Computer graphics topics are algorithmic and diagram-heavy. PSC questions may ask raster scan, DDA/Bresenham line algorithm, circle drawing, 2D transformations, homogeneous coordinates, clipping, viewing pipeline, projection and rendering concepts.

Concept Teaching

Graphics pipeline converts mathematical objects into pixels. Modeling defines objects, transformations place them, viewing and projection map them to screen, clipping removes invisible parts, rasterization fills pixels, and rendering/shading makes the image visually meaningful.

Raster Algorithms

Raster algorithms decide which pixels approximate ideal geometry.

• DDA line algorithm uses incremental slope calculation.
• Bresenham line algorithm uses integer decision parameter.
• Midpoint circle algorithm uses symmetry and decision parameter.
• Scan conversion turns geometric primitives into pixels.
• Aliasing creates jagged edges; anti-aliasing reduces visual artifacts.

2D and 3D Transformations

Transformations are usually represented by matrices.

Viewing, Clipping and Projection

Viewing pipeline maps world coordinates to display.

• Window selects world-coordinate region.
• Viewport selects screen region.
• Clipping removes primitives outside window/view volume.
• Orthographic projection preserves parallel lines.
• Perspective projection creates depth realism with convergence.
• Hidden surface removal decides visible surfaces.

Rendering and Shading

Rendering models light-object-camera interaction.

• Ambient, diffuse and specular components model lighting.
• Flat shading uses one normal per polygon.
• Gouraud shading interpolates vertex intensities.
• Phong shading interpolates normals for smoother highlights.
• Z-buffer stores nearest depth per pixel.
• Ray tracing simulates rays for reflection/shadow realism.

Engineering Mechanism

• Define object geometry.
• Apply modeling transformation.
• Transform to viewing coordinates.
• Clip against window/view volume.
• Project to 2D screen.
• Rasterize primitives into pixels.
• Shade/render using light/material/depth.

Diagrams / Models To Draw

• Draw graphics pipeline.
• Draw DDA/Bresenham line pixel selection.
• Draw 2D transformation matrix flow.
• Draw window-to-viewport mapping.
• Draw perspective vs orthographic projection.
• Draw Z-buffer concept.

Formulas, Algorithms and Rules

• 2D translation matrix uses homogeneous coordinates.
• Rotation: x'=x cos theta – y sin theta; y'=x sin theta + y cos theta.
• Scaling: x'=sx x, y'=sy y.
• Window-to-viewport mapping is linear scaling and translation.
• Perspective projection makes farther objects appear smaller.

Worked Example

A square can be scaled, rotated and translated by multiplying its vertex coordinate vectors with transformation matrices. Order matters: rotate then translate gives a different final position than translate then rotate.

Subjective Answer Pattern

• Define raster graphics.
• Explain raster line/circle algorithms.
• Describe transformations and homogeneous coordinates.
• Explain viewing/clipping/projection.
• Discuss rendering/shading and hidden surface removal.

Common Engineering Mistakes

• Ignoring transformation order.
• Confusing clipping with cropping after rendering.
• Saying orthographic gives realistic perspective depth.
• Forgetting homogeneous coordinates for translation matrix.
• Mixing Gouraud and Phong shading.

MCQ Revision

• Which line algorithm uses integer decision parameter?
• What is viewport?
• Which projection has vanishing point?
• What does Z-buffer store?
• What is anti-aliasing?
• Which shading interpolates normals?

Final Summary

• Graphics pipeline turns geometry into pixels.
• Raster algorithms approximate primitives.
• Transformations position objects.
• Projection maps 3D to 2D.
• Rendering adds lighting, shading and visibility.