Material

The Material struct defines the visual appearance of surfaces, controlling how they interact with light.

Definition

cpp/include/Material.h

struct Material {
    Vec3 color;              // Base color (RGB normalized)
    float ambient;           // Ambient light factor
    float diffuse;           // Diffuse reflection factor
    float specularIntensity; // Specular highlight intensity
    float shininess;         // Specular exponent (tightness)
    float reflectivity;      // Mirror reflection factor
    float transparency;      // Transparency (0 = opaque, 1 = fully transparent)
    float refractiveIndex;   // Index of refraction (1.0 = air, 1.5 = glass)
    
    Material() 
        : color(Vec3(0.9f, 0.2f, 0.15f))  // Default red
        , ambient(0.1f)
        , diffuse(0.7f)
        , specularIntensity(0.5f)
        , shininess(32.0f)
        , reflectivity(0.0f)
        , transparency(0.0f)
        , refractiveIndex(1.0f) {}

    Material(const Vec3& col, float spec, float shine)
        : color(col)
        , ambient(0.1f)
        , diffuse(0.7f)
        , specularIntensity(spec)
        , shininess(shine)
        , reflectivity(0.0f)
        , transparency(0.0f)
        , refractiveIndex(1.0f) {}
};

Properties Explained

Color

Base surface color as RGB values in the range [0, 1]:

Vec3 red(0.9f, 0.2f, 0.15f);    // Warm red
Vec3 gold(1.0f, 0.84f, 0.0f);   // Gold
Vec3 chrome(0.95f, 0.95f, 0.95f); // Chrome/silver

Ambient

Simulates indirect lighting. Even in shadow, surfaces aren't completely black:

float ambient = 0.1f;  // 10% of color visible in shadow
Vec3 ambientColor = material.color * ambient;

Diffuse

Lambertian reflection - light scatters equally in all directions. This is what makes matte surfaces look matte:

float diffuse = 0.7f;  // 70% diffuse contribution
float lambert = std::max(0.0f, normal.dot(lightDir));
Vec3 diffuseColor = material.color * lambert * diffuse;

Specular Intensity

Controls the brightness of the specular highlight (shiny spot):

• 0.0 - No highlight (pure matte)
• 0.5 - Moderate shine
• 1.0 - Maximum shine

Shininess

The specular exponent controls how tight/focused the highlight is:

Value	Appearance
8	Very soft, spread out
32	Moderate, plastic-like
128	Tight, metallic
256	Very tight, mirror-like

// Blinn-Phong specular
Vec3 halfDir = (lightDir + viewDir).normalize();
float specAngle = std::max(0.0f, normal.dot(halfDir));
float specular = std::pow(specAngle, shininess) * specularIntensity;

Reflectivity

How much the surface acts as a mirror:

• 0.0 - No reflection (opaque)
• 0.3 - Subtle reflection
• 0.7 - Highly reflective
• 0.95 - Nearly perfect mirror

Transparency

How see-through the material is:

• 0.0 - Fully opaque
• 0.5 - Semi-transparent
• 0.9 - Mostly transparent (glass-like)
• 1.0 - Fully transparent

When transparency > 0, refraction is calculated using Snell's law.

Refractive Index (IOR)

Controls how much light bends when entering the material:

Material	IOR	Effect
Air	1.0	No bending
Water	1.33	Slight bending
Glass	1.5	Noticeable bending
Crystal	2.0	Strong bending
Diamond	2.4	Maximum sparkle

Higher IOR = more light bending = more distortion of objects behind.

Factory Methods

Pre-configured materials for common transparent materials:

// Clear glass material
static Material glass(const Vec3& tint = Vec3(1.0f, 1.0f, 1.0f)) {
    Material m;
    m.color = tint;
    m.transparency = 0.95f;
    m.refractiveIndex = 1.5f;
    m.specularIntensity = 1.0f;
    m.shininess = 256.0f;
    return m;
}

// Diamond material (high dispersion)
static Material diamond() {
    Material m;
    m.transparency = 0.95f;
    m.refractiveIndex = 2.4f;
    m.specularIntensity = 1.0f;
    m.shininess = 512.0f;
    return m;
}

// Water-like material
static Material water() {
    Material m;
    m.color = Vec3(0.8f, 0.9f, 1.0f);  // Slight blue tint
    m.transparency = 0.9f;
    m.refractiveIndex = 1.33f;
    return m;
}

Material Presets

The UI provides these presets:

Opaque Materials

Preset	Specular	Shininess	Reflectivity	Transparency
Matte	0.1	8	0.0	0.0
Plastic	0.4	32	0.1	0.0
Glossy	0.6	64	0.3	0.0
Metal	0.9	128	0.7	0.0
Chrome	1.0	256	0.95	0.0

Transparent Materials

Preset	Specular	Shininess	Transparency	IOR
Glass	1.0	256	0.95	1.5
Diamond	1.0	512	0.95	2.4
Water	0.8	128	0.9	1.33

Shading Calculation

The complete shading equation combines all components:

Vec3 shade(const Ray& ray, const HitRecord& hit) {
    Vec3 viewDir = (ray.origin - hit.point).normalize();
    Vec3 color(0, 0, 0);

    for (const auto& light : lights) {
        Vec3 lightDir = (light.position - hit.point).normalize();
        
        // Shadow factor
        float shadow = isInShadow(hit.point, light.position) ? 0.3f : 1.0f;
        
        // Diffuse (Lambertian)
        float diff = std::max(0.0f, hit.normal.dot(lightDir));
        Vec3 diffuse = hit.material.color * diff * hit.material.diffuse;
        
        // Specular (Blinn-Phong)
        Vec3 halfDir = (lightDir + viewDir).normalize();
        float spec = std::pow(
            std::max(0.0f, hit.normal.dot(halfDir)), 
            hit.material.shininess
        );
        Vec3 specular = light.color * spec * hit.material.specularIntensity;
        
        color = color + (diffuse + specular) * shadow;
    }

    // Ambient
    color = color + hit.material.color * hit.material.ambient;

    // Reflections (if material is reflective)
    if (hit.material.reflectivity > 0.001f) {
        Vec3 reflectDir = ray.direction.reflect(hit.normal);
        Ray reflectRay(hit.point + hit.normal * 0.001f, reflectDir);
        Vec3 reflected = traceRay(reflectRay, depth + 1);
        
        // Blend with Fresnel-like effect
        float fresnel = calculateFresnel(viewDir, hit.normal, reflectivity);
        color = color * (1.0f - fresnel) + reflected * fresnel;
    }

    return color.clamp();
}

Fresnel Effect

Real materials are more reflective at grazing angles. We approximate this:

float cosTheta = std::abs(normal.dot(viewDir * -1.0f));
float fresnelFactor = reflectivity + (1.0f - reflectivity) * std::pow(1.0f - cosTheta, 3.0f);

This makes edges of spheres more reflective than their centers.