Universidad de Jaén

Detailed contents of Mathematical Cartography

THEORETICAL PROGRAM

Objective: To acquire knowledge and general capacities about reference systems, projections and transformation between them.

Lesson 1. Introduction. Differential geometry of surfaces.

Earth shape (Introduction. Geoid. Ellipsoid. Geographical coordinates. Datum. Map Projection. Map scales. Reference systems).

Lesson 2. ISO Standards related to reference systems and projections. EPSG.

ISO 19111, 19112, 6709, etc. EPSG Reference System Catalog and Transformations

Lesson 3. First approach to CRS transformations and Projection transformations. EPSG. Cartographic adjustments.

Transformations and conversions between references systems and projections. EPSG Catalog of these transformations. Cartographic adjustments (2D adjust, Rubber Sheeting, ...).

Lesson 4. Differential geometry.

Differential geometry of surfaces (Distortions. Tissot's indicatrix. Map projection properties. Map projections parameters. Classification of map projections based on properties and geometry.

Lesson 5. Map projections (Planes and based on developable surfaces). UTM.

Azimuthal and Plane based map projections.

Projections based on developable surfaces (Conics, Lambert conformal projection. Cylindrical, Mercator's projection).

UTM (Convergence, distance scale factor, UTM grid, coordinate transformations, etc.).

PRACTICAL PROGRAM

Objective 1: To acquire knowledge to find help about problems mathematical cartography.

Objective 2: To solve general problems of mathematical cartography.

Objective 3: To quantify distortions of map projections. To choose the adequate map projection based on the use and these distortions

Objective 4: To be capable of transforming point data.

Objective 5: To program several solutions in mathematical cartography.

Previous objectives are developed in the following practices:

• Introduction: Web links, ISO standards, etc. Geoid models and standards. Metadata about map projections and common reference systems.
• Direct and inverse transformation in map projections. Implementation of these transformations.
• Polynomial transformation of point data. Parameter determination between homologous point data. Implementation.
• Rubber sheeting transformation of point data. Parameter determination between homologous point data. Implementation.
• Area distortion, lineal distortion and angular distortion calculation of several map projections. Practical applications.

• Theoretical lessons will develop the theoric subjects and proposing activities in order to incentivate student participation.
• Practical lessons will be divided in an introductory part describing the lessons and solving example problems and a second part developed by the student following the previous examples.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

About the results:

• Aspect S2: Knowledge of theorical and practical contents of the subject:
• • Abilities: CE25,CE30, CT2, CB2R.
  • Results : 5.
• Aspect S3: Homework problem resolutions and discussions.
• • Abilities: CE25,CE30, CT4, CT6, CB2R.
  • Results to evaluate: 5.

About the final qualifications:

To successfully complete the subject is necessary to obtain a 5 over 10 qualification both in the personal project and in the written exam.
The exam will be a written test with contents and problems similar to the one explained in lectures and practical classes. The exam will represent a 65% of the final qualification.
With regards to the personal project, it will be chosen in the first month of the semester among a set of defined proposals. The qualification will be separate in 30% in a first deliver and 70% of the final deliver. The first deliver is optional and will occur approximately one month and a half after the selection of the project. The final deliver will be the same day as the written part.
Note: It is forbidden to use programming devices or any other unauthorized electronic device in exams.