6. Normals and Surface Materials

A hit tells us that a ray met a surface first. It does not yet tell us how that surface faces the ray or how it should respond to light. Those two questions are related but they are not the same. The normal belongs to the surface geometry at a position. The material describes how the surface will be interpreted. Keeping them separate allows one sphere equation to support clay, metal or glass without becoming three different sphere equations.

The normal is also the first result that exposes orientation. A sphere has an obvious outward direction, but a ray may begin outside or inside it. Later reflection and refraction calculations need a normal that is consistently oriented against the incoming ray, along with a separate fact recording which side was hit.

The sphere normal follows from its definition

Every point on a sphere is one radius from its centre. The displacement P - C therefore points directly outwards. Dividing by the radius gives unit length:

Nout = (P − C) / r

This formula assumes the hit point is on the surface and the radius is positive. If an implementation allows a zero radius, the geometry has no usable surface normal. If finite precision places P slightly away from the exact surface, the result may not be exactly unit length; normalising defensively can be reasonable, although it adds work and may conceal a larger intersection error. The teaching code uses division by the known radius so the connection remains visible.

const position = pointOnRay(ray, t);
const outward = scale(
    subtract(position, sphere.centre),
    1 / sphere.radius
);

Record which side was entered

Take the dot product between the incoming ray direction and the outward normal. A negative result means they oppose one another: the ray met the outside of the surface. A positive result means the ray is moving in roughly the same direction as the outward normal, so it is leaving from inside.

const frontFace = dot(ray.direction, outward) < 0;
const normal = frontFace ? outward : scale(outward, -1);

return {
    t,
    position,
    normal,
    frontFace,
    material: sphere.material
};

The stored normal now points against the incoming ray in both cases. The frontFace flag preserves which side was originally encountered. Replacing the outward normal without preserving the flag would lose information required by a refractive material, which must know whether the ray is entering or leaving.

Turn records into diagnostic views

The normal components lie between -1 and 1. Remapping each component with 0.5 × (N + 1) produces a displayable RGB colour. This creates a normal diagnostic in which smoothly changing colour across a sphere exposes its curvature. The albedo view instead reads the material's base colour.

function normalColour(hit) {
    return scale(add(hit.normal, [1, 1, 1]), 0.5);
}

function albedoColour(hit) {
    return hit.material.albedo;
}

Switch between the two in the laboratory. The intersection distances and visible object boundaries do not change. Only the field read from the record changes. This is a useful debugging habit: display an intermediate quantity directly before asking a more elaborate lighting calculation to conceal it. A normal image can reveal inverted orientation, discontinuities and wrong coordinate spaces far more clearly than a polished material.

The material is a set of decisions

For now a material stores albedo, specular strength and shininess. Later it may state reflection, transmission and index of refraction. A material is not merely a final RGB colour. It supplies values and rules that determine how the hit contributes to the ray's result and whether more rays are created.

const blueMaterial = {
    albedo: [0.14, 0.42, 0.82],
    specular: 0.34,
    shininess: 32,
    reflectivity: 0
};

Attaching a material reference to geometry is convenient because the geometry knows which surface was intersected. The sphere intersection must not start performing lighting in response. It should populate the record and stop. This boundary allows the same closest-hit traversal to support diagnostic normals, local lighting and recursive materials without rewriting the geometric tests.

We now have a position, an oriented normal and a material for the nearest surface. Lesson 7 introduces a light and calculates what the relationships between its direction, the normal and the viewer permit that surface to contribute.