CG SET key terms

A triple of weights that expresses a point inside a triangle as a weighted average of its three vertices, summing to one. Rasterizers use them to interpolate attributes such as depth, color, normals, and texture coordinates across a triangle's surface.

A representation that adds an extra coordinate w to a point or vector so that translation, rotation, scaling, and perspective projection all become matrix multiplications in four dimensions. Dividing by w after transformation yields the projected 2D or 3D position.

A transformation that maps 3D points to a view plane so distant objects appear smaller, dividing by a depth-dependent factor. It preserves straight lines but not lengths or angles, and it produces the characteristic vanishing-point convergence of real cameras and eyes.

The matrix that repositions and reorients the scene so the camera sits at the origin looking down a chosen axis. It converts world-space coordinates into eye or camera space, simplifying projection and lighting computations downstream.

A surface described by a function that returns zero on the surface, such as ax+by+cz+d=0 for a plane. Implicit forms make inside/outside tests and ray intersections cheap, which is why they are common in intersection routines and clipping.

A unit vector perpendicular to a surface at a point, used to compute how light reflects and shades. Normals may be geometric (from the polygon) or interpolated per vertex, and their orientation must be consistent to avoid lighting artifacts.

The test that finds whether a ray hits a triangle and where, typically using Moller-Trumbore or a plane-plus-barycentric approach. It is the innermost loop of ray tracing and must be fast and numerically robust against grazing hits and edge cases.

The process of converting vector primitives, mainly triangles, into fragments covering pixels. It determines which pixels a primitive touches and their coverage, forming the bridge between geometry processing and per-pixel shading in the real-time pipeline.

A per-pixel array storing the nearest depth written so far, used to resolve visibility by discarding fragments behind existing ones. Depth precision is limited by the projection and buffer format, causing z-fighting when surfaces are nearly coplanar.

Cutting primitives against view frustum or user-defined planes so only visible portions proceed to rasterization. Clipping in homogeneous space avoids division by zero and handles geometry crossing behind the camera correctly.

Discarding triangles whose winding indicates they face away from the camera, based on signed screen-space area. It roughly halves the primitives processed for closed meshes but requires consistent winding and correct handling of mirrored transforms.

Interpolating vertex attributes divided by w and then dividing by the interpolated reciprocal w, so texture coordinates and colors vary correctly with depth. Naive linear screen-space interpolation causes visible warping on surfaces viewed at an angle.

Techniques that reduce jagged edges by averaging multiple samples or coverage per pixel. Common forms include supersampling, multisampling, and post-process methods such as FXAA, trading memory and bandwidth for smoother silhouettes and reduced temporal shimmer.

A pipeline that first renders geometry into a G-buffer of surface attributes, then shades pixels in a second pass. It avoids redundant lighting for overdrawn fragments but complicates transparency and requires large memory bandwidth.

A function describing how much light arriving from one direction is reflected toward another for a given surface point. Physically based BRDFs obey reciprocity and energy conservation, and their form determines whether a material looks matte or glossy.

An integral equation stating that outgoing radiance equals emitted radiance plus the integral of incoming radiance times the BRDF over the hemisphere. It is the theoretical foundation of global illumination algorithms such as path tracing and radiosity.

Estimating an integral by averaging randomly sampled function values. In rendering it evaluates the light transport integral, converging slowly as the inverse square root of sample count, so variance reduction and many samples are needed for clean images.

A global illumination algorithm that traces random light paths from the camera, bouncing at surfaces according to the BRDF, and averages their contributions. It captures soft shadows, color bleeding, and caustics but is noisy at low sample counts.

The tendency of surfaces to reflect more light at grazing angles than head-on, described by the Fresnel equations and approximated by Schlick's formula. It explains strong reflections at silhouette edges on water, glass, and polished materials.

A reflectance model treating a surface as many tiny mirrors with a statistical distribution of orientations, plus shadowing and masking terms. It produces realistic highlights whose width and intensity depend on roughness.

An approximation of how much nearby geometry blocks ambient light at a point, darkening creases and contact areas. It is often computed from depth or precomputed per vertex and multiplied into indirect lighting for a grounded look.

Lighting that accounts for light bouncing between surfaces, not just direct illumination from sources. It produces indirect shadows, color bleeding, and softer contrast, and is approximated in real time by probes, screen-space effects, or baked lightmaps.

Selecting and blending texels to compute a color for a sample that falls between texel centers. Nearest, bilinear, and trilinear or anisotropic filtering trade sharpness and cost, and poor filtering causes blockiness or shimmer under motion.

Precomputing a pyramid of progressively downsampled texture levels and choosing a level based on screen-space footprint. It reduces aliasing and cache misses for distant or oblique surfaces but can blur detail and causes seams without trilinear blending.

Texture filtering that takes multiple samples along the direction of a surface's compressed footprint, improving clarity on floors and roads viewed at grazing angles. It costs more bandwidth than isotropic mipmap filtering but greatly reduces blur.

Assigning two-dimensional texture coordinates to mesh vertices so a 2D image can be painted onto a 3D surface. Good unwraps limit stretching and seams, and coordinates may be wrapped, clamped, or mirrored by the sampler.

Perturbing shading normals using values stored in a texture, faking small-scale bumps without extra geometry. Tangent-space encoding requires a consistent tangent basis, and incorrect tangents cause lighting to look skewed.

A parametric curve defined by control points and Bernstein basis polynomials, always passing through its endpoints and lying within the convex hull of its controls. Cubic Bezier segments are chained to form smooth paths and font outlines.

A piecewise polynomial curve whose shape is controlled by control points and a knot vector, offering local control and adjustable continuity. Unlike Bezier curves, control points generally do not lie on the curve, and uniform or nonuniform knots change its behavior.

Non-uniform rational B-splines: B-spline curves or surfaces with weights on control points, allowing exact representation of circles, ellipses, and other conics. They are standard in CAD and modeling tools for smooth, precise shapes.

A smooth surface generated by repeatedly refining a coarse control mesh with rules such as Catmull-Clark. It gives artists simple low-poly cages that yield smooth, watertight surfaces, widely used in character and product modeling.

The connectivity of vertices, edges, and faces in a polygonal model, including valence and genus. Good topology supports deformation, subdivision, and efficient rendering; non-manifold or n-gon-heavy meshes cause artifacts and pipeline problems.

Representing orientation with a four-component unit quaternion that avoids gimbal lock and interpolates smoothly via slerp. It is preferred over Euler angles for animation and camera control, though it is less intuitive to author directly.

Driving a mesh by a hierarchy of bones whose transforms deform vertices through skin weights. It enables efficient articulated motion, but poor weights cause collapsing joints, and blending multiple clips requires careful normalization.

Generating in-between values from sparse authored keys using linear, spline, or stepped curves. Easing and tangent control shape motion timing, and interpolation choices strongly affect whether animation feels mechanical or natural.

A numerical scheme updating particle positions from current and previous positions plus acceleration, without storing explicit velocity. It is simple and stable for cloth, ropes, and soft bodies, though it handles damping and constraints approximately.

Finding whether and where moving objects intersect, usually split into a broad phase using bounding volumes and a narrow phase using exact tests. Correct response also needs penetration depth and contact normals to resolve overlap believably.

The ordered hardware and software steps from vertex input through vertex shading, primitive assembly, rasterization, and fragment shading to output merging. Knowing each stage's inputs, outputs, and fixed versus programmable parts is essential for debugging and performance work.

A program run on the GPU for stages such as vertex, fragment, geometry, or compute work. Shaders define per-vertex transforms and per-pixel lighting, and their cost, branching, and memory access patterns dominate real-time performance.

A command submitting geometry to the GPU, with per-call CPU overhead that can bottleneck rendering. Batching or instancing merges many objects into fewer submissions, and excessive draw calls are a classic cause of low frame rates.

A data structure such as a bounding volume hierarchy or grid that prunes empty space so ray or collision queries avoid testing every primitive. Build quality and traversal order strongly affect ray tracing and broad-phase performance.

Converting between linear light values used in shading math and nonlinear encoded values stored in images and sent to displays. Skipping it makes lighting look wrong, blending darkens edges, and gradients band or appear muddy.

A defined system for representing colors numerically, such as sRGB, linear RGB, or CIELAB, each with its own primaries, white point, and transfer function. Mismatched spaces cause washed-out or oversaturated results when textures meet lighting.

Compressing high dynamic range radiance into a displayable range while preserving apparent contrast and color. Operators range from simple Reinhard curves to filmic and ACES-style mappings, and they strongly shape the final look of rendered images.

The color quality of light independent of its brightness, often plotted as coordinates on a diagram derived from tristimulus values. It lets engineers specify primaries and white points precisely when defining a display or color space.

Designing visuals and interfaces usable by people with color vision deficiency, low vision, or motion sensitivity. Practices include sufficient contrast, non-color cues, scalable text, and motion-reduction options, and they are an ethical and often legal expectation.

The legal terms governing reuse of models, textures, fonts, and code, including attribution, redistribution, and commercial-use limits. Violating licenses exposes projects to takedowns and liability, so provenance should be tracked from acquisition.

Designing instruction so learning objectives, teaching activities, and assessment tasks all target the same measurable outcomes. In graphics courses it means grading what students practiced, such as shading math or pipeline debugging, rather than unrelated recall.

Low-stakes checks during learning, such as in-class exercises, critiques, or auto-graded shader tasks, used to guide improvement before final grading. It gives instructors evidence of misconceptions while feedback can still change student work.