1. OPĆE INFORMACIJE

1.1. Nositelj predmeta

Nikol Radović

1.6. Godina studija

I. godina/ II.semestar

1.2. Naziv predmeta

Računalna geometrija 

1.7. Bodovna vrijednost (ECTS)

5 

1.3. Suradnici

-

1.8. Način izvođenja nastave (broj sati P+V+S+e-učenje)

60 (30 P + 30 V (projektanske)) + e - učenje

1.4. Studijski program (preddiplomski, diplomski, integrirani)

preddiplomski

1.9. Očekivani broj studenata na predmetu

90

1.5. Status predmeta

obvezni

1.10. Razina primjene e-učenja (1, 2, 3 razina), postotak izvođenja predmeta on line (maks. 20%)

2 razina

2. OPIS PREDMETA

2.1. Ciljevi predmeta

Cilj predmeta je obnova i nadopunjavanje stečenih vještina i kompetencija srednjoškolske geometrije/ matematike, uporabom programa dinamične geometrije kao alata za crtanje s posebnim naglaskom na primjenu u geodeziji i geoinformatici.

2.2. Uvjeti za upis predmeta i ulazne kompetencije potrebne za predmet

 

2.3. Ishodi učenja na razini programa kojima predmet pridonosi

-    razumjeti matematičke metode i fizikalne zakone koji se primjenjuju u geodeziji i geoinformatici

-    primijeniti znanja matematike i fizike u prepoznavanju, formuliranju i rješavanju inženjerskih zadataka

-    poznavati teorijska načela, postupke računske obrade i vizualizacije podataka geodetskih izmjera

-    upotrebljavati informatičku tehnologiju u rješavanju geodetskih i geoinformatičkih zadataka

-    planirati nastavak akademskog obrazovanja u području geodezije i geoinformatike ili srodnih disciplina, te razviti kulturu cjelo životnog i stručnog obrazovanja

2.4. Očekivani ishodi učenja na razini predmeta (4-10 ishoda učenja)

-    znanje i razumijevanje temeljnih geometrijskih koncepata, principa, teorija i rezultata

-    riješiti konstruktivni zadatak primjenom različitih metoda (transformacije ravnine, mjesta točaka, iteracije, . . . )

-    konstruirati geometrijsku figuru animacijom

-    definirati i konstruirati krivulje 2 . i višeg reda animacijom s posebnim naglaskom na krivulje primjenjive u geodeziji i geoinformatici

-    usvojiti osnovne geometrijskog (matematičkog) modeliranja i primjenjivati ih

-    sposobnost formuliranja problema geodezije geometrijskim (matematičkim) jezikom te njihova analiza i rješavanje

-    demonstrirati vještine geometrijskog zaključivanja

2.5. Sadržaj predmeta detaljno razrađen prema satnici nastave

 

Sadržaj predavanja: Kratka povijest Računalne geometrije (1 sat). Transformacije ravnine (definicija i svojstva) (3 sata). Rješavanje konstruktvinih zadataka metodama transformacije ravnine (4 sata). Rješavanje konstruktivnih zadataka metodom geometrijskog mjesta točaka (4 sata). Kompozicija transformacija ravnine i grupe simetrija (4 sata). Osnovni pojmovi teorije kaosa, fraktalne geometrije i metode iteracije (2 sata). Animacija kao temelj računalne grafike, nekad i danas . Prikaz geometrijskih figura animacijom (4 sata). Vizualizacija projektivne ravnine. Prikaz krivulja 2. i višeg stupnja animacijom (4 sata). Matematičko/ geometrijsko modeliranje (2 sata) Neeuklidska geometrija (2 sata).

2.6. Vrste izvođenja nastave:

 predavanja

 seminari i radionice

 vježbe

 on line u cijelosti

 mješovito e-učenje

 terenska nastava

 samostalni zadaci

 multimedija i mreža

 laboratorij

 mentorski rad

       (ostalo upisati)

2.7. Komentari:

     

2.8. Obveze studenata

- nazočnost na više od 80 % vježbi i predavanja.

- za potpis iz predmeta potrebno je predati (točne) domaće zadaće na vrijeme i položiti 1. kolokvij /teoretski/.

