Geometry in Graphics

This document covers the fundamental concepts of geometric representation and manipulation within the graphics pipeline. Understanding geometry is crucial for creating and rendering 3D scenes, from simple shapes to complex environments.

Core Concepts

Vertices

The fundamental building blocks of geometric models are vertices. A vertex represents a point in space, typically defined by its coordinates (x, y, z). In graphics, vertices often carry additional attributes such as color, texture coordinates (UV), and normal vectors.

Vertex Example (3D)


struct Vertex {
    float position[3]; // x, y, z
    float color[4];    // r, g, b, a
    float texCoords[2]; // u, v
    float normal[3];   // nx, ny, nz
};

Polygons and Primitives

Vertices are connected to form geometric primitives, which are the basic shapes used in rendering. The most common primitive is the triangle. By combining many triangles, complex surfaces can be approximated.

Points: A single vertex.
Lines: Two connected vertices.
Triangles: Three vertices connected to form a closed surface.
Quads: Four vertices (often represented as two triangles).

A single triangle primitive.

Geometric Data Structures

Efficiently storing and accessing geometric data is crucial for performance. Common data structures include:

Vertex Buffer Objects (VBOs): Storing vertex attribute data on the GPU for fast access during rendering.
Index Buffer Objects (IBOs) / Element Buffer Objects (EBOs): Storing indices that reference vertices in a VBO, allowing multiple primitives to share vertices and reduce memory usage.

Normals

Normal vectors are essential for lighting calculations. A normal vector at a vertex or face points perpendicularly outwards from the surface, indicating its orientation. This helps determine how light reflects off the surface.

A face normal (perpendicular to the triangle's surface).

Texture Coordinates

Texture coordinates (UV coordinates) are 2D values that map points on a 2D texture image to corresponding points on a 3D model's surface.

U: Typically represents the horizontal axis of the texture.
V: Typically represents the vertical axis of the texture.

A common convention is that U and V range from 0.0 to 1.0.

Advanced Topics

Subdivision Surfaces

Techniques for generating smoother, more detailed geometry from a coarser initial mesh. Examples include Catmull-Clark and Loop subdivision.

Tessellation

Dynamically adding detail to geometry based on camera distance or other factors, often implemented using hardware tessellation shaders.

Procedural Geometry

Generating geometry algorithmically, rather than defining it explicitly with vertices and faces. This is useful for creating complex and varied environments.

This section provides an introduction to the core geometric concepts. Refer to specific API documentation for implementation details and advanced features.

Graphics Documentation