Add a new advanced visualization example showing the curve vectors

Author: Onur R. Bingol

visualization/mpl_curve3d_vectors.py

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+# -*- coding: utf-8 -*-
+
+"""
+    Visualization Examples for the NURBS-Python Package
+    Released under The MIT License
+    Developed by Onur Rauf Bingol (c) 2018
+"""
+from geomdl import BSpline
+from geomdl import utilities
+
+import numpy as np
+import matplotlib
+from mpl_toolkits.mplot3d import Axes3D
+import matplotlib.pyplot as plt
+
+#
+# Curve Evaluation
+#
+
+# Create a BSpline curve instance
+curve = BSpline.Curve()
+
+# Set evaluation delta
+curve.delta = 0.001
+
+# Set up the NURBS curve
+curve.read_ctrlpts_from_txt("../curve3d/ex_curve3d02.cpt")
+curve.degree = 3
+
+# Auto-generate knot vector
+curve.knotvector = utilities.generate_knot_vector(curve.degree, len(curve.ctrlpts))
+
+# Evaulate curve
+curve.evaluate()
+
+#
+# Tangent Vector Evaluation
+#
+
+# Store tangent vectors in a list for plotting
+curvetans = []
+
+# Evaluate curve tangent at u = 0.0175
+ct1 = curve.tangent(0.0175, normalize=True)
+curvetans.append(ct1)
+
+# Evaluate curve tangent at u = 0.075
+ct2 = curve.tangent(0.075, normalize=True)
+curvetans.append(ct2)
+
+# Evaluate curve tangent at u = 0.375
+ct3 = curve.tangent(0.375, normalize=True)
+curvetans.append(ct3)
+
+# Evaluate curve tangent at u = 0.535
+ct4 = curve.tangent(0.535, normalize=True)
+curvetans.append(ct4)
+
+# Evaluate curve tangent at u = 0.65
+ct5 = curve.tangent(0.65, normalize=True)
+curvetans.append(ct5)
+
+# Evaluate curve tangent at u = 0.85
+ct6 = curve.tangent(0.85, normalize=True)
+curvetans.append(ct6)
+
+# Evaluate curve tangent at u = 0.975
+ct7 = curve.tangent(0.975, normalize=True)
+curvetans.append(ct7)
+
+#
+# Normal Vector Evaluation
+#
+
+# Store normal vectors in a list for plotting
+curvenorms = []
+
+# Evaluate curve normal at u = 0.0175
+cn1 = curve.normal(0.0175, normalize=True)
+curvenorms.append(cn1)
+
+# Evaluate curve normal at u = 0.075
+cn2 = curve.normal(0.075, normalize=True)
+curvenorms.append(cn2)
+
+# Evaluate curve normal at u = 0.375
+cn3 = curve.normal(0.375, normalize=True)
+curvenorms.append(cn3)
+
+# Evaluate curve normal at u = 0.535
+cn4 = curve.normal(0.535, normalize=True)
+curvenorms.append(cn4)
+
+# Evaluate curve normal at u = 0.65
+cn5 = curve.normal(0.65, normalize=True)
+curvenorms.append(cn5)
+
+# Evaluate curve normal at u = 0.85
+cn6 = curve.normal(0.85, normalize=True)
+curvenorms.append(cn6)
+
+# Evaluate curve normal at u = 0.975
+cn7 = curve.normal(0.975, normalize=True)
+curvenorms.append(cn7)
+
+#
+# Normal Vector Evaluation
+#
+
+# Store binormal vectors in a list for plotting
+curvebinorms = []
+
+# Evaluate curve binormal vector at u = 0.0175
+cbn1 = curve.binormal(0.0175, normalize=True)
+curvebinorms.append(cbn1)
+
+# Evaluate curve binormal vector at u = 0.075
+cbn2 = curve.binormal(0.075, normalize=True)
+curvebinorms.append(cbn2)
+
+# Evaluate curve binormal vector at u = 0.375
+cbn3 = curve.binormal(0.375, normalize=True)
+curvebinorms.append(cbn3)
+
+# Evaluate curve binormal vector at u = 0.535
+cbn4 = curve.binormal(0.535, normalize=True)
+curvebinorms.append(cbn4)
+
+# Evaluate curve binormal vector at u = 0.65
+cbn5 = curve.binormal(0.65, normalize=True)
+curvebinorms.append(cbn5)
+
+# Evaluate curve binormal vector at u = 0.85
+cbn6 = curve.binormal(0.85, normalize=True)
+curvebinorms.append(cbn6)
+
+# Evaluate curve binormal vector at u = 0.975
+cbn7 = curve.binormal(0.975, normalize=True)
+curvebinorms.append(cbn7)
+
+#
+# Control Points, Curve and Tangent Vector Plotting using Matplotlib
+#
+
+# Arrange control points and evaluated curve points for plotting
+ctrlpts = np.array(curve.ctrlpts)
+curvepts = np.array(curve.curvepts)
+
+# Convert tangent, normal and binormal vector lists into NumPy arrays
+ctarr = np.array(curvetans)
+cnarr = np.array(curvenorms)
+cbnarr = np.array(curvebinorms)
+
+# Draw the control points polygon, the 3D curve and the tangent vectors
+fig = plt.figure(figsize=(10.67, 8), dpi=96)
+ax = fig.gca(projection='3d')
+
+# Plot 3D lines
+ax.plot(ctrlpts[:, 0], ctrlpts[:, 1], ctrlpts[:, 2], color='black', linestyle='-.', marker='o')
+ax.plot(curvepts[:, 0], curvepts[:, 1], curvepts[:, 2], color='cyan', linestyle='-')
+
+# Plot tangent vectors
+ax.quiver(ctarr[:, 0, 0], ctarr[:, 0, 1], ctarr[:, 0, 2], ctarr[:, 1, 0], ctarr[:, 1, 1], ctarr[:, 1, 2], color='blue', length=2.5)
+
+# Plot normal vectors
+ax.quiver(cnarr[:, 0, 0], cnarr[:, 0, 1], cnarr[:, 0, 2], cnarr[:, 1, 0], cnarr[:, 1, 1], cnarr[:, 1, 2], color='red', length=2.5)
+
+# Plot normal vectors
+ax.quiver(cbnarr[:, 0, 0], cbnarr[:, 0, 1], cbnarr[:, 0, 2], cbnarr[:, 1, 0], cbnarr[:, 1, 1], cbnarr[:, 1, 2], color='green', length=2.5)
+
+# Add legend to 3D plot, @ref: https://stackoverflow.com/a/20505720
+ctrlpts_proxy = matplotlib.lines.Line2D([0], [0], linestyle='-.', color='black', marker='o')
+curvepts_proxy = matplotlib.lines.Line2D([0], [0], linestyle='none', color='cyan', marker='o')
+tangent_proxy = matplotlib.lines.Line2D([0], [0], linestyle='none', color='blue', marker='>')
+normal_proxy = matplotlib.lines.Line2D([0], [0], linestyle='none', color='red', marker='>')
+binormal_proxy = matplotlib.lines.Line2D([0], [0], linestyle='none', color='green', marker='>')
+ax.legend([ctrlpts_proxy, curvepts_proxy, tangent_proxy, normal_proxy, binormal_proxy], ['Control Points', 'Curve', 'Tangents', 'Normals', 'Binormals'], numpoints=1)
+
+# Display the 3D plot
+plt.show()