Bezier Curve and Surface

Experiment Purpose

The purpose of this experiment is to deepen the understanding of free-form curve and surface modeling using Bezier curves and surfaces. This involves mastering relevant algorithms and familiarizing oneself with the methods of Bezier curve and surface modeling.

Summary

This experiment demonstrates the creation and visualization of Bezier curves and surfaces. A Bezier curve is generated from a set of control points, showing how these points influence the curve's shape without the curve passing through intermediate points (except the endpoints). Similarly, a Bezier surface is constructed using a grid of control points, forming a smooth, continuous surface influenced by the control points. Both the curve and the surface plots effectively illustrate the properties and behavior of Bezier forms.

Major Classes and Functions

BezierCurve Class

• init(self, control_points): Initializes the Bezier curve with control points.
• bernstein_poly(self, i, n, t): Computes the Bernstein polynomial value.
• curve(self, num_points=100): Computes the Bezier curve points.
• plot(self, num_points=100, save_path=None): Plots the Bezier curve and optionally saves the plot to a file.

BezierSurface Class

• init(self, control_points): Initializes the Bezier surface with control points.
• bernstein_poly(self, i, n, t): Computes the Bernstein polynomial value.
• surface(self, num_points=20): Computes the Bezier surface points.
• plot(self, num_points=20, save_path=None, title="Bezier Surface"): Plots the Bezier surface and optionally saves the plot to a file.

Main Script

• main(): The entry point of the program. It demonstrates the usage of the BezierCurve and BezierSurface classes by initializing them with sample control points, generating the curves and surfaces, and plotting the results.

Setup

To run this code, follow the steps below:

1. Clone the Repository:

   git clone https://github.com/Hetawk/bezier_curve_and_surface.git
   cd bezier_curve_and_surface

2. Install Dependencies: Ensure you have Python installed (version 3.6+ recommended). Then, install the required packages:

   pip install -r requirements.txt

3. Run the Main Script:

   python main.py

Outputs

Bezier Curve

Bezier Surface

Directory Structure

bezier_curve_and_surface/
│
├── bezier_curve.py
├── bezier_surface.py
├── main.py
├── requirements.txt
├── bezier_curve.png
├── bezier_surface.png
└── README.md