1. Radiometry:
    Spherical coordinates, direction and solid angle in 3D
    Radiometry and photometry, Lambert law, radiometric quantities 
        (radiant energy, radiant flux, radiant intensity, irradiance, radiant exitance, radiance)
    Light sources (point light, spot light, area light, sun light, general light source)
    Calculation radiometric quantities from radiance
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2. Light reflection:
    Interaction light with physical objects
    BRDF formal definition, BRDF properties, iso- vs aniso-tropic BRDF
    Derivation of the reflection equation
    Reflectance (Hemispherical-hemispherical, Hemispherical-directional, Directional-hemispherical) and albedo
    BRDF components (diffuse + specular + glossy)
       Ideal diffuse reflection, ideal mirror reflection, ideal refraction, Fresnel equations, glossy reflection
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3. BRDF models:
    Empirical models (Phong illumination model)
    Physical models and microfacets theory (Cook-Torrance, Torrance-Sparrow, Oren-Nayar)
    Models based on measured data
    BRDF vs BSDF vs BSSRDF
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4. Shading:
    Smooth shading with interpolation and normals calculation (constant/flat shading, Goraud shading, Phong shading)
    Phong and Blinn-Phong reflection/illumination model
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5. Ray tracing - definition and implementation:
    Ray tracing - definition, used vectors, backward vs. forward tracing, implementation
    Intersection computation (ray vs plane, ray vs sphere) - basic informations
    Computer solid geometry (CSG) and ray tracing
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6. Ray tracing - intersection of ray with objects:
    Global vs local coordinates, viewing plane, ray construction, parametric vs algebraic defined surfaces
    Intersection of ray with objects (ray vs plane, ray vs triangle, ray vs polygon, ray vs polyhedron)
    Ray intersection with algebraic defined surfaces (intersection with implicit surfaces - sphere, cylinder, cone)
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7. Acceleration methods for ray tracing - bounding objects/volumes:
    Ray intersection with scene objects
    Bounding solids (sphere, box, polytop, k-dop, polyhedron), bound solid efficiency, solids combinations
    Algorithm for efficient ray intersection calculation with objects enclosed by bounding solids
    Bounding volume hierarchy (complexity, efficiency, construction, types) 
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8. Acceleration methods for ray tracing - scene subdivisions:
    Space subdivisions (uniform, non-uniform)
    Ray traverse in uniform/lattice grid
    Non-uniform space subdivisions (octree, BSP-tree, kD-tree)
    Directional speedup techniques (directional cube, light buffer, ray coherence)
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9. Distributed ray tracing:
    Distributed ray tracing
    Glossy reflection effect, soft refraction, soft shadows, motion blur effect, depth of field, light dispersion
    Implementation
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10. Monte Carlo (MC) integration and the reflection equation:
    Definite integral calculation in 3D (classic numerical integration vs stochastic integration)
    Random variable, uniform vs. non-uniform distribution, pdf(), cdf(), expected value, variance, random variable transformat.
    Monte Carlo integration (integral estimator - primary vs secondary, unbiased vs biased)
    Estimate of irradiance using Monte Carlo estimator (uniform sampling vs cosine sampling vs area light source sampling)
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11.Monte Carlo integration and sampling:
    Generating samples (transformation method vs rejection sampling)
    Direction (vector) calculation using importance sampling of BRDF (diffuse component sampling, specular component sampling)
    Variance reduction for MC estimators (importance sampling, control variates, stratified sampling, Quasi MC)
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12.Multiple importance sampling (MIS):
    BRDF sampling vs light source sampling
    Combined estimator definition
    Weight functions calculation (simple average vs balance heuristic)
    Strategies for direction calculation (MC estimator for BRDF sampling, MC estimator for area light source sampling)
    Multiple importance sampling and weights calculation (pdf() for BRDF sampling, pdf() for area light source sampling)
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13.Rendering equation (RE):
    Global vs local illumination
    Derivation of the rendering equation
    Angular form vs area form of the rendering equation
    Rendering equation and rendering algorithms (radiosity, raytracing, distributed ray tracing, path tracing) - basic inform.
    Operator form of the RE (transport operator, solution of the RE using Neumann series)
    Rendering equation and path tracing
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14.Path tracing and bidirectional path tracing:
    Path tracing algorithm (Russian roulette and loop termination, direction sampling /BRDF vs area light source/ and MIS)
    Measurement equation and visual importance (emitted importance)
    Light tracing
    Light transport and path integral (measurement contribution function, MC evaluation of the path integral, path sampling)
    Bidirectional path tracing (sampling techniques - from camera, from light, connections between camera and light sub-paths)
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15.Radiosity:
    Area form of the rendering equation for ideal diffuse surfaces (objects surfaces discretization by planar polygons)
    Radiosity equation (definition, formfactors, system of linear equations)
    Rendering surfaces in the radiosity method (constant shading of polygons vs Gouraud shading)
    Formfactor calculation (numerical vs stochastic methods, Nusselt's analogy, hemicube, hemiplane, Monte Carlo)
    Numerical solutions of the radiosity system of equations (Gauss-Seidel /gathering/ vs Southwell /shooting/)
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16.Textures:
    Texturing (texture quantities - reflectance, opacity, normal, geometry, environment illumination)
    Types of textures (light, opacity, shadow, bump, displacement, environment, reflection maps)
    Texture mapping (forward vs inverse mapping, surface parametrization - triangle or rectangle, cylinder, sphere)
    Two-stage mapping (texture -> intermediate surface -> textured object)
    Procedural textures (noise and Perlin noise, turbulence)
    Mipmapping, texture filtering
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17:Shadows:
    Importance of shadows
    Hard vs soft shadows (area lights, multiple light sources)
    Shadows calculations (projected/planar shadows, shadow volumes, shadow maps, shadow wedges)