Time, place
Tuesday 10:15 am - 11:45 am; É7.87 (Drawing room)
Thematic
In this course we learn the mathematical base of non-conical map projections.
Suggested reading Lecture notes, 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 hemispheral or global maps (>10 000 km extent) in the map library to a file with lossless compression. 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!
| Task 2: Talk about the theory | Task 3: Talk about the map projections | Task 4: Derive the formula of the projection | |
|---|---|---|---|
| 1. | Classification of non-conical projections | Map projections based on transverse azimuthal projections | Winkel III projection |
| 2. | Detecting the projection of a map with an unknown grid | Pseudopolyconic projections | Lagrange projection |
| 3. | Decreasing distortions with distortion criteria | Rectangular and equal-area polyconics | War Office projection (sphere) |
| 4. | Decrasing distortions manually (Baranyi, Robinson, Flex Projector etc.) | American polyconic | American polyconic (sphere) |
| 5. | Conformal mappings as complex functions | Pseudoconic projections | Bonne projection (sphere) |
| 6. | Decreasing distortions by rotating the graticule (7 aspects) | Non-conical projections in rotated aspects | Hammer projection (normal aspect) |
| 7. | Needs for special distortions (e.g. retroazimuthal, loximuthal) | Pseudoazimuthal projections | Loximuthal projection |
| 8. | Comparison of conical and non-conical projections (look, distortions) | Blended projections | Eckert V projections |
| 9. | Guidelines of selecting a map projection | Wagner projections, Kavrayskiy VII projection | Kavrayskiy VI projection |
| 10. | Decreasing distortions visually with curved surfaces | Equal-area projections developed using an auxiliary latitude | Mollweide projection |
| 11. | Decreasing distortions using interruptions or polyhedra | Globular projections | Apian II projection |
| 12. | Lichtenstern projection and its approximation | Goode and Érdi-Krausz projections | Sinusoidal projection (sphere) |
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.