CG SET flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Homogeneous coordinates

Represent points as (x,y,z,1) and directions as (x,y,z,0) in 4D; allows translation, rotation, and perspective projection to be expressed as 4×4 matrix multiplication.

Rodrigues rotation formula

Rotates a vector about unit axis a by angle θ: R = I cosθ + sinθ [a]× + (1−cosθ) aaᵀ, where [a]× is the skew-symmetric cross-product matrix.

Barycentric coordinates

Weights α, β, γ with α+β+γ=1 that express a point as αA+βB+γC; a point lies inside triangle ABC exactly when all three weights are non-negative.

Ray–sphere intersection

Substitute ray o+td into |p−c|²=r² to get a quadratic in t; discriminant below zero means miss, zero means tangent, positive gives two intersections; choose smallest positive t.

Perspective-correct interpolation

Screen-space linear interpolation of attributes divided by w, then divided by interpolated 1/w, recovers correct values under perspective projection and avoids texture warping.

Edge function rasterization

For each pixel, evaluate E(x,y)=(x−x₀)(y₁−y₀)−(y−y₀)(x₁−x₀) for all three triangle edges; consistent signs indicate the pixel center is inside.

Top-left fill rule

Pixels exactly on a shared triangle edge are shaded by only one triangle, chosen by a consistent top-left convention, preventing gaps and double-blending along shared edges.

Early-Z rejection

GPU discards fragments failing the depth test before running the fragment shader; disabled by discard, alpha-to-coverage, or shader depth writes, which require late depth testing.

Blinn–Phong specular model

Specular term k_s (N·H)^n I with half-vector H=normalize(L+V); exponent n controls highlight size, larger n gives tighter, brighter highlights.

Rendering equation

L_o(x,ω_o)=L_e+∫_Ω f_r(x,ω_i,ω_o) L_i(x,ω_i)(n·ω_i)dω_i; outgoing radiance equals emission plus integrated incoming radiance weighted by BRDF and cosine.

Fresnel Schlick approximation

F(θ)≈F₀+(1−F₀)(1−cosθ)⁵ with F₀=((n₁−n₂)/(n₁+n₂))²; reflectance rises toward 1 at grazing angles for all dielectrics.

Cook–Torrance microfacet BRDF

f=F·D·G/(4(n·l)(n·v)); D is the microfacet normal distribution (GGX or Beckmann), G is geometric shadowing-masking, F is Fresnel reflectance.

Russian roulette

Unbiased path termination: continue a path with probability q and divide throughput by q; terminates long paths without introducing bias in the Monte Carlo estimate.

Mipmap level selection

Level L=log₂(max(|du/dx|,|dv/dx|)·textureSize) chosen from screen-space UV derivatives; trilinear filtering blends adjacent levels to reduce minification aliasing.

Normal mapping

Perturbs the shading normal using a tangent-space normal texture: N'=normalize(TBN·n_sample), where TBN columns are tangent, bitangent, and interpolated vertex normal.

sRGB transfer function

Encodes linear color for storage: L≤0.0031308 uses 12.92L, otherwise 1.055L^(1/2.4)−0.055; decode to linear before lighting and re-encode for display.

Separable Gaussian blur

A 2D Gaussian kernel factors into two 1D passes, reducing per-pixel cost from O(n²) to O(2n) while producing identical results for symmetric kernels.

de Casteljau algorithm

Evaluates a Bézier curve by recursively interpolating control points at parameter t; numerically stable and yields the same result as the Bernstein polynomial form.

NURBS curve

Rational B-spline with control-point weights: C(t)=ΣwᵢPᵢNᵢ(t)/ΣwⱼNⱼ(t); exactly represents conics such as circles and ellipses.

Catmull–Clark subdivision

Subdivision surface scheme generalizing cubic B-splines to arbitrary meshes; each step inserts face and edge points and smooths vertices, converging to a C² limit surface.

Euler characteristic

For a closed polyhedron, V−E+F=2; for genus g, V−E+F=2−2g. Used to validate mesh topology and detect holes or handles.

Quaternion slerp

Spherical linear interpolation q(t)=(sin((1−t)Ω)q₀+sin(tΩ)q₁)/sinΩ; interpolates rotations along the shortest arc and avoids gimbal lock.

Gimbal lock

Loss of one rotational degree of freedom when Euler angles align two axes (middle rotation ±90°); avoided by using quaternions or rotation matrices.

Linear blend skinning

Vertex deformation p'=ΣwᵢMᵢp with weights summing to one; simple and fast, but can produce candy-wrapper twisting and volume loss at joints.

Verlet integration

Position update x_{n+1}=2x_n−x_{n−1}+aΔt²; symplectic and stable for cloth and particle systems, deriving velocity implicitly from position differences.

Critical damping

For spring–damper m a=−k x−c v, critical damping occurs at c=2√(km); system returns to equilibrium fastest without oscillation.

Vulkan explicit API

Low-level graphics API exposing command buffers, pipelines, descriptor sets, and memory heaps; the application manages synchronization and resource lifetimes rather than the driver.

Instanced rendering

Draws many copies of a mesh with one draw call, using per-instance attributes (transform, color) fetched by instance index; reduces CPU overhead.

Staging buffer

Host-visible GPU buffer used to upload data to device-local memory; the CPU writes the staging buffer, then a copy command transfers it to VRAM.

CIE XYZ color space

Tristimulus space from integrals X=∫S(λ)x̄(λ)dλ, Y=∫S(λ)ȳ(λ)dλ, Z=∫S(λ)z̄(λ)dλ; Y equals luminance and all visible colors map inside the spectral locus.

sRGB primaries and white

Red (0.64,0.33), green (0.30,0.60), blue (0.15,0.06) chromaticities with D65 white (0.3127,0.3290); defines the standard display gamut triangle.

Delta E color difference

Metric for perceptual color difference; CIE76 is Euclidean distance in L*a*b*. Values below 1 are generally imperceptible, above 5 clearly visible.

Constructive alignment

Instructional design principle that learning outcomes, teaching activities, and assessments share the same action verbs, so assessment directly measures the stated outcome.