Examples
========

Basic Examples
-------------

Creating a Cline Directly from Parameters
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. plot::
    :include-source: true
    :context: close-figs

    import matplotlib.pyplot as plt
    from cline import Cline

    # Create a cline directly by specifying c, alpha, and d parameters
    # c=1, d=1, alpha=2+1j
    cline = Cline(c=1, alpha=2+1j, d=1)

    # Print cline information
    print(cline)

    # Create plot
    fig, ax = plt.subplots(figsize=(8, 8))
    cline.plot(ax=ax, color='purple', label='Cline from Parameters')

    ax.grid(True, linestyle='--', alpha=0.7)
    plt.legend()
    plt.title('Cline with c=1, d=1, alpha=2+1j')

Creating and Visualizing Circles
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. plot::
    :include-source: true
    :context: close-figs

    import matplotlib.pyplot as plt
    from cline import Cline

    # Create a circle with center at 1+2j and radius 2
    circle = Cline.from_circle(center=1+2j, radius=2)

    # Print circle information (only shown in code, not in output)
    print(circle)

    # Create plot
    fig, ax = plt.subplots(figsize=(8, 8))
    circle.plot(ax=ax, color='blue', label='Circle')

    # Set limits and add legend
    ax.set_xlim(-3, 5)
    ax.set_ylim(-1, 5)
    ax.grid(True, linestyle='--', alpha=0.7)
    plt.legend()
    plt.title('Circle with Center at 1+2j and Radius 2')

Creating and Visualizing Lines
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. plot::
    :include-source: true
    :context: close-figs

    import matplotlib.pyplot as plt
    from cline import Cline

    # Create a line passing through points 0 and 1+1j
    line = Cline.from_line(z0=0, z1=1+1j)

    # Create plot - the limits are now automatically calculated
    # based on the points used to create the line
    fig, ax = plt.subplots(figsize=(8, 8))
    line.plot(ax=ax, color='red', label='Line', show_points=True)
    plt.legend()
    plt.title('Line Through Points 0 and 1+1j')

Combining Multiple Clines
~~~~~~~~~~~~~~~~~~~~~~~

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    :include-source: true
    :context: close-figs

    import matplotlib.pyplot as plt
    from cline import Cline

    # Create multiple clines
    circle = Cline.from_circle(center=1+1j, radius=2)
    line1 = Cline.from_line(z0=-2-2j, z1=2+2j)
    line2 = Cline.from_line(z0=-2+2j, z1=2-2j)

    # Create plot
    fig, ax = plt.subplots(figsize=(8, 8))

    # Plot the clines
    circle.plot(ax=ax, color='blue', label='Circle')
    line1.plot(ax=ax, color='red', label='Line 1')
    line2.plot(ax=ax, color='green', label='Line 2')

    # Set limits and add legend
    ax.set_xlim(-3, 5)
    ax.set_ylim(-3, 5)
    ax.grid(True, linestyle='--', alpha=0.7)
    ax.set_aspect('equal')
    plt.legend()
    plt.title('Multiple Clines')

Advanced Examples
----------------

Circle Through Three Points
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. plot::
    :include-source: true
    :context: close-figs

    import matplotlib.pyplot as plt
    from cline import Cline

    # Create three points in the complex plane
    z0 = 0
    z1 = 1
    z2 = 1j

    # Create a cline passing through these three points
    cline = Cline.from_three_points(z0, z1, z2)

    # Create plot with automatic limits
    fig, ax = plt.subplots(figsize=(8, 8))
    cline.plot(ax=ax, color='purple', label='Circle through 3 points', show_points=True)
    plt.legend()
    plt.title('Circle Through Three Points')

Line Through Three Collinear Points
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. plot::
    :include-source: true
    :context: close-figs

    import matplotlib.pyplot as plt
    from cline import Cline

    # Create three collinear points (these all lie on the line y = 2x)
    z0 = 1 + 2j  # (1,2)
    z1 = 2 + 4j  # (2,4)
    z2 = 3 + 6j  # (3,6)

    # Create a cline passing through these three points
    # Because the points are collinear, this will create a line
    cline = Cline.from_three_points(z0, z1, z2)

    # Print information about the cline (not shown in output)
    print(cline)
    print(f"Is circle: {cline.is_circle}")
    print(f"Is line: {cline.is_line}")

    # Create plot with automatic limits
    fig, ax = plt.subplots(figsize=(8, 8))
    cline.plot(ax=ax, color='orange', label='Line through 3 collinear points', show_points=True)

    # Add a grid to visualize the collinearity
    ax.grid(True, linestyle='-', alpha=0.3)

    # Add text annotation
    ax.text(0.5, 0.05,
           "The points (1,2), (2,4), and (3,6) are collinear\nand lie on the line y = 2x",
           transform=ax.transAxes, fontsize=12,
           horizontalalignment='center', verticalalignment='bottom')

    plt.legend()
    plt.title('Line Through Three Collinear Points')

Grid of Clines
~~~~~~~~~~~~

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    :include-source: true
    :context: close-figs

    import matplotlib.pyplot as plt
    from cline import Cline
    import numpy as np

    # Create a figure with 2x2 subplots
    fig, axes = plt.subplots(2, 2, figsize=(10, 10))
    axes = axes.flatten()

    # Example 1: A simple circle
    circle = Cline.from_circle(center=0, radius=2)
    circle.plot(ax=axes[0], color='blue')
    axes[0].set_title('Simple Circle')
    axes[0].set_aspect('equal')
    axes[0].grid(True, linestyle='--', alpha=0.7)

    # Example 2: A simple line
    line = Cline.from_line(z0=-2, z1=2)
    line.plot(ax=axes[1], color='red')
    axes[1].set_title('Simple Line')
    axes[1].set_aspect('equal')
    axes[1].grid(True, linestyle='--', alpha=0.7)

    # Example 3: Circle through three points
    points = Cline.from_three_points(0, 2, 1+1j)
    points.plot(ax=axes[2], color='green', show_points=True)
    axes[2].set_title('Circle Through Points')
    axes[2].set_aspect('equal')
    axes[2].grid(True, linestyle='--', alpha=0.7)

    # Example 4: Multiple circles
    centers = [1+1j, -1-1j, -1+1j, 1-1j]
    for i, c in enumerate(centers):
        Cline.from_circle(center=c, radius=0.8).plot(
            ax=axes[3],
            color=plt.cm.tab10(i),
            label=f'Circle {i+1}'
        )
    axes[3].set_title('Multiple Circles')
    axes[3].set_aspect('equal')
    axes[3].grid(True, linestyle='--', alpha=0.7)
    axes[3].legend()

    # Adjust layout
    plt.tight_layout()
    plt.suptitle('Various Cline Examples', y=1.02, fontsize=16)
    plt.subplots_adjust(top=0.9)