Computer Graphics Lecture (English)

2025/26 fall

First half:

Requirements

Prerequisites: Basic mathematics (linear algebra!).

Attendance is mandatory for everyone by default.

• 1st half-exam (1-6 presentations): 7-9th week of semester
• 2nd half-exam (7-12 presentations): 1st or 2nd week in exam period

The lecture grade is derived from two written half-exams:

Retake exam opportunities (from all presentations 1-12!!) will be available

Each exam is 90 minute written exam where 50% of the exercises need actual (hand-)calculations and 50% are theoretical questions.The exact dates will be sent out via Neptun emails and Canvas announcements.

Grading

On both part-exams, 32-32 points can be obtained, on each, 15 points are needed to pass. If both are passed, then the grading limits are as follows:

Grade	Points (/64)	Min %
2	32 –	50%
3	38 –	60%
4	46 –	72%
5	54 – 64	85%

Curriculum

First part

• Human vision, properties of light.
• Display devices. Color representation on the computer.
• Coordinate systems (Cartesian, polar, spherical, barycentric, homogeneous).
• Affine transformations
• Projective transformations.
• Curve representations: line, segment, parabola, circle, ellipse
• Surfaces: plane, sphere, ellipsoid, paraboloid
• Raycasting, raytracing fundamentals. Calculating ray directions when casting from the camera. Ray intersections: with plane, triangle, polygon, spheres, and AAB. Ray intersection with transformed objects.
• Ray tracing: coherent and incoherent rays. Simplified rendering equation. Optimizing ray intersections: Bounding volumes, intersection with convex polyhedron, hierarchical bounding volumes, space subdivisions.
  • Note: Calculating exercises about ray-surface intersections belong to the second part, but the theory is also needed for the first part.

Second part

• Stages of the graphics pipeline (incremental image synthesis). Pipeline on the GPU.
• Local illumination: shading (constant, Phong, Gouraud).
• Culling: Point- and segment culling. Culling polygons.
• Rasterization: line rasterization, optimizations. Bresenhem algorithm. Triangle filling.
• Light sources: ambient light, directional, omni, and spotlight.
• Light-reflecting models: diffuse surfaces, reflection, refraction. BRDF.
• Texturing: texture mapping and methods, triangle parameterization, general surface parameterization. Perspective-corrected texturing. Texture filtering, mipmap.
• Special textures: procedural, non-color textures.
• Storing geometry and topology: index buffers, winged edge, and half-edge data structures.
• Line strips, splines, subdivision curves.
• Bézier curves, de Casteljau algorithm.
• Surface representations. Bilinear and Bezier surfaces. Subdivision surfaces: Doo-Sabin, Catmull-Clark.
• Animation types and methods. Animating camera and objects, including position and orientation.
• Animation with formulas. Keyframe animation, interpolation. Trajectory animation.
• Hierarchical systems: Kinematics, inverse kinematics.