Computer Graphics and Animation
Semester VI · BCA 351 · 3 credits
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chapters done
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The syllabus asks for
- Applications and areas
- Display devices
- The frame buffer and its arithmetic
- The graphics pipeline and the GPU
- Seeing the ideas: pixels, tubes, tables and the pipeline
Key points
- Graphics covers modelling, rendering, animation and image processing; applications range from CAD to games to maps.
- Raster displays store every pixel and give filled colour images with aliasing; vector displays store lines and scale perfectly.
- Frame-buffer size = width × height × bits ÷ 8: 1920 × 1080 × 24 bits needs 62,20,800 bytes and about 373.2 MB/s at 60 Hz.
- A look-up table trades colour range for memory; double buffering prevents flicker.
- The pipeline runs from modelling through viewing, projection, clipping and rasterisation to display, and GPUs execute it in parallel.
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The syllabus asks for
- Requirements for line drawing
- The DDA algorithm
- Bresenham's line algorithm
- The midpoint circle algorithm
- The midpoint ellipse algorithm
- Filling areas
- Seeing the ideas: pixel grids, decisions and symmetry
Key points
- Scan conversion picks pixels for primitives; step along the major axis and update an error term.
- DDA: steps = max(|Δx|, |Δy|), increments Δ/steps, round at each step; Bresenham uses p₀ = 2Δy − Δx and integer updates 2Δy or 2(Δy − Δx).
- Midpoint circle: p₀ = 1 − r, update by 2x + 1 (inside) or 2(x − y) + 1 (outside) with eight-way symmetry; midpoint ellipse uses two regions with four-way symmetry.
- Scan-line fill uses the odd–even rule; boundary and flood fill spread from a seed; antialiasing uses supersampling or coverage.
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The syllabus asks for
- Points, vectors and homogeneous coordinates
- The basic transformations
- Transforming an object
- Composite transformations
- Coordinate systems and the window-to-viewport transformation
- Seeing the ideas: moving shapes, order and the viewport
Key points
- Homogeneous coordinates (x, y, 1) turn translation into matrix multiplication; sequences collapse into one matrix applied right to left.
- Translation, scaling, rotation, reflection and shear have standard 3 × 3 matrices; rotation matrices are orthogonal with determinant 1.
- Order matters: translate-then-rotate differs from rotate-then-translate.
- Rotation or scaling about a point is T(p) · R or S · T(−p).
- Window-to-viewport mapping scales and shifts with sx and sy; unequal factors distort.
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The syllabus asks for
- The clipping problem
- The Cohen–Sutherland line-clipping algorithm
- The Liang–Barsky algorithm
- Polygon clipping: Sutherland–Hodgman
- Seeing the ideas: region codes, parameters and polygon clipping
Key points
- Clipping discards geometry outside the window; efficient algorithms accept or reject trivially before computing intersections.
- Cohen–Sutherland: a 4-bit outcode per endpoint; OR = 0 accepts, AND ≠ 0 rejects; otherwise cut at one boundary and repeat.
- Liang–Barsky: pₖt ≤ qₖ; t₀ = max of entering r, t₁ = min of leaving r; at most two intersections.
- Sutherland–Hodgman clips a polygon against each boundary in turn with four in/out cases; concave polygons need Weiler–Atherton.
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The syllabus asks for
- Three-dimensional homogeneous transformations
- Projection
- Viewing
- Back-face detection
- Seeing the ideas: axes, perspective, frustum and culling
Key points
- 3D transformations are 4 × 4 matrices; rotations about x, y, z are orthogonal matrices with determinant 1; order of composition matters.
- Orthographic projection drops z; perspective projection divides by depth: x′ = x·d/z, y′ = y·d/z, via a matrix and a perspective divide.
- Perspective causes foreshortening and vanishing points; parallel projection preserves parallel lines and sizes.
- Viewing needs an eye, a look-at point and an up vector, a view volume (frustum) and a pipeline ending in the viewport transform.
- Back-face culling tests N · V > 0 using the polygon normal.
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The syllabus asks for
- Hidden-surface removal
- Illumination models
- Surface shading methods
- Beyond local shading
- Seeing the ideas: depth buffers, vectors, highlights and shading
Key points
- The Z-buffer keeps the nearest depth per pixel and works for any surface; painter's algorithm sorts and overwrites; back-face culling removes rear faces.
- The Phong model is ambient + diffuse (N · L) + specular (R · V)ⁿ; Blinn–Phong uses N · H.
- Flat shading uses one intensity per polygon, Gouraud interpolates vertex intensities, Phong interpolates normals and lights every pixel.
- Gouraud shading can miss a highlight inside a polygon; Phong shading captures it.
- Textures, shadow maps, alpha blending and ray tracing add realism.
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The syllabus asks for
- Representing curves
- Bézier curves
- B-spline curves
- Surfaces and 3D models
- Computer animation
- Seeing the ideas: curves, continuity, easing and morphing
Key points
- Parametric curves with control points give designers local, predictable shape control; continuity is described as C⁰, C¹, C².
- Bézier curves use Bernstein weights, pass through the end points, lie in the convex hull and are evaluated by de Casteljau subdivision; the cubic B-spline gives C² continuity and local control but does not pass through the end points.
- 3D shapes are polygon meshes, patches, subdivision surfaces, CSG or procedural models.
- Animation uses keyframes and interpolation; easing (smoothstep 3t² − 2t³) replaces robotic constant speed; morphing interpolates corresponding vertices.
- A 90-second 24 fps full-HD clip is 2,160 frames and 13.44 GB uncompressed.
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The paper
TU assessment: 60% final examination set by the university, 40% internal (assignments, lab work, attendance). Confirm the split in your college's notice.
Where the hours go
Teaching hours are the board's guide to how much of the paper each part carries.
- Unit 2 · Scan Conversion - Lines, Circles, Ellipses and Area Filling8 h
- Unit 3 · Two-Dimensional Transformations and Viewing7 h
- Unit 5 · Three-Dimensional Transformations, Projection and Viewing7 h
- Unit 6 · Visible Surfaces, Illumination and Shading7 h
- Unit 4 · Clipping6 h
- Unit 1 · Introduction and Graphics Hardware5 h
- Unit 7 · Curves, Surfaces and Computer Animation5 h