2.9. Praćenje rada studenata (upisati udio u ECTS bodovima za svaku aktivnost tako da ukupni broj ECTS bodova odgovara bodovnoj vrijednosti predmeta):

Pohađanje nastave

0.5

Istraživanje

 

Praktični rad

 

Eksperimentalni rad

 

Referat

 

Domaće zadaće

1

Esej

 

Seminarski rad

 

      (Ostalo upisati)

 

Kolokviji

1.2

Usmeni ispit

1.2

      (Ostalo upisati)

 

Pismeni ispit

1.1

Projekt

 

      (Ostalo upisati)

 

2.10.    Ocjenjivanje i vrjednovanje rada studenata tijekom nastave i na završnom ispitu

Kontinuirano praćenje rada na vježbama, domaćim zadaćama i kolokvijima.

U tijeku semestra je (5 obveznih, 2 bonus) domaćih zadaća, koje se ocjenjuju.

Sve domaće zadaće se crtaju programom dinamične geometrije Sketchpad 5.03HR i predaju kako datoteke.

U semestru su 3 kolokvija, 1. kolokvij je teoretski i uvjet je za potpis. 2. i 3. kolokvij se sastoje od

dva dijela /teoretskog i konstruktivnog/ (koji se izvodi na računalima uporabom programa dinamične geometrije

Sketchoad 5.03HR). Za prolaz potrebno je oba dijela pozitivno riješiti.

1. KOLOKVIJ - TEORETSKI (max. 150 bodova)

 0 - 75 bodova - nedovoljan (1)

 76 - 109 bodova - dovoljan (2)

110 - 129 bodova - dobar (3)

130 - 139 bodova - vrlo dobar (4)

140 - 150 bodova - izvrstan (5).

2. KOLOKVIJ/3. KOLOKVIJ

TEORETSKI DIO (max. 30 bodova)

0 - 15 bodova - nedovoljan (1)

16 - 20 bodova - dovoljan (2)

21 - 24 boda - dobar (3)

25 - 27 bodova - vrlo dobar (4)

28 - 30 bodova - izvrstan (5)

KONSTRUKTIVNI DIO (max. 230 bodova)

0 - 115 bodova - nedovoljan (1)

116 - 189 bodova - dovoljan (2)

190 - 209 bodova - dobar (3)

210 - 219 bodova - vrlo dobar (4)

220 - 230 bodova - izvrstan (5).

Pismenog dijela ispita oslobađaju se svi studenti koji ostvare minimalno dovoljan (2)po svakoj od aktivnosti.

Usmenog dijela ispita oslobađaju se studenti koji ostvare minimalno vrlo dobar (4) po svakoj od aktivnosti.

2.11.    Obvezna literatura (dostupna u knjižnici i putem ostalih medija)

Naslov

Broj primjeraka u knjižnici

Dostupnost putem ostalih medija

D. Palman. Trokut i kružnica. Element, Zagreb, 1994.

5

 

D. Palman. Geometrijske konstrukcije, Element, Zagreb, 1996.

5

 

D. Palman. Stereometrija, Element, Zagreb, 2005. 

5

 

D. Palman. Projektivne konstrukcije, Element, Zagreb, 2005.

5

 

D. Palman. Planimetrija, Element, Zagreb, 1999.

5

 

     

     

     

svi nastavni materijali su dostupi studentima u elektroničkom obliku

     

     

2.12.Dopunska literatura (u trenutku prijave prijedloga studijskoga programa)

G.R. Bertoline, E.N. Wiebe, N.W. Hartman, W.A. Ross. Technical Graphics Communication, McGraw - Hill, Higher Education, Boston, 2007.

C.V. Sanders. Geometric Graphic, Key Curriculum Press, Emeryville, 2003.

B.E. Reynolds, W. E. Fenton. College Geometry Using The Geometer's Sketchpad, Key College Publishing, 2006.

2.13.Načini praćenja kvalitete koji osiguravaju stjecanje izlaznih kompetencija

Periodično testiranje teoretskih i konstruktivnih znanja kroz 3 kolokvija.

Polaganjem pismenog i usmenog dijela ispita.

