CG SET study plan

Derive and use the 4x4 affine transform matrices for translation, rotation, and non-uniform scale, then multiply them in both row-vector and column-vector conventions and verify that the results agree.

Compute a 3D rotation about an arbitrary unit axis with Rodrigues' formula and confirm it against the quaternion sandwich product on at least three test vectors.

Convert between model, view, and clip space by hand for two sample points, including the perspective divide, and state which coordinate is lost at each stage.

Classify handedness, winding order, and normal direction conventions, then predict the sign of a face normal for eight given triangle vertex orderings.

Solve five line-plane and ray-triangle intersection problems analytically, including the barycentric coordinates of each hit point.

Trace a single triangle through the full fixed-function pipeline stages and write down the input and output data of each stage.

Implement or hand-simulate a scanline or barycentric triangle rasterizer on a 6x6 pixel grid, listing every covered pixel and its interpolated depth.

Apply the z-buffer and painter's algorithm to the same overlapping scene and identify a configuration where the painter's algorithm fails.

Derive the perspective-correct interpolation of a per-vertex attribute and compare it with naive screen-space linear interpolation on a foreshortened quad.

Explain and compute the effect of backface culling, clipping against the near plane, and viewport mapping on a given set of vertices.

Compare Lambert, Phong, and Blinn-Phong specular models by computing shading values at five angles and identifying where each model diverges.

Set up and solve the rendering equation for a simple direct-lighting case, and state clearly which terms are approximated in real-time shading.

Derive the Monte Carlo estimator and show why dividing by the probability density function yields an unbiased estimate, using a cosine-weighted hemisphere example.

Contrast path tracing, photon mapping, and radiosity in terms of transport handled, bias, and variance, and match each to a scene type where it is preferred.

Compute a form factor or ambient occlusion approximation for a simple corner geometry and interpret the result physically.

Implement or hand-compute bilinear, trilinear, and anisotropic filtering on a small mip chain and compare the resulting color for a steeply angled surface.

Explain UV mapping, wrapping modes, and texture atlas bleeding, and propose a concrete fix for seam artifacts.

Evaluate a Bezier curve with de Casteljau's algorithm at four parameter values and verify the result with the Bernstein polynomial form.

Derive the first derivative of a cubic B-spline basis and explain C0 versus C1 versus C2 continuity at a knot.

Compare polygon meshes, NURBS, and subdivision surfaces for a character model and a mechanical part, justifying each choice.

Map each programmable pipeline stage (vertex, tessellation, geometry, fragment, compute) to its inputs, outputs, and typical cost.

Explain the role and cost of early-z, deferred versus forward rendering, and MSAA, and choose an approach for a given scene and target frame budget.

Distinguish draw call overhead, state changes, and bandwidth limits, and estimate which one dominates for a described frame.

Describe the memory hierarchy and latency hiding in a GPU, and explain why occupancy and coherence matter for a fragment shader.

Sketch the data flow for a shadow-mapping pass and identify where precision and aliasing problems arise.

Derive and apply the forward kinematics of a two-link arm, then compute the inverse kinematics solution for three target positions.

Explain keyframe interpolation, slerp versus lerp for rotations, and gimbal lock, and demonstrate the failure with a concrete Euler-angle sequence.

Integrate a simple particle system with explicit Euler and semi-implicit Euler, and show how step size changes stability.

Convert between RGB, linear RGB, and CIE XYZ for three sample colors, and explain why shading must happen in linear space.

Compare sRGB, Rec.709, and Display P3 gamuts and explain gamma correction, tone mapping, and perceptual uniformity (CIELAB) with numeric examples.

Re-derive the key formulas from weeks 1 and 3 from memory and check them against the week 1 formula sheet.

Solve 20 mixed problems combining transforms, intersection tests, shading models, and sampling under timed conditions.

Diagnose and correct the three most common errors in your earlier worked sets, documenting the root cause of each.

Explain the rendering equation and the Monte Carlo estimator aloud in under five minutes without notes.

Apply a structured ethical decision framework to three scenarios involving asset licensing, attribution, and generative content.

Outline a 50-minute lesson on rasterization for undergraduates, including learning objectives, an activity, and an assessment item.

Build a two-page condensed review sheet covering all nine domains, with at least three formulas per heavy domain.

Take one full-length timed practice run and record per-domain accuracy to target final review.