Polygon & Quadric Surfaces

1. Introduction

Surface representation defines the outer boundary of 3D objects. Polygon surfaces approximate objects using flat faces, while quadric surfaces represent smooth curved shapes mathematically.

• Used in 3D modeling
• Essential for rendering

2. Polygon Surfaces

Polygon surfaces represent objects using a collection of polygons (usually triangles or quadrilaterals).

• Vertices, edges, and faces
• Common in real-time graphics

3. Polygon Mesh

A polygon mesh is a network of connected polygons that define the surface of a 3D object.

• Triangle mesh most common
• Easy to process and render

4. Advantages of Polygon Surfaces

• Simple and flexible
• Efficient for hardware rendering
• Widely supported by GPUs

5. Limitations of Polygon Surfaces

• Curves approximated by flat faces
• High polygon count for smoothness

6. Quadric Surfaces

Quadric surfaces are defined using second-degree polynomial equations and represent smooth curved objects.

• Mathematical surface definition
• Exact representation of curves

7. Types of Quadric Surfaces

• Sphere
• Cylinder
• Cone
• Ellipsoid
• Paraboloid

8. General Quadric Equation

Ax² + By² + Cz² + Dxy + Exz + Fyz +
Gx + Hy + Iz + J = 0

9. Polygon vs Quadric Surfaces

Polygon Surfaces        Quadric Surfaces
---------------------   -------------------------
Flat faces              Smooth curved surfaces
Approximate curves      Exact curves
Easy rendering          Complex computation
Used in games           Used in CAD & modeling

10. Applications

• 3D modeling software
• Games and simulations
• CAD and engineering design

Practice Questions

1. What are polygon surfaces?
2. Define quadric surfaces.
3. List types of quadric surfaces.
4. Compare polygon and quadric surfaces.
5. Where are quadric surfaces used?

Practice Task