3. DESCRIPTIVE GEOMETRY

4. What is descriptive geometry? The construction of the majority of the objects around us (houses, motorcycles, televisions, telephones, computers, etc.) requires that these objects to be previously defined (design process) and subsequently represented with exact precision on plans (objective description of the form).

5. Think about objects that require a design

8. Are these objects two-dimensional? How can we draw a three-dimensional object in a paper (2D)?

9. Descriptive geometry makes it possible to objectively represent objects and elements that pertain to the three- dimensional space on two-dimensional supports. So, do you think that descriptive geometry affects our lives? In what way? Talk in groups of four people.

10. We can represent objects by the representation systems. Representation systems are graphic languages to link elements in 3D to elements in 2D and vice versa. They are a very important part of descriptive geometry. These languages are universal. They can be understood all over the world.

11. Representation systems are based on the projections of the geometrical three- dimensional elements on plans. The projections vary according to the representation system. It is as if we take a photo of the object and we print it out.

12. TYPES OF PROJECTIONS We can project the objects in different ways: ORTHOGONAL PROJECTION OBLIQUE PROJECTIONS CONIC PROJECTIONS IN GREEK ORTHO= 90 Degrees GONAL= angle

13. PARALLEL ORTHOGRAPHIC PROJECTIONS – Used in technical drawings

14. OBLIQUE PROJECTIONS

15. CONIC projectionF

16. CLASSIFICATION OF THE REPRESENTATION SYSTEMS Representation Systems DIEDRIC.- Uses parallel orthographic projections AXONOMETRICUses parallel orthographic projections. (ISOMETRIC is the variation of the axonometric system that we are going to use) AXONOMETRIC: Uses parallel orthographic projections. (ISOMETRIC is the variation of the axonometric system that we are going to use) CAVALIER PERSPECTIVE.- Uses oblique parallel projections CONICUses conic projections CONIC: Uses conic projections

17. This is an example of how an object is represented in each system

18. DIEDRIC SYSTEM

19. (1746 –1818) was a French mathematician, a revolutionary, and the inventor of descriptive geometry, the theoretical basis on which technical drawing is based. During the French Revolution he served as a minister of the Marine and was involved in the reformation of the French educational system, founding the École Polytechnique.descriptive geometrytechnical drawingFrench RevolutionÉcole Polytechnique Gaspar Monge

21. Representation of an object Vert.projection Horizontal projection Observer

23. a´ a

24. Example of projection

26. Elevation or Front view Plan or top viiew Left side view Representation of the views of an object

27. ISOMETRIC PERSPECTIVE

28. In general, perspectives aim to represent three- dimensional objects in a single view or projection,allowing the viewer to clearly see how the object is in reality.

29. ISOMETRIC PERSPECTIVE This system is composed of three planes forming a trihedral (XOY, YOZ and ZOX), which is projected, forming the same angle, onto the drawing plane. This gives us the isometric perspective. In other words, it is the corner of a cube. o Z XY

30. How to pass from diedric system to isometric Front view Plan Left side view o Z X Y Front view

31. One point perspective With conic perspective we can draw reality the way we see it. It is just the way that a camera captures reality. Conic perspective is a method that gives us the sensation of distance and depth in a flat support. It is an optical illusion.

35. One point perspective

36. RICHARD ESTES: "Bridge"

37. Basic elements in linear perspective Point of view : It is the observer’s eye. Horizon line: The height of this line coincides with the height of the point of view. Ground line: It is a theoretical line that help us to draw the figures. The distance between the horizon line and the ground line is the height of the observer. Vanishing point: It is always on the horizon line. Distance points: They are the vanishing points of the lines that form 45º with the representation plane

38. (P.V.) Horizon line Ground line Height of the point of view Distance points Vanishing point

39. Example: Drawing a chessboard in one point perspective (P.V.) Horizon line Ground line V.P.

40. Example of how to rise an object (P.V.) Horizon line Ground line

41. Summary Descriptive geometry represents 3D objects in a paper (2D) The four systems of representation are: –DIEDRIC SYSTEM for technical drawings –ISOMETRIC SYSTEM give us an idea of how the object is in 3D (perspective of the object) –CAVALIER SYSTEM the same –LINEAR PERSPECTIVE (CONIC PERSPECTIVE) is a perspective of the object as we see it