Course content (32 lessons)

1. Unit I: Overview - Foundations of Computer Graphics — Welcome to Unit I Unit I lays the bedrock of Computer Graphics. We begin with what graphics actually means to a computer (a grid of pixels driven by mathematics) and then progress…
2. 1.1 Introduction, Applications and Interactive Framework — What Computer Graphics Is Computer Graphics (CG) is the synthesis and manipulation of visual content using a computer. Unlike image processing, which starts from an image, CG…
3. 1.2 Raster vs Random Scan and Display Characteristics — Two Families of CRT-Era Displays Although flat panels dominate today, the conceptual distinction between raster and random (vector / calligraphic) scan still shapes how we think…
4. 1.3 Aliasing and Antialiasing Techniques — Why Lines Have Stairs A digital display can only set a finite grid of samples. Mathematical objects (lines, curves) are continuous. Sampling a continuous signal below the Nyquist…
5. 1.4 Modern Display Technology - LED, OLED, Curved — From CRT to Self-Emissive Pixels Display technology has evolved through CRT - LCD - LED-backlit LCD - OLED - microLED, with curved variants of each. Each generation trades cost,…
6. 1.5 DDA Line Drawing Algorithm — Goal Given two integer endpoints (x1,y1) and (x2,y2), light up the pixels that best approximate the straight line segment between them. Idea DDA = Digital Differential Analyzer.…
7. 1.6 Bresenham Line Drawing Algorithm — Goal Draw a line using only integer arithmetic by maintaining a decision variable that tells us, after each step in the major axis, whether to also step in the minor axis.…
8. 1.7 Bresenham / Midpoint Circle Algorithm — Goal Scan-convert a circle of radius r centered at origin (later translated) using only integer arithmetic, exploiting 8-way symmetry . 8-Way Symmetry For a pixel (x, y) on the…
9. Unit II: Overview - Clipping and Transformations — What This Unit Covers Unit II is the algebra of moving, sizing, and trimming geometry. We meet clipping (deciding what to keep when geometry leaves the visible window), 2D…
10. 2.1 Cohen-Sutherland Line Clipping — Problem Given a rectangular clip window and a line segment, output the part of the line inside the window (or nothing if it lies entirely outside). Region Codes (Outcodes) Divide…
11. 2.2 Cyrus-Beck Parametric Line Clipping — Why Another Clipper Cohen-Sutherland is restricted to axis-aligned rectangles. Cyrus-Beck clips a line against any convex polygon (including the rectangular window) by working in…
12. 2.3 Sutherland-Hodgman Polygon Clipping — From Lines to Polygons Clipping a polygon is harder than clipping a line because the result must remain a closed polygon, possibly with new vertices on the clip boundary.…
13. 2.4 Basic 2D Transformations — Five Building Blocks Translation, Rotation, Scaling, Reflection, Shearing. Each maps a point (x, y) to a new point (x', y'). Translation x' = x + tx, y' = y + ty. Moves geometry…
14. 2.5 Homogeneous Coordinates and Matrix Form — The Trick In ordinary 2D, translation is x' = x + tx, which is not linear in (x, y), so we cannot write it as a 2x2 matrix multiplication. In homogeneous coordinates we represent…
15. 2.6 Composition of 2D Transformations — Order Matters Matrix multiplication is associative but not commutative in general. Translating then rotating is different from rotating then translating. Composition Rule…
16. 2.7 Window-to-Viewport Transformation — Two Coordinate Spaces World window : a rectangle in world coordinates that we want to display, with bounds [xw min, xw max] x [yw min, yw max]. Viewport : a rectangle on the…
17. 2.8 3D Transformation Matrices (Forms) — Step Up to 4x4 3D points become (x, y, z, 1) and transformations are 4x4 matrices in homogeneous coordinates. Translation T(tx, ty, tz) [ 1 0 0 tx ] [ 0 1 0 ty ] [ 0 0 1 tz ] [ 0…
18. Unit III: Overview - Surfaces, Curves and Shading — Where We Are Unit III leaves flat 2D and dives into how 3D shapes are represented and shaded . Real surfaces are curved; computers prefer flat triangles. The art is in choosing…
19. 3.1 Polygon Meshes and Mesh Representations — What Is a Mesh A polygon mesh is a finite set of vertices, edges, and faces that approximates the surface of an object. Triangles dominate today because GPUs are optimized for…
20. 3.2 Parametric Cubic Curves and Continuity — Cubic Form A parametric cubic curve segment is P(u) = a + b u + c u^2 + d u^3, u in [0, 1], where a, b, c, d are 3D vectors. With four vector coefficients we have 12 scalar…
21. 3.3 Hermite Curves — Defining Data A Hermite cubic segment is defined by: Two endpoints P0 and P1 . Two tangent vectors R0 at P0 and R1 at P1. This is intuitive: "where it starts, where it ends, how…
22. 3.4 Bezier Curves and de Casteljau — Defining Data A degree-n Bezier curve is defined by n+1 control points P0, P1, ..., Pn: P(u) = sum over i=0..n of B (i,n)(u) P i, u in [0, 1], where B (i,n)(u) = C(n, i) u^i…
23. 3.5 B-Spline Curves — Why B-Splines Bezier curves of degree n are global: moving one control point changes the entire curve. B-Splines decouple degree from number of control points and provide local…
24. 3.6 Illumination Model - Ambient, Diffuse, Specular — What Is Illumination An illumination model computes the color of a point on a surface based on light sources, the surface material, and the viewing direction. The classical model,…
25. 3.7 Gouraud and Phong Shading — Two Strategies on a Triangle Mesh Both shading methods use the same illumination equation; they differ in where they evaluate it: at vertices then interpolate the color (Gouraud),…
26. Unit IV: Overview - 3D Viewing, Projections, Hidden Surfaces — From 3D Models to 2D Pictures Unit IV closes the course: how do we view a 3D scene on a 2D display? We classify projections, derive their matrices, and remove hidden surfaces so…
27. 4.1 3D Object Representation and Projection Overview — Representing 3D Objects Common 3D representations: 1. Polygon Meshes - dominant for real-time (Unit III). 2. Sweep Representations - rotate or translate a 2D shape (lathe /…
28. 4.2 Parallel Projections - Orthographic and Axonometric — Orthographic Projectors are perpendicular to the view plane. No foreshortening along axes parallel to the plane. Multiview Views generated by projecting along the principal axes:…
29. 4.3 Oblique Projections - Cavalier and Cabinet — Definition An oblique projection is a parallel projection where the projectors are not perpendicular to the view plane. Faces parallel to the view plane keep their true size and…
30. 4.4 Perspective Projection - 1, 2, 3 Point — How Perspective Works Perspective projection mirrors how lenses (and eyes) work: parallel lines that recede from the viewer converge at one or more vanishing points on the…
31. 4.5 Hidden Surface Removal - Z-Buffer — Why Hidden Surface Removal Multiple polygons may project onto the same pixel; the closest one to the viewer wins. The z-buffer algorithm (Catmull, 1974) is the most common…
32. 4.6 Painter Algorithm and Comparison — Idea Paint farther polygons first, closer polygons over them - exactly how an oil painter layers brush strokes (background sky first, foreground figures last). Sort polygons by…

