Introduction

Ray tracing is a powerful rendering technique that simulates the physical behavior of light to produce photorealistic images. Unlike rasterization, which projects 3D objects onto a 2D screen, ray tracing works by casting rays from the camera into the scene and simulating their interactions with objects. This method naturally handles complex effects like reflections, refractions, and soft shadows.

This tutorial will guide you through the core concepts of implementing a basic ray tracer using DirectX. We will cover:

• The fundamental ray-object intersection tests.
• Shading models and light interaction.
• Recursive ray casting for reflections and refractions.
• Integration with DirectX for hardware acceleration.

The Core Concept: Ray-Object Intersection

The foundation of ray tracing lies in determining if a ray intersects with any objects in the scene and, if so, where the closest intersection occurs. A ray is defined by an origin point (O) and a direction vector (D).

An object can be represented by a mathematical equation. For instance, a sphere can be defined by its center (C) and radius (r). The equation of a sphere is: (P - C) · (P - C) = r², where P is a point on the sphere's surface.

A point P on a ray can be expressed as P(t) = O + tD, where t is a scalar representing the distance along the ray. Substituting this into the sphere equation yields a quadratic equation in terms of t:

(O + tD - C) · (O + tD - C) = r²
t²(D · D) + 2t(D · (O - C)) + (O - C) · (O - C) - r² = 0
                

This quadratic equation at² + bt + c = 0 can be solved for t using the quadratic formula: t = (-b ± sqrt(b² - 4ac)) / 2a.

• If the discriminant (b² - 4ac) is negative, the ray misses the sphere.
• If the discriminant is zero, the ray is tangent to the sphere.
• If the discriminant is positive, there are two intersection points. We are interested in the smallest positive value of t, as this represents the closest intersection point.

Similar intersection tests exist for other primitive shapes like planes, triangles, and boxes, often involving parametric equations and geometric formulations.

Shading and Lighting

Once an intersection point (P) is found, we need to determine its color. This involves calculating the light reaching that point. We cast a "shadow ray" from P towards each light source.

If the shadow ray intersects another object before reaching the light source, the point P is in shadow for that light. Otherwise, we calculate the contribution of that light using a shading model, such as the Phong reflection model:

Illumination = Ambient + Diffuse + Specular
                

• Ambient: A base level of light that illuminates all surfaces uniformly.
• Diffuse: Light scattered equally in all directions, dependent on the angle between the surface normal (N) at P and the light direction (L). Calculated using max(0, N · L).
• Specular: Highlights that appear shiny, dependent on the angle between the view vector (V) and the reflection vector of the light (R). Calculated using max(0, V · R)^shininess.

The surface normal at the intersection point is crucial and is typically calculated by differentiating the object's surface equation or by interpolating vertex normals for meshes.

Recursive Ray Casting

To achieve realistic reflections and refractions, ray tracing employs recursion. When a ray hits a reflective surface, a new ray is cast in the reflection direction. Similarly, for transparent or refractive surfaces (like glass or water), a ray is cast in the refraction direction.

The color of a point is then computed as a combination of its direct illumination and the recursively computed colors from reflected and refracted rays. The recursion depth is limited to prevent infinite loops and excessive computation.

Color(P) = DirectLight(P) + ReflectiveComponent * TraceRay(ReflectionRay) + RefractiveComponent * TraceRay(RefractionRay)
                

The intensity of the reflected and refracted components is modulated by the material properties (e.g., reflectivity, transparency, refractive index).

Integration with DirectX

While ray tracing can be implemented on the CPU, modern graphics hardware offers significant acceleration potential. DirectX provides features and APIs that can be leveraged for high-performance ray tracing:

• DirectX Raytracing (DXR): Introduced in DirectX 12 Ultimate, DXR allows developers to utilize the GPU for ray tracing workloads. It defines shader stages like Ray Generation, Intersection, Any Hit, Closest Hit, and Miss shaders.
• Shader Model 6.2 and later: Introduces ray tracing intrinsics and capabilities, allowing shaders to cast rays, handle intersections, and process hit results.
• Resource Binding: Efficiently bind acceleration structures (like BVH - Bounding Volume Hierarchy), shaders, and scene data to the GPU.

Implementing DXR involves setting up an acceleration structure to quickly find potential ray-object intersections, defining different shader programs for various stages of the ray tracing pipeline, and dispatching ray tracing commands from the CPU.

Next Steps

This tutorial covered the foundational concepts. To proceed, you can explore:

• Implementing acceleration structures (BVH, KD-trees) for faster intersection testing.
• Advanced material properties (e.g., subsurface scattering, anisotropic reflections).
• Global illumination techniques (e.g., path tracing, irradiance caching).
• Optimizing ray tracing performance for real-time applications.

Refer to the DirectX Raytracing API documentation for detailed implementation guides and sample code.