Time, place
Monday 2:00 pm - 3:30 pm; É7.85 (seminary) and Tuesday 12:15 am - 1:45 pm; É7.55 (computer lab)
Thematic
In this course we learn the mathematical base of conical map projections.
Suggested reading Superb lecture notes by prof. Kerkovits, http://www.progonos.com/furuti/MapProj/Normal/TOC/cartTOC.html and http://mercator.elte.hu/~saman/edu/proj/
Expectations
The exam is subject to the completion of a homework assignment: scan five lossless maps of at least 3500 km (group of countries) and up to 15 000 km (continents, oceans) in the map library. The maps should be from at least three different atlases. There must be at least one map whose projection you consider inappropriate (e.g. it is not appropriate for this topic or it is outrageously distorted). Upload the images to the K:\ drive and write in a text file for each map what you think its projection is, whether you agree with the choice of map projection and why (about 10-30 words per map.) If you disagree, suggest another projection!
The course ends with an oral exam. You get four tasks in the exam. The first task is a short discussion about your assignment. This is followed by getting your tasks from the following table and time for preparation.
| Task 2: Talk about the theory | Task 3: Talk about the map projections | Task 4: Derive the formula | |
|---|---|---|---|
| 1 | The concept of map projections | Equal-area conics | Albers equal-area conic |
| 2 | Classification of map projections | Conformal conics | Lambert conformal conic |
| 3 | Types of distortion in map projections | The projection system of NATO | Intersection angle between graticule lines |
| 4 | Data of the ellipse of distortion and map distortions | Equidistant conic | Equidistant conic |
| 5 | The theory of Tissot | Aphylactic non-perspective cylindricals | Minimal and maximal linear scale |
| 6 | Isocols, the maximal angular deviation | Perspective and quasi-perspective cylindricals | Maximal angular deviation |
| 7 | Map projections in the GIS | Equal-area cylindricals | Behrmann projection |
| 8 | Basics of ellipsoidal geometry (shape, radii of curvature, geodesics) | Mercator and Web Mercator projections, EOV | Conformal cylindricals |
| 9 | Distorted cartograms, focussed projections | Gauss–Krüger and Cassini–Soldner projections | General formula for areal scale |
| 10 | The geodetic datum | Azimuthal equidistant and Ginzburg mappings | Azimuthal equidistant |
| 11 | The concept and usefulness of the metagraticule system | Lambert azimuthal equal-area | Lambert azimuthal equal-area |
| 12 | Basics of spherical geometry (notable lines and surfaces, trigonometry) | Perspective azimuthals | General formula of perspective azimuthals |
Procedure for the oral exam: students are free to decide the order among themselves. The next victim should wait at the front of the room, so that I do not have to dig him from the other end of the corridor! (If there are four students before you, feel free to leave for the buffet.) The student rolls a dice to choose a row. The student may request a new roll to replace the task at the cost of –5 points penalty for each new roll. The task can be drafted during the previous student's answer (you can only use a pen, I will provide paper), and then you can present it in about 10 minutes, after which I will ask questions. In your answer, you may complete the tasks in any order and combine them as you wish. The fourth task is to derive a map projection or a basic formula. The constants of the conic projections do not need to be expressed in terms of the standard parallels. You should at least be able to recall the steps of the derivation! Don't try to skip it, it scores lots of points!
Grading
Task 1 (assignment): 0.5 point is awarded for each map for the correct identification of the map projection. An additional 0.5 point is awarded for the reasoning whether the projection is appropriate or not. If the map chosen does not correspond to the requirements of the specification, but the answer is otherwise assessable, a penalty of –0.5 point per map is applied. A total of 5 points can be scored.
Task 2 (theory): Explanation of basic concepts and relationships: 2 points. Correct use of terminology, definitions: 1 point. Examples of the application of the methods or classification described: 2 points.
Task 3 (present a projection): Classification of the map projections to be presented: 1 point. Examples of the proper application of the projection presented (area of interest, theme): 2 points. Describing the parameters of the projection (e.g. two equidistant parallels can be chosen) or indicating that the projection cannot be parameterized: 1 point. Historical context (name of inventor, approximate date of invention accurate to the century): 1 point.
Task 4 (derivation): “Professor, I can't do this”: 0 points + the professor will be very grumpy (not recommended for any student). If you manage to derive with help: 3–4 points depending on the amount of help. If you can do it on your own: 5 points.
Classification of map projections: it is essential that the student knows for each projection which class it belongs to according to the graticule, distortions, geometrical construction and aspect. If the student is wrong in this at any time during the exam, or if there is a mistake in the assignment, then: no penalty for the first two mistakes, three mistakes –3 points, four mistakes –8 points, five mistakes –20 points.
Grading: 7 points and below fail (1), 9–10 points pass (2), 12–13 points fair (3), 15–16 points good (4), 18 points and above excellent (5). A student between two grades will be given three quick questions from one of the other rows, receiving the better grade for at least two correct answers and the lower grade otherwise.