Materials¶

Materials define how surfaces interact with light. In RayON, every material implements two functions: emitted() (returns radiance emitted by the surface) and scatter() (returns a scattered ray direction and an attenuation factor).

Material overview¶

Type	Enum	Scatters	Emits	Key parameter
Lambertian	`LAMBERTIAN`	✓	—	`albedo` (RGB)
Mirror	`MIRROR`	✓	—	—
Rough Mirror	`ROUGH_MIRROR`	✓	—	`roughness` [0–1], `tint` (RGB)
Glass	`GLASS`	✓	—	`ior` (index of refraction)
Area Light	`LIGHT`	—	✓	`emission` (RGB)
Show Normals	`SHOW_NORMALS`	—	—	debug: normal → RGB
Constant	`CONSTANT`	—	—	debug: solid colour

Lambertian (diffuse)¶

A perfectly diffuse surface scatters light equally in all directions weighted by the cosine of the angle from the surface normal (Lambert's cosine law):

\[ f_r^{\text{Lambert}} = \frac{\rho}{\pi} \]

where \(\rho\) is the albedo — the fraction of light the surface reflects.

Scatter direction: a random point on a unit sphere offset along the surface normal (cosine-weighted hemisphere — see Sampling).

materials:
  - name: diffuse_red
    type: lambertian
    albedo: [0.8, 0.1, 0.1]

Old uniform hemisphere sampling — Old: uniform hemisphere sampling — too much noise at grazing angles.

Improved cosine-weighted sampling — New: cosine-weighted sampling — smoother gradients, same mean.

Mirror (perfect specular)¶

A perfect mirror reflects rays using the reflection formula:

\[ \mathbf{r} = \mathbf{d} - 2(\mathbf{d} \cdot \hat{n})\hat{n} \]

where \(\mathbf{d}\) is the incoming direction and \(\hat{n}\) is the surface normal. Attenuation is always 1.0 (no energy loss).

materials:
  - name: perfect_mirror
    type: mirror

Rough Mirror (microfacet)¶

Extends the perfect mirror with a roughness parameter that adds a random perturbation to the reflected direction:

\[ \mathbf{r}_\text{fuzzy} = \mathbf{r}_\text{perfect} + \text{roughness} \cdot \xi \]

where \(\xi\) is a random vector in the unit sphere. Rays that scatter back below the surface are absorbed (energy conservation).

A tint (RGB colour) modulates the reflection to produce metallic effects:

\[ \text{attenuation} = \text{tint} \times 0.7 \]

Preset tints:

Metal	Tint RGB
Gold	(1.00, 0.85, 0.57)
Copper	(0.95, 0.50, 0.30)
Steel	(0.80, 0.85, 0.90)
Iron	(0.56, 0.57, 0.58)
Bronze	(0.80, 0.50, 0.20)

materials:
  - name: gold_sphere
    type: rough_mirror
    albedo: [1.0, 0.85, 0.57]   # tint = gold
    roughness: 0.03              # near-perfect reflection

Tinted rough mirrors — gold, copper, steel — Gold, copper, and steel spheres at `roughness=0.05`. The warm tint is visible in highlights.

Roughness gradient from 0 to 0.5 — Left to right: roughness 0.0 → 0.5. The reflected image progressively blurs.

Glass (dielectric)¶

Glass both reflects and refracts light. The ratio of reflected to transmitted energy is governed by the Fresnel equations, approximated efficiently using Schlick's formula:

\[ R(\theta) = R_0 + (1 - R_0)(1 - \cos\theta)^5, \quad R_0 = \left(\frac{n_1 - n_2}{n_1 + n_2}\right)^2 \]

Refraction direction follows Snell's law:

\[ n_1 \sin\theta_1 = n_2 \sin\theta_2 \]

When \(n_1 > n_2\) and \(\theta_1\) exceeds the critical angle, total internal reflection occurs and the surface acts as a perfect mirror.

materials:
  - name: glass
    type: glass
    ior: 1.5      # crown glass (water ≈ 1.33, diamond ≈ 2.42)

Glass spheres refracting the background. The caustic ring under the sphere is not explicit — it emerges from the path tracing integral.

Area Light¶

Light sources are geometry (rectangles or spheres) with the LIGHT material. The scatter() function returns false (no further bouncing) and emitted() returns the emission colour.

Soft shadows emerge naturally — a larger light source means more rays from the scene "see" the light directly, producing smooth penumbrae.

materials:
  - name: warm_white_light
    type: light
    emission: [5.0, 4.5, 3.5]     # HDR — values > 1 are physically valid

geometry:
  - type: rectangle
    material: warm_white_light
    position: [-1.0, 3.0, -2.0]
    u_vec: [2.5, 0.0, 0.0]
    v_vec: [0.0, 0.0, 1.5]

Cornell box lit by a single rectangular area light on the ceiling. The coloured walls produce visible colour bleeding on the floor and white sphere.

Debug materials¶

Two materials are available for development and debugging:

ShowNormals — maps the surface normal to RGB: [ \text{colour} = 0.5(\hat{n} + \mathbf{1}) ] Red = +X axis, Green = +Y axis, Blue = +Z axis.

Constant — emits a fixed solid colour regardless of lighting. Useful for environment backgrounds.

All surfaces shown with the ShowNormals material. Note how the smooth normal interpolation on the imported mesh makes the face boundaries invisible.

The CRTP material system¶

Both CPU and GPU renderers share the same material dispatch logic. On the CPU, standard C++ virtual functions are used. On the GPU, virtual dispatch is not allowed, so RayON uses a Curiously Recurring Template Pattern (CRTP) with a flat union:

// MaterialParamsUnion — POD struct, GPU safe
union MaterialParamsUnion {
    LambertianParams  lambertian;
    MirrorParams      mirror;
    RoughMirrorParams rough_mirror;
    GlassParams       glass;
    LightParams       light;
};

At runtime the enum tag selects the correct branch — the compiler inlines each case completely, zero virtual-function overhead. See Architecture → Scene System for details about how materials are transferred to the GPU.