Introduction to Geometry

In the realm of DirectX computational graphics, geometry is the fundamental building block of all visible objects. It defines the shape, form, and spatial relationships of the elements that make up a 3D scene. Effectively managing and manipulating geometry is crucial for creating realistic and performant graphics.

DirectX primarily deals with geometry by representing it as a collection of vertices and primitives. A vertex is a point in 3D space, typically defined by its coordinates (x, y, z) and often including other attributes like color, texture coordinates, and normal vectors. Primitives are the basic shapes that are constructed from vertices. The most common primitives in DirectX are:

• Triangles: The fundamental primitive for most modern rendering pipelines.
• Lines: Used for wireframe rendering or specific visual effects.
• Points: Represented as single pixels, often used for particle systems.

Vertex Buffers and Index Buffers

DirectX employs vertex buffers and index buffers to efficiently manage and transfer geometric data to the GPU. This approach minimizes redundant data and optimizes rendering performance.

Vertex Buffers

A vertex buffer is a region of GPU memory that stores vertex data. Each vertex within the buffer can contain multiple attributes, such as position, normal, color, and texture coordinates. By storing these attributes together, the GPU can efficiently access and process them during the rendering pipeline.

Index Buffers

An index buffer stores a sequence of indices. Each index is an integer that refers to a specific vertex in a vertex buffer. This allows multiple primitives to share the same vertices, significantly reducing the amount of data that needs to be sent to the GPU. For example, two adjacent triangles sharing an edge can reuse the vertices along that edge.

Consider a scenario where you need to render two triangles that form a square. Without index buffers, you would define 6 vertices. With index buffers, you define only 4 unique vertices and use indices to specify how they form the two triangles.

                    
// Example of vertex and index data
struct Vertex
{
    float x, y, z;
    float nx, ny, nz; // Normal
    float u, v;       // Texture coordinates
};

// Vertex buffer data (4 vertices for a square)
Vertex vertices[] =
{
    { -1.0f, -1.0f, 0.0f, 0.0f, 0.0f, -1.0f, 0.0f, 1.0f }, // Bottom-left
    {  1.0f, -1.0f, 0.0f, 0.0f, 0.0f, -1.0f, 1.0f, 1.0f }, // Bottom-right
    { -1.0f,  1.0f, 0.0f, 0.0f, 0.0f, -1.0f, 0.0f, 0.0f }, // Top-left
    {  1.0f,  1.0f, 0.0f, 0.0f, 0.0f, -1.0f, 1.0f, 0.0f }  // Top-right
};

// Index buffer data (2 triangles forming the square)
WORD indices[] =
{
    0, 1, 2, // First triangle
    1, 3, 2  // Second triangle
};
                    
                

Transformations

Geometry rarely stays in its original defined position. Transformations are applied to alter the position, orientation, and scale of objects in 3D space. DirectX uses matrix transformations to achieve this.

• Translation: Moving an object from one point to another.
• Rotation: Spinning an object around an axis.
• Scaling: Resizing an object.

These transformations are typically combined into a single world matrix, which is then applied to each vertex. The pipeline further involves view and projection matrices to define the camera's perspective and the final rendering viewport.

Primitive Assembly

Once vertices and indices are set up, the GPU enters the primitive assembly stage. Here, the indices are used to group vertices into primitives (e.g., triangles). These assembled primitives are then passed to the rasterization stage.