Analytical Geometry

LEARNING OUTCOMES

The main goal of the course is to have the student acquainted with the geometrical properties of the two- and three-dimensional space. A combined synthetic-analytical method, with geometric views of three-dimensional objects as the primary instructional tool is employed. Once the course is completed, the student will:

• have understood elementary notions of analytic geometry in two-dimensional and three-dimensional space, which, along with the courses of linear algebra and calculus, form a solid theoretical backbone in engineering
• have a deeper understanding of three-dimensional space, as a primary component in every professional and scientific subfield in modern topography
• have learned about basic projection methods (top view, front view, axonometric, perspective) in the light of the underlying geometric-algebraic theory that is used for computer-aided (CAD) visualization
• be able to solve basic problems in 3D space geometry
• be able to solve linear coordinate transformations (scale, translation, rotation, rigid, affine, projective)
• Be in a solid position to implement the acquired knowledge in the context of subsequent department courses, as well as solve complex problems concerning representations of three- dimensional objects as well as their projections in two- dimensional space.

 

General Competences

• Search for, analysis and synthesis of data and information, with the use of the necessary technology
• Working independently
• Production of free, creative and inductive thinking

 

SYLLABUS

Geometry for the topographical engineer: Elements of Euclidean geometry. Vectorial algebra. Coordinate reference systems. Point. Line. Curve. Plane. Surface. Study of relations between objects: Point to Plane, polygon, plane. Relation of line to a plane. Slope/direction of line. Directional cosines. Parallel lines and planes, orthogonal lines and planes, collinearity, coplanarity. Equivalent analytic expressions. Conics. Second degree surfaces. Applications to topography. Linear transforms. Scale. Translation. Rotation. Rigid-body transformation. Similarity transformation. Affine and Projective transformations. Parameters. Properties. Non-linear transformations. Applications to geomatics. Generalities concerning projections. Central projection. Parallel projection. Methods of visualization. Top-view. Front-view. Axonometry. Perspective. Vision and central projection. Photography fundamentals. Vanishing points and lines. Introduction to projective geometry. 3D computerized visualization. Introduction to computer graphics and CAD.

 

STUDENT PERFORMANCE EVALUATION

Language of evaluation: Greek
Methods of evaluation:
• Written exam at the end of the semester (multiple choice questionnaires, short-answer questions, & problem-solving questions)
• Homework (practical exercises on both theoretical and practical objectives related to the course)

 

RECOMMENDED LITERATURE

In Greek:
1. Γεωργίου Δ., Ηλιάδης Σ., 2017, “Αναλυτική Γεωμετρία”.
2. Ξένος Θ., 2004, “Αναλυτική Γεωμετρία”.
3. Λευκαδίτης Γ., 2006. “Μέθοδοι Παραστάσεων”.

In English:
3. Kindle J. H., 1968. Theory and problems of plane and solid analytic geometry. McGraw-Hill, New York.