DirectXMath API - Windows Graphics

Introduction to DirectXMath

The DirectXMath library is a set of common math types and functions used in DirectX development. It is designed to be fast, flexible, and easy to use, leveraging SIMD instructions for performance critical operations.

This API provides essential mathematical types like vectors (XMVECTOR), matrices (XMMATRIX), and quaternions (XMVECTOR with specific packing), along with functions for common operations such as:

Vector operations (addition, subtraction, dot product, cross product, normalization)
Matrix transformations (translation, rotation, scaling, projection, view matrices)
Quaternion operations (rotation, interpolation)
Intersection tests and ray casting

Key Concepts

SIMD Intrinsics: DirectXMath is heavily optimized for SIMD (Single Instruction, Multiple Data) processors. Understanding how data is packed into XMVECTOR and XMMATRIX is crucial for performance.
Immutability: Many DirectXMath functions return new values rather than modifying existing ones in place, promoting a more functional programming style.
Row-Major vs. Column-Major: DirectXMath typically uses row-major matrices for input and column-major for internal calculations to align with DirectX pipeline expectations.

Core Data Types

XMVECTOR

A 4-component vector. Can represent points, directions, colors, or packed matrix rows.

Typically uses 128-bit SIMD registers.

XMMATRIX

A 4x4 matrix, typically represented as an array of four XMVECTOR objects, each representing a row.

Used for transformations.

XMFLOAT2, XMFLOAT3, XMFLOAT4

Structs for 2D, 3D, and 4D floating-point vectors with standard C++ alignment.

Useful for data structures not requiring SIMD optimization.

XMFLOAT4X4

A 4x4 matrix struct using standard C++ alignment.

Common Functions

The library is organized into functional categories. Here are a few examples:

Vector Operations

XMVectorAdd(): Adds two vectors.
XMVectorSubtract(): Subtracts one vector from another.
XMVectorDot(): Computes the dot product of two vectors.
XMVector3Cross(): Computes the 3D cross product.
XMVector3Normalize(): Normalizes a 3D vector.
XMVectorSet(): Creates an XMVECTOR from individual components.
XMVectorGetX(), XMVectorGetY(), etc.: Extracts components from an XMVECTOR.

Matrix Transformations

XMMatrixIdentity(): Creates an identity matrix.
XMMatrixTranslation(): Creates a translation matrix.
XMMatrixRotationX(), XMMatrixRotationY(), XMMatrixRotationZ(): Creates rotation matrices around the axes.
XMMatrixScaling(): Creates a scaling matrix.
XMMatrixPerspectiveFovLH(): Creates a left-handed perspective projection matrix.
XMMatrixLookAtLH(): Creates a left-handed view matrix.
XMMatrixMultiply(): Multiplies two matrices.

Quaternion Operations

XMQuaternionRotationMatrix(): Creates a quaternion from a rotation matrix.
XMQuaternionMultiply(): Multiplies two quaternions.
XMQuaternionSlerp(): Performs spherical linear interpolation between two quaternions.

Example Usage (C++)

Here's a simple example demonstrating how to create a translation matrix and apply it to a vector:

#include <DirectXMath.h>
#include <iostream>

using namespace DirectX;

int main() {
    // Define a translation vector
    XMVECTOR translation = XMVectorSet(10.0f, 5.0f, -2.0f, 0.0f);

    // Create a translation matrix
    XMMATRIX translationMatrix = XMMatrixTranslationFromVector(translation);

    // Define a point (as a vector)
    XMVECTOR point = XMVectorSet(1.0f, 2.0f, 3.0f, 1.0f); // W=1 for a point

    // Apply the translation matrix to the point
    XMVECTOR transformedPoint = XMVector4Transform(point, translationMatrix);

    // Output the results (requires helper functions to print XMVECTOR)
    std::cout << "Original Point: (" << XMVectorGetX(point) << ", " << XMVectorGetY(point) << ", " << XMVectorGetZ(point) << ")" << std::endl;
    std::cout << "Translated Point: (" << XMVectorGetX(transformedPoint) << ", " << XMVectorGetY(transformedPoint) << ", " << XMVectorGetZ(transformedPoint) << ")" << std::endl;

    return 0;
}

DirectXMath API Reference - Windows Graphics