiple modulus scaling modes:

Mode	Description	Best For
`constant`	Flat (no height)	Phase-only visualization
`linear`	Direct \|z\|	Simple functions
`arctan`	Smooth bounded	Most functions (recommended)
`logarithmic`	log(1 + \|z\|)	Poles and zeros
`adaptive`	Auto-adjust	Unknown behavior
`linear_clamp`	Linear with cap	Controlled height
`power`	\|z\|^p	Emphasize features
`sigmoid`	S-curve	Smooth transitions
`hybrid`	Combination	Complex landscapes

Custom Parameters Example:

# Arctan with custom scaling
cp.plot_landscape_pv(domain, f,
                     modulus_mode='arctan',
                     modulus_params={'r_min': 0.3, 'r_max': 0.9})

# Power scaling with custom exponent
cp.plot_landscape_pv(domain, f,
                     modulus_mode='power',
                     modulus_params={'exponent': 0.5})

Performance Comparison¶

2D Plotting¶

Resolution 500: ~0.5-1 second
Resolution 800: ~1-2 seconds
Resolution 1200: ~3-5 seconds

3D Plotting (Matplotlib)¶

Resolution 300: ~2-5 seconds
Resolution 500: ~8-15 seconds

3D Plotting (PyVista)¶

Resolution 300: ~0.5-1 second (15-30x faster)
Resolution 800: ~2-4 seconds

Recommendation: Use PyVista for resolutions above 400x400 or for interactive exploration.

File Formats¶

2D Plots¶

PNG: Raster, web-friendly, transparency support
PDF: Vector, publication-ready, scalable
SVG: Vector, editable in Inkscape/Illustrator
JPG: Raster, compressed (use PNG instead)

3D Plots (PyVista)¶

PNG: Screenshot at window resolution
High-res PNG: Use large window_size parameter

Example:

# 2D vector format
cp.plot(domain, f, filename='figure.pdf')

# 3D high-resolution screenshot
cp.plot_landscape_pv(domain, f, window_size=(1920, 1080),
                      filename='landscape.png', show=False)

Plotting API Reference¶

High-Level API¶

Quick Plot Function¶

show()¶

2D Plotting Functions¶

plot()¶

pair_plot()¶

3D Plotting Functions (Matplotlib)¶

plot_landscape()¶

pair_plot_landscape()¶

3D Plotting Functions (PyVista)¶

plot_landscape_pv()¶

pair_plot_landscape_pv()¶

Riemann Sphere Functions (Matplotlib)¶

riemann()¶

Riemann Sphere Functions (PyVista)¶

riemann_pv()¶

Preset Configurations¶

publication_preset()¶

interactive_preset()¶

high_contrast_preset()¶

Modulus Scaling Modes¶

Performance Comparison¶

2D Plotting¶

3D Plotting (Matplotlib)¶

3D Plotting (PyVista)¶

File Formats¶

2D Plots¶

3D Plots (PyVista)¶

See Also¶