Interactive Bezier Curves & Surfaces

An interactive, real-time 3D and 2D modeling tool built with C++, OpenGL, and GLUT. This project implements De Casteljau's algorithm to render and manipulate Bezier curves and bicubic Tensor-Product surfaces from scratch.

Table of Contents

• Demos
  • 2D Surface
  • 3D 4x4 Mesh
  • 3D Utah Teapot
• Features
  • 2D Curve Editor
  • 3D Surface Rendering
• Prerequisites & Dependencies
• Controls & Interaction
  • Global Controls
  • 2D Mode Specific
  • 3D Mode Specific
• Architecture Overview

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Demos

2D Surface

bezier2D.mp4

3D 4x4 Mesh

bezier3D.mp4

3D Utah Teapot

bezier3D-teapot.mp4

Features

2D Curve Editor

• Draw & Edit Modes: Dynamically draw new curves by clicking, and snap lines to existing control points to create continuous paths.
• Degree Elevation: Mathematically add control points (+ key) to an existing curve without altering its shape, or destructively simplify the curve by removing points (- key).
• Dynamic Resolution: Increase or decrease the rendering resolution (number of line segments) in real-time.
• Coincident Point Dragging: Points overlapping in space are linked and drag together automatically.

3D Surface Rendering

• Tensor-Product Surfaces: Evaluates 3D surfaces as a "curve of curves" using generic, dynamic-sized control grids.
• Procedural Generation: Spawns flat 4x4 control meshes ready for user manipulation.
• Classic Datasets: Includes full support for rendering the standard Utah Teapot and a custom Rocket object directly from raw patch indices and vertex data.
• Ray Picking: Implements 3D unprojection (mouse-to-world rays) to allow clicking and dragging 3D control points in perspective space.
• Camera System: Fully featured orbital camera with panning, zooming, and 3-axis rotation.

Prerequisites & Dependencies

To build and run this project, you will need:

• C++ Compiler (GCC, Clang, or MSVC)
• OpenGL (Included with most OS graphics drivers)
• FreeGLUT (Windowing and inputs)
• GLEW (OpenGL Extension Wrangler)

Controls & Interaction

Right-click anywhere on the screen to access the Contextual Menu (Options change depending on whether you are in 2D or 3D mode).

Global Controls

Input	Action
Left Click	Select curves, drag control points, or draw new points.
Right Click	Open contextual tools menu.
Spacebar	Toggle between 2D Curve Mode and 3D Surface Mode.
C	Toggle visibility of Control Points.
P	Toggle visibility of the Control Polygon (Mesh cage).
ESC	Quit application.

2D Mode Specific

Input	Action
D	Toggle between Draw Mode and Edit Mode.
+ / -	Increase / Decrease the degree (control point count) of the selected curve.
Page Up / Down	Increase / Decrease the line resolution of the selected curve.

3D Mode Specific

Input	Action
Arrow Keys	Pan the camera (Up, Down, Left, Right).
I / O	Zoom camera In / Out.
x / X	Rotate camera on the X-Axis.
y / Y	Rotate camera on the Y-Axis.
z / Z	Rotate camera on the Z-Axis.
R	Reset camera to default position.
N	Spawn a new flat surface.

Architecture Overview

• main.cpp: Entry point, GLUT initialization, rendering loop, and input handling.
• BezierMath.h: Core mathematical implementation of Linear Interpolation and De Casteljau's algorithm for curves and grids.
• Camera.h: Struct managing 3D viewport state.
• Utils.h: Helper math for Ray-picking, vector projection, and coordinate mapping.
• Point.h: Data structure representing a 3D coordinate with color and size properties.
• TeapotData.h & RocketData.h: Stored arrays of vertices and indices for complex 3D patch models.