230-0442/03 – Geometry with Computer (GP)
| Gurantor department | Department of Mathematics | Credits | 5 |
| Subject guarantor | Mgr. Dagmar Dlouhá, Ph.D. | Subject version guarantor | Mgr. Dagmar Dlouhá, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 2 | Semester | summer |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | HGF | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
• to solve planimetric and stereometric tasks with the help of computer
• to know how to characterize geometric curves and surfaces by synthetic and also analytic way
• to acquaint with geometric and physical principles of 3D modeling
Teaching methods
Lectures
Individual consultations
Tutorials
Project work
Other activities
Summary
The course combines geometric and computer disciplines - planimetry, stereometry, analytic geometry, 3D modeling, computer graphics and programming.
In the exercise there is used free software GeoGebra and POV-Ray.
Compulsory literature:
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Credit and test requirements
Conditions for granting credit
- participation in seminars
Term project
- Creating an animated movie of your own using POV-Ray
- the theme is, if possible, a real scene with several objects in a suitable composition
- Up to 2 members can work on one subject
- Creation in POV-Ray environment is evaluated: suitable choice of geometric objects, level of execution of their external appearance, use of set operations CSG, realization of more identical or similar objects by means of programming directives (use of cycles, conditions, etc.), transparency of source code (use of notes), parameterization of objects in the scene (suitable parameter names), resulting animation
- overall: the idea, using as many objects and options as possible, using unexplored objects and options (own initiative)
Exam
- The exam will be divided into two parts and can be completed in one regular and two correction terms
- practical part - defense of semester project
- theoretical question
Scoring
- Practical part of the exam is evaluated by max. 80 points, minimum 25 points are required
- at the theoretical part it is possible to reach max. 20 points, at least it is necessary to have at least 5 points
- The overall rating is based on a standard table
points mark
86-100 1 excellent
66-85 2 very good
51-65 3 well
0-50 4 failed
E-learning
Other requirements
They are no other requests fo students.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Basic geometric objects (point, line, plane), terms and constructions
2. Planimetry - properties and constructions of triangles (altitudes, medians, angles, identity mappings, inscribed circle, add to trapezium), homothety (tangent of two circles, triangle inscribed to square)
3. Conics - derived from right circular conical surface, the definition and construction of an ellipse, a hyperbola and a parabola
4. Kinematic Geometry - elliptical and cadioidical motion, conchoidical and cyclical movements
5. Stereometry - cuts of a cube and other solids
6. Introduction to PovRAY, basic elements of the scene (camera, light, background)
7. Basic solids (sphere, cylinder, cone, cuboid)
8. Colors, textures
9. Transformations (translation, rotation, scaling)
10. Set operations (union, intersection, difference)
11. Creating of a realistic static scene
12. PovRay programming (variables, while loop, mathematical function), Implicit surfaces (BLOB)
13. Creating dynamically generated static scene
14. Animation (clock variables and framenumber, controlling of animated objects trajectories), Realistic animation of static scene
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction