Editing Neural Radiance Fields and 3D AI (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
**The NeRF idea**: Represent a scene as a function f(x,y,z,θ,φ) → (RGB color, density σ), where (x,y,z) is a 3D position and (θ,φ) is a viewing direction. This function is parameterized by a neural network. To render a novel view: for each pixel, cast a ray through the scene, sample points along the ray, query the network for color and density at each point, and integrate (volume rendering) to produce the pixel color. The network is trained on input images with known camera poses by minimizing pixel color reconstruction error.

**Why it's remarkable**: The network implicitly encodes the geometry, appearance, and lighting of the scene — without any explicit 3D model. Photorealistic novel view synthesis from 20–100 input photographs of a real scene is possible after a few minutes of training.

**Gaussian Splatting** (Kerbl et al., 2023) replaced the implicit MLP with an explicit representation: millions of 3D Gaussian distributions, each with position, covariance (shape), opacity, and color (spherical harmonics for view-dependent appearance). Splatting renders these Gaussians as 2D projections onto the camera plane — far faster than ray marching. Result: real-time rendering of NeRF-quality scenes at 100+ FPS. 3DGS has become the dominant approach for practical applications.

**Text-to-3D** (DreamFusion): Use a 2D diffusion model as a "prior" to supervise NeRF optimization. For each training step: render the NeRF from a random viewpoint; apply the diffusion model's score function (SDS - Score Distillation Sampling) to push the rendered image toward the text prompt; backpropagate through NeRF. This transfers 2D generative model knowledge to 3D without any 3D training data. Quality is improving rapidly (Shap-E, Zero123, Wonder3D).
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