1.1 Flat Affinity . - Affinity's properties and definition. 1.2 Affinity's definition: by the axis and two affinity points. 1.3 Affinity figure. Double straight lines and double points.

Dedication

2.1 Plane's rebatment on the horizontal plane: - Point's rebatment. - Straight line's rebatment. Horizontal and frontal straight lines. - Flat figure's rebatment. - Vertical and horizontal trace rebatment. 2.2 Rebatment using the affinity. 2.3 Counter-rebatment: - Horizontal projection's determination. - Vertical projection's determination. 2.4 Plane's rebatment on another one: - Plan defined by its two traces. - Plan defined by two straight lines. 2.5 Vertical plane's rebatment.

Dedication

3.1 Distance between 2 points: segment's true magnitude. 3.2 Minimum distance between two crossing straight lines. 3.3 Two parallel planes' distance. 3.4 Two parallel lines's distance. 3.5 Two points' distance in a plane. 3.6 Distance between a point and an straight line.

Dedication

4.1 Straight line's angles with projection planes. - Angle's determination when straight line's are known. - Straight line's determination when angles are known. 4.2 Planes projection angles with a plane. - Angles' determination when plane are known. - Plane's determination when angles are known. 4.3 Angles between two lines: - when they cut themselves. - when they cross themselves. 4.4 Angle of two planes. 4.5 Angle between a straight line and a plane. 4.6 Determination of a plane knowing the angles with the projection planes. 4.7 Plane's determination when angles between traces are known and the angle between a projection plane and the plane itself are known aswell.

Dedication

5.1 Concepts, definitions and types. 5.2 Parallel and focal light. 5.3 Own and cast shadow. 5.4 Point's shadow cast: - over any plane. - over an horizontal plane. - over a vertical plane. - over the two projection's planes. 5.5 Segment shadow cast: - over any plane. - over the horizontal plane. - over the vertical plane. - over the two projection's planes. 5.6 Flat figure released shadow. 5.7 Flat figure's own shadow. 5.8 Straight line cast shadow over a flat figure. 5.9 Flat figure's cast shadow over another flat figure one.

Dedication

6.1 Plane's changing method. Horizontal and vertical's changing plane. - Point's representation. - Line's representation. - Plane's representation. 6.2 Change of planes of projection: applications. - Straight line's conversion into a vertical one. - Straight line's conversion into a straight edge one.

Dedication

7.1 REGULAR AND SEMI-REGULAR POLYHEDRA 7.1.1 Convex regular polyhedra (Platonic solids) 7.1.2 Conjugate polyhedra 7.1.3 Semi-regular polyhedra (general) 7.2 TETRAHEDRAHEDRA Definition and description 7.2.2. Properties 7.2.3. Principal section 7.2.4. Planar sections 7.2.5. Representation: - With one face in the horizontal plane - With one vