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POSTS 12 posts

12 | Animation and Simulation

Animation basics (keyframes and interpolation, physical simulation); mass-spring systems (Hooke's law, non-zero rest length springs, internal damping, structural/shear/bending springs, the finite element method); particle systems (force analysis, gravitational attraction, flocking, position-based fluids); kinematics (articulated skeletons, forward and inverse kinematics, style-based IK, rigging, blend shapes, motion capture and the uncanny valley, the production pipeline); solving ODEs (explicit Euler, errors and instability, midpoint method, modified Euler, adaptive step size, implicit Euler, Runge-Kutta, Verlet integration); rigid body simulation and fluid simulation (Eulerian vs Lagrangian, SPH, Stable Fluids, the material point method)

• 4305 words • 21 min
games101 graphics

11 | Light Fields, Color and Perception

Light fields and the plenoptic function (7D to 5D to 4D), ray reuse and the outside-the-convex-hull assumption, two-plane parameterization (s,t,u,v), light field capture (camera arrays, integral imaging), light field cameras and computational refocusing, the cost of light fields; the physical basis of colour (Newton's prism, the visible spectrum, spectral power distribution and its linearity); the biological basis of colour (rods and cones, S/M/L spectral response, the tristimulus theory); metamerism and colour reproduction; additive colour and colour matching experiments (the negative-value problem, CIE RGB matching functions); colour spaces (sRGB, CIE XYZ, separating luminance from chromaticity, the CIE chromaticity diagram, gamut, HSV, CIELAB, opponent colour theory, chromatic adaptation, CMYK)

• 3037 words • 15 min
games101 graphics

10 | Cameras and Lenses

Imaging as synthesis plus capture, what is inside a camera (lens, aperture, shutter, sensor), the history of pinhole imaging, field of view and its relation to focal length and sensor size, the three exposure controls (aperture, shutter speed, ISO), the f-number and aperture diameter, motion blur and rolling shutter, the thin lens approximation and the Gaussian thin lens equation, ray diagrams and the similar-triangle derivation, circle of confusion, rendering defocus blur with ray tracing, depth of field and depth of focus

• 2772 words • 14 min
games101 graphics

09 | Advanced Light Transport and Complex Appearance Modeling

Biased vs unbiased vs consistent estimators; unbiased light transport methods BDPT and MLT; biased methods photon mapping (photon tracing plus final gathering, density estimation) and VCM (vertex connection plus vertex merging); instant radiosity and virtual point lights; non-surface models (participating media, hair, granular materials); surface models and BRDF/BTDF/BSDF/BSSRDF; subsurface scattering and the dipole approximation; cloth rendering; detailed/glinty materials and p-NDF; wave optics appearance; procedural appearance

• 2553 words • 12 min
games101 graphics

08 | Materials and Appearances

A material is a BRDF, diffuse (Lambertian) materials, glossy materials, ideal specular reflection and refraction (Snell's law, total internal reflection, Snell's window), the Fresnel term and the Schlick approximation, microfacet theory (F/G/D and the normal distribution function), isotropic vs anisotropic materials, properties of BRDFs (non-negativity, reciprocity, energy conservation), BRDF measurement and the MERL database

• 1991 words • 10 min
games101 graphics

07 | Ray Tracing (Whitted-Style, Radiometry and Path Tracing)

Limitations of rasterization, ray casting and Whitted-style ray tracing, ray-sphere/plane/triangle intersection, Möller-Trumbore algorithm, bounding boxes AABB and the slab method, spatial partitioning vs BVH, radiometry (radiant energy/flux/intensity/irradiance/radiance), solid angle, Lambert's cosine law, BRDF and the reflection equation, the rendering equation, probability and Monte Carlo integration, path tracing, Russian roulette and direct light sampling

• 5826 words • 28 min
games101 graphics

05 | Shading (Illumination Models and Texture Mapping)

Z-buffer depth test, Blinn-Phong reflectance model, shading frequencies, graphics pipeline and shaders, texture mapping, barycentric coordinates, bilinear interpolation, Mipmap and trilinear interpolation, environment mapping, normal mapping, shadow mapping

• 5441 words • 26 min
games101 graphics
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