cubic b spline and ex

Author: GiorgioMedico

examples/b_spline_cubic_ex.py

@@ -0,0 +1,77 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+from interpolatepy.b_spline_cubic import CubicBSplineInterpolation
+from mpl_toolkits.mplot3d import Axes3D  # noqa: F401
+
+
+def example_8_8() -> None:
+    """
+    Implementation of Example 8.8 from the document:
+    3D cubic B-spline interpolation through the given points.
+    """
+    # Define the points to interpolate as given in the matrix
+    points = np.array(
+        [
+            [83, -54, 119],
+            [-64, 10, 124],
+            [42, 79, 226],
+            [-98, 23, 222],
+            [-13, 125, 102],
+            [140, 81, 92],
+            [43, 32, 92],
+            [-65, -17, 134],
+            [-45, -89, 182],
+            [71, 90, 192],
+        ]
+    )
+
+    # Create the cubic B-spline interpolation
+    # Use chord length parameterization as recommended for 3D curves
+    interpolation = CubicBSplineInterpolation(points, method="chord_length", auto_derivatives=True)
+
+    # Create a figure for 3D visualization
+    fig = plt.figure(figsize=(12, 10))
+    ax = fig.add_subplot(111, projection="3d")
+
+    # Plot the B-spline curve with control polygon using inherited method
+    interpolation.plot_3d(num_points=200, show_control_polygon=True, ax=ax)
+
+    # Add the interpolation points
+    ax.scatter(
+        points[:, 0],
+        points[:, 1],
+        points[:, 2],
+        color="green",
+        marker="o",
+        s=100,
+        label="Interpolation points",
+    )
+
+    # Set labels and adjust the view
+    ax.set_xlabel("X")
+    ax.set_ylabel("Y")
+    ax.set_zlabel("Z")
+    ax.set_title("3D Cubic B-spline Interpolation (Example 8.8)")
+
+    # Add a legend
+    ax.legend()
+
+    # Adjust the viewing angle to better see the 3D shape
+    ax.view_init(elev=30, azim=45)
+
+    plt.tight_layout()
+    plt.show()
+
+    # Print some information about the interpolation
+    print("Cubic B-spline Interpolation Information:")
+    print(f"Number of interpolation points: {len(points)}")
+    print(f"Degree of B-spline: {interpolation.degree}")
+    print(f"Control points:\n [{(interpolation.control_points)}]")
+    print(f"Knots vector: \n[{interpolation.knots}]")
+    print(f"V0: \n[{interpolation.v0}]")
+    print(f"Vn: \n[{interpolation.vn}]")
+
+
+if __name__ == "__main__":
+    example_8_8()