ACG Auswendig lernen

Raytracing
geometric algorithm to compute intersections of rays with the scene (aka. ray-based visibility)

Primary Rays
⇒ Camera Model
Secondary rays and shadow feelers
⇒ Secondary Rays
→ Reflection and Refraction
Combining all incoming light into “one” outgoing light
⇒ Lighting models

Pathtracing
Algorithm to compute global illumination by shooting rays in all kinds of (random) directions (aka. random sampling, aka. Monte Carlo integration)

Intersection

Ray Triangle Intersection
Ray Box Intersection
Ray Sphere Intersection

Distribution Ray Tracing

⇒ Solution for Anti-Aliasing

Poisson Disk Sampling

Implicit Surfaces

Root Finding

Metaballs

S = {x ∣ x \in R^{3}, P (x) = \sum a_{i} p (d_{i} (x)) = τ}

The Normal on Implicit Surfaces
⇒ The gradient of the field is the normal

Marching Cubes
Weighted Moving Least Squares Method

Mailbox Technique
Problem: Bei Spatial Hashing kann es passieren das ein Ray mehrmals gegen ein Object getestet wird.
→ Gib jedem Ray eine ID (Counter)
→ Vor jedem interesction check teste ob teste ob der Punkt (das t) aus der Mailbox geladen werden kann.
→ Wenn nicht speichere den Punkt (das t) mit der Ray ID in der Mailbox

Optimisation: Ein Hash Table per Ray
⇒ funktioniert parrallel

Hierarchical Grid

Irregular Grids

Octree

kD-Trees

Finding a splitting plane

kD-Tree Splitting Plane
K-D tree Surface Area Heuristic

Distance Fields

K-DOPS

Laufzeit: $O (k)$

Bounding Volume Hierarchy

Running time: $T (n) = T (α n) + T ((1 - α) n) + O (n l o g n) \in O (n l o g^{2} n)$

The Collision Detection Pipeline

Separating Planes Algorithm

Perlin Noise

Gradient Noise

Simplex Noise

Voronoi Noise
Variations

Ambient Occlusion

1- Methode

Sample point in second renderpass in G-buffer (on fragment)

2. Methode

Average all pixel colors of neigbor positions in worldspace.

Refraction

Geometry Shader

Physically-Based Lighting

Flux
how much energy flows from/to/through a surface per unit of time.
Symbol: Φ
Units = Watt
Link to original

Irradiance
energy density = flux per area
$E = \frac{d ϕ}{d A}$
Link to original

Lambert's law
$E_{1} = \frac{d ϕ}{d A ^{⊥}} E_{2} = \frac{d ϕ}{d A} = \frac{d ϕ cos θ}{d A ^{⊥}} = E_{1} cos θ$
since: $A^{⊥} = A cos θ$
Link to original

Exitance
same thing as Irradiance, except for light leaving a surface

$M_{1} = \frac{d ϕ}{d A ^{⊥}} = \frac{d ϕ}{cos θ d A} = \frac{E _{2}}{cos θ}$
Link to original

Intensity
Flux over solid angles

$I = \frac{d ϕ}{d ω}$

Link to original

Radiance

The BRDF
$p = p_{d i ff} + p_{s p ec}$
$p_{d i ff} (l, v) = \frac{1}{π} C_{ba se}$

The Micro-Facet BRDF

The Normal Distribution Function
$D (h) = \frac{a ^{2}}{π (( n \cdot h ) ^{2} ( a ^{2} - 1 ) + 1 ) ^{2}}$
Geometry Function
$G (l, v) = G^{'} (l) G^{'} (v)$
$G^{'} (x) = \frac{n \cdot x}{( n \cdot x ) ( 1 - β ) + β}$
$β = (\frac{roughness + 1}{2})^{2}$
Fresnel Function
$F (l, h) = F_{0} + (1 - F_{0}) (1 - l \cdot h)$

Generating Normals

Lapaceing Smoothing

Global Laplacian Smoothing

Mesh Simplification

Subdivision Surfaces

The Catmull-Clark Subdivision Scheme

Mesh

A Mesh with no border is called a closed Mesh
No dangiling Edges

Homeomorphism
topology equivalent

Two-Manifolds
A surface is called two-manifold if for each point on the surface there is an open ball such that the intersection of the ball and the surface is topologically equivlent to a two-dimensional disc.

Polyhedron