Samo vrednovanjem nastavnika i studentskom anketom.

2.14.Ostalo (prema mišljenju

 predlagatelja)

Geometrijski/ matematički pristup geodetskim problemima primjenom programa dinamične geometrije kao alata za crtanje/ konstruiranje studentima omogućava odabir i pravilnu primjenu osnovnih geometrijskih/ matematičkih vještina i koncepata, otkrivanje pravilnosti u oblicima, izradu modela te prepoznavanje i izmjenu (međusobnu komunikaciju) ideja.

 Rješavanje geodetskih problema geometrijskim pristupom zahtjeva kreativnost i sustavna pristup, što je jedan od temelja u znanstvenim i tehničkim otkrićima, kao i iznalaženju novih inovacija. 

1. GENERAL INFORMATION

1.1.  Course teacher

Nikol Radović

1.6. Year of the study programme

II.semester

1.2. Name of the course

Computer geometry

1.7. Credits (ECTS)

5

1.3. Associate teachers

 

1.8. Type of instruction (number of hours L + S + E + e-learning)

30(L) + 30(E) + e-learning

1.4. Study programme (undergraduate, graduate, integrated)

undergraduate

1.9. Expected enrolment in the course

90

1.5. Status of the course

mandatory

1.10. Level of application of e-learning (level 1, 2, 3), percentage of online instruction (max. 20%)

Level 2

2. COUSE DESCRIPTION

2.1. Course objectives

The goal of course Computational geometry is the renewal and replenishment secondary education of geometry, using the dynamic geometry (Geometer's Sketchpad 5.03HR) as a tool for drawing / design, with particular emphasis on applications in geodesy and geoinformatics.

2.2. Course enrolment requirements and entry competences required for the course

knowledge of secondary school mathematics/ geometry programs

2.3. Learning outcomes at the level of the programme to which the course contributes

Knowledge and understanding

-          To know theoretical principals, procedures of computer processing and visualisation of surveying data.

-          To understand the mathematical methods and physical laws applied in geodesy and geoinformatics.

Application of knowledge and understanding

-          To apply the knowledge in mathematics and physics for the purpose of recognizing, formulating and solving problems in the field of geodesy and geoinformatics,

-           To use information technology in solving geodetic and geoinformation tasks.

Learning and ethical skills

-          To plan the continuation of academic education in the field of geodesy and geoinformatics, or related disciplines, and to develop the lifelong learning attitude.

2.4. Learning outcomes expected at the level of the course (4 to 10 learning outcomes)

-         Troubleshoot and draw constructive task of applying the transformation plane / space using dynamic geometry Sketchpad 5:03CRO

-         To construct geometric figures by animation using the dynamic geometry sketchpad 5:03

-         To solve constructive tasks by iteration method

-         The basics of mathematical (geometric) model and apply them

-         Ability to formulate problems of geodesy on geometric (mathematical) language as well as their analysis and resolution

-         Demonstrate skills geometric reasoning

2.5. Course content broken down in detail by weekly class schedule (syllabus)

- A brief history of geometry / Computer geometry (1 hour)
- Transformation of the plane (translation, symmetry, rotation, slide symmetry). (3 hours)
- Solving constructive tasks by methods of plane transformation s. (4 hours)
- Solving constructive tasks using as the locus of points. (4 hours)

-The composition of plane transformations and symmetry groups and their display using the dynamic geometry (4 hours)
- Basic concepts of fractal geometry and structure fractal iteration method using dynamic geometry (2 hours)
- Visualization of projective planes (2 hours)
- Display plane curves 2 and a higher degree with the program dynamic geometry as tool for for drawing (2 hours)
- Animation as the foundation of computer graphics, construction geometric figure animation (2 hours)
- The use of dynamic geometry (2 hours)
- Non-Euclidean geometry (4 hours)

2.6. Format of instruction:

lectures

 seminars and workshops

exercises

 on line in entirety

partial e-learning

 field work

independent assignments

 multimedia and the internet

 laboratory

 work with mentor

homeworks

2.7. Comments:

     

2.8. Student responsibilities

-    Presence in more than 80% lecture and 80% of exercises; homework (five compulsory and two bonuses).