Unit I: Overview - Foundations of Computer Graphics

Welcome to Unit I

Unit I lays the bedrock of Computer Graphics. We begin with what graphics actually means to a computer (a grid of pixels driven by mathematics) and then progress through display hardware, sampling artifacts, and the very first algorithms that turn ideal mathematical primitives like lines and circles into a finite array of glowing dots.

Why Computer Graphics?

Computer graphics is the discipline of generating images from models. It powers GUIs, CAD/CAM, scientific visualization, gaming, AR/VR, medical imaging, simulators, animation, and data dashboards. A single GPU today schedules billions of fragment operations per second, but the algorithmic core - turning shapes into pixels - was largely settled between 1965 and 1985, and it is exactly that core that this unit teaches.

Learning Objectives

• Distinguish interactive vs non-interactive graphics and describe the conceptual framework (application model, application program, graphics system, display, user).
• Compare raster and random scan displays.
• Define resolution, refresh rate, persistence, aspect ratio, and color depth.
• Explain why aliasing occurs and how supersampling, area sampling, prefiltering, and postfiltering reduce it.
• Describe LED, OLED, and curved LED panels.
• Derive and trace DDA, Bresenham line, and midpoint circle algorithms.

What You Will Build Mentally

By the end of Unit I you should be able to look at a slanted line on screen and answer: which pixels lit up, why those, and how the staircase could be smoothed.

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Frequently asked questions

Is the Computer Graphics course really free?

Yes. The entire Computer Graphics course on Siksha Sarovar is free to read with no account required. You can optionally sign in with Google to save your progress.

Do I get a certificate for Computer Graphics?

Yes — finish the lessons and pass the quiz to earn a free, verifiable certificate you can share on LinkedIn or with recruiters.

Can I run code while learning?

Yes. The built-in online compiler runs C, C++, Python, Java, PHP, JavaScript, C# and SQL directly in your browser — no installation needed.