Expert-level computer graphics covering the rendering pipeline, rasterization, ray tracing, shaders, transformations, lighting models, and GPU programming.
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Vertex processing: transform 3D positions to clip space. Primitive assembly: group vertices into triangles. Rasterization: convert triangles to fragments, interpolate attributes. Fragment processing: compute color per fragment, depth test. Output merger: blend fragments, write to framebuffer.
Model matrix: object space to world space. View matrix: world space to camera space. Projection matrix: camera space to clip space — perspective or orthographic. MVP matrix: Model x View x Projection applied to each vertex. Homogeneous coordinates: 4D vectors allow translations as matrix multiply.
Phong model: ambient + diffuse + specular components. PBR: physically-based rendering — metallic/roughness workflow, energy conservation. Lambertian diffuse: max(dot(N,L), 0) * diffuse_color. Shadow mapping: render depth from light, compare in main pass. Global illumination: ambient occlusion, SSAO, ray-traced GI.
Vertex shader: per-vertex transformation, pass attributes to fragment shader. Fragment shader: per-pixel color computation. Geometry shader: per-primitive processing, can generate new geometry. Compute shader: general GPU computation, not part of fixed pipeline.
Ray casting: shoot ray from camera through each pixel. Intersection tests: ray-sphere, ray-triangle, ray-AABB. BVH: bounding volume hierarchy accelerates intersection queries. Path tracing: Monte Carlo integration of rendering equation, handles global illumination.
| Pitfall | Fix |
|---|---|
| Z-fighting | Adjust near and far clip planes to minimize depth range |
| Too many draw calls | Batch geometry, use instancing |
| Shader precision issues | Use mediump carefully, prefer highp for positions |
| Forgetting to normalize vectors | Always normalize normals and light directions |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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