-     For homework students receive tasks that must be addressed to one of constructive methods or must apply one or more of the default method, with their implementation (task open-ended).

-    Every homework is evaluated.

-     (Correct) homework’s delivered on time and pass on first colloquium (theoretically) are the condition for signature.

-    Accessing three colloquiums to which the student responds to the theoretical issues and solves problems.

-    In writing: the written part of the exam students may be released if such material is deposited through two theoretical and constructive three colloquia that take place during the semester.
Oral: theoretical knowledge is tested on regular examination periods

2.9. Screening student work (name the proportion of ECTS credits for each activity so that the total number of ECTS credits is equal to the ECTS value of the course )

Class attendance

0.5

Research

     

Practical training

     

Experimental work

     

Report

     

homeworks

1

Essay

     

Seminar essay

     

      (other)

     

Tests

1.2

Oral exam

1.2

      (other)

     

Written exam

1.1

Project

     

      (other)

     

2.10. Grading and evaluating student work in class and at the final exam

Continuous monitoring of the exercises, homework, and colloquia.
During the semester the five compulsory and two bonus homework, to be evaluated.
All are drawn in the program dynamic geometry sketchpad 5.03CRO and submit such files.
In the semester are three colloquia. 1. Colloquium is theoretically and a condition for signature. 2nd and 3rd Colloquium consist of theoretical and constructive parts (which are delineated in the program dynamic geometry sketchpad 5:03 CRO).
To pass the colloquium should be both theoretically and constructive part of affirmative solve.

  1. 1st Colloquium (theoretically) (max. 150 points)
    0-75 points ------------- >insufficient (1)
    76-109 points ---------- > sufficient (2)
    110-129 points -------- > good (3)
    130-140 points -------- > very good (4)
    141-150 points -------- >excellent (5)

    2nd / 3rd COLLOQUIUM
    THEORETICAL (max. 30 points)
    0-15 points ------------ > insufficient (1)
    16-20 points ---------- >sufficient (2)
    21-24 points ----------à good (3)
    25-27 points ----------- > very good (4)
    28-30 points ---------- > excellent (5)

    CONSTRUCTIVE (max. 230 points)
    0-115 points ---------- --- >insufficient (1)
    116-189 points ------- --à sufficient (2)
    190-209 points ---------à good (3)
    210-219 points --- ----- > very good (4)
    220-230 points ---------à excellent (5)

    All students who have earned a minimum of sufficient (2) per each of the activities, will be exempt from the written exam.
    All students who have earned a minimum of very good (4) per each of the activities, will be exempt from the exem.

 

2.11. Required literature (available in the library and via other media)

Title

Number of copies in the library

Availability via other media

D. Palman, The triangle and circle, Element, Zagreb, 1994.

     

     

D. Palman, Geometrical constructions, Element, Zagreb, 1996.

     

     

D. Palman, Stereometry, Element, Zagreb, 2005.

     

     

D. Palman, Projective constructions, Element, Zagreb, 2005.

     

     

D. Palman, Planimetry, Element, Zagreb, 1999.

     

     

All course materials are available in electronic form for students.

     

     

2.12.Optional literature (at the time of submission of study programme proposal)

V. Gutenmacher, N. B. Vasilyev: Lines and Curves A Practical Geometry Handbook, Birkhauser Boston Inc., 2004.

B. E. Reynolds, W. E. Fenton: College Geometry Using The Geometer's Sketchpad, Key College Publishing, 2006.

C. V. Sanders: Geometric Graphic, Key Curriculum Press, Emeryville, 2003.

2.13.Quality assurance methods that ensure the acquisition of exit competences

- A survey on the quality of teaching and learning materials
- Class attendance and class participation
- Evaluation of the results of the examination (year)

2.14.Other (as the proposer wishes to add)

The mathematical/ geometric approach to problems by applying dynamic geometry as a tool to draw enable students to select the correct application of basic mathematical/ geometrical skills, discover patterns in forms, templates, and to recognize and communicate with them related ideas. Solving mathematical/ geometry with a focus on geosciences requires creativity and a systematic approach, which plays a major role innovation and scientific and technical and scientific discoveries..