| Name of Module Unit | Descriptive Geometry I |
| Name in polish language | Geometria wykreślna I |
| Module type | obligatory |
| Level of study | intermediate |
| Responsible person | Dr Cecylia Łapińska
Zakład Systemów Ciepłowniczych i Gazowniczych, Wydział Inżynierii Środowiska |
| Minimal preparation in geometry: Basic knowledge of plane geometry (secondary school program of mathematics): properties of triangles; regular polygons; parallelism and perpendicularity; constructions (by using a ruler and compasses) involving straight lines and circles, particularly tangents to circles. Elementary knowledge of 3D-space geometry (secondary school program of mathematics): straight lines, planes and relationships; dihedral angles; distances; parallelism and perpendicularity in the space; solids; regular polyhedrons, etc. |
| Mathematical approach to engineering graphics. Introductory course in engineering geometry - a review of principal geometric methods to give a one-to-one representation of 3D-space on a plane. Aims of the subject are pedagogical, mathematical and practical. Pedagogical: To introduce the student to ideas and ways of thinking, without use of numbers, which generally are new to him and thus to form and develop his 3D-space imagination, as well as the ability of logical thinking and coming to right conclusions concerning 3D-space systems. Mathematical: To give rudiments of projective geometry. To study fundamental properties of central projection (perspective). To study the principle and properties of parallel projection: axonometric and orthogonal projections (Monge's projections). Practical: To give a working knowledge of the engineer's language: how to make and how to read drawings. To become familiar with presented methods and acquire the ability to specify their use with assurance, particularly: to make pictorial drawings (freehand or with instruments) of polyhedrons or surfaces of revolution with cut-out by using the principle of vertical perspective or axonometry, to represent objects by drawing their orthogonal projections and to use principal constructions of this method to find the true shape and size of objects represented by their orthographic views as well. To apply obtained skills to solve some problems concerning certain roofs. |
| Ideal elements and projective space. Central projection: The principle of the one-to-one transformation and basic constructions. Image of points, straight lines and planes. Restitution. Ground plane; relationships between plan and perspective of this plane. Vertical perspective of a polyhedron with sections by frontal, horizontal or vertical planes. Vertical perspective of a set of rectangular prisms if a plan and heights are given. Parallel projection: Oblique axonometric projection. The most often used axonometric systems. Representation of polyhedrons and surfaces of revolution with removed parts. Associate axonometric systems applied for drawing joints of wooden pieces. Orthogonal projection as a particular case of parallel projection. Characteristic invariant of this projection. Reversibility of the transformation and Monge's projections. Construction of common elements. Intersection of polygons and polyhedrons. Three projections of a prism or pyramid with removed parts. Transformation of the projection planes system - auxiliary projection planes. Application of the transformation to find dihedral angles, perpendiculars to a plane, distances, the projections of polyhedrons sections and their true shape and size as well. Revolutions and rabatments; application to obtain the normal view of a plane. Complete geometric design of roofs satisfying certain conditions. |
| Activity - 10 points [10%] Workshops: ten exercises, two tests - (10x2 + 2x30 ) points [80%] Lectures: one test - 10 points [10%] |
| [1] Bieliński A.: Geometria wykreślna Oficyna Wydawnicza PW, Warszawa 2005 [2] French Th. E.: Graphic Science and Design Mc GRAW-HILL Book Company, Inc. [3] French Th. E., Vierck Ch. J.: Graphic Science Mc GRAW-HILL Book Company, Inc. [4] Przewłocki S.: Geometria wykreślna w budownictwie Arkady Warszawa 1997 [5] Ryan D. L.: CAD/CAE Descriptive Geometry CRC Press, Inc. 1992 |
| Name of Module Unit | Descriptive Geometry II |
| Name in polish language | Geometria wykreślna II |
| Module type | obligatory |
| Level of study | intermediate |
| Responsible person | Dr Cecylia Łapińska
Zakład Systemów Ciepłowniczych i Gazowniczych, Wydział Inżynierii Środowiska |
| Skills achieved in the course of Descriptive Geometry I, particularly the ability to apply the principles and fundamental constructions of the orthogonal projections method. |
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Continuing the pedagogical aims from I semester. Application of the orthogonal projection method to study surfaces of revolution and ruled surfaces. Introduction to a new method to represent 3-D space onto plane: the marked orthogonal projection (map projection). Application of this method for a geometric design of a road. Exercises in reading more complicated orthographic views and translating into pictorial sketches or models. Proficiency in the ability to visualize. Proficiency in operating of 3-dimensional systems and drawing them by some advanced projection methods. |
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Affinity. Ellipse as image of a circle under an affinity. Surfaces of revolution represented by the Monge's method. Intersection of these surfaces by straight lines and planes. Classification of conic sections. Three projections of a cone, cylinder and sphere with parts removed by projecting planes. Developments of conical and cylindrical surfaces; geodesics on these surfaces. Intersection of surfaces of revolution - cutting-plane and cutting-sphere methods. Reducibility of intersection line of two second-order surfaces. Application of the intersection line reducibility to geometrical constructing of cylindrical vaults and conical connections and transitions. Ruled surfaces. Constructions and classification. Applications in architecture, building or engineering. Map projection. Ground plane, mark. Image of points, straight lines and planes; modulus, gradation, slope. Rabatment. Parallelism and perpendicularity. Intersection of simple geometric objects. Topographic surfaces. Application for a geometrical design of a road. Orthogonal axonometric projection. Isometric drawing. Image of a sphere. Pictorial drawings. |
| Activity - 10 points [10%] Workshops: ten exercises, two tests - (10x2 + 2x30 ) points [80%] Lectures: one test - 10 points [10%] |
| [1] Bieliński A.: Geometria wykreślna Oficyna Wydawnicza PW, Warszawa 2005 [2] French Th. E.: Graphic Science and Design Mc GRAW-HILL Book Company, Inc. [3] French Th. E., Vierck Ch. J.: Graphic Science Mc GRAW-HILL Book Company, Inc. [4] Przewłocki S.: Geometria wykreślna w budownictwie Arkady Warszawa 1997 [5] Ryan D. L.: CAD/CAE Descriptive Geometry CRC Press, Inc. 1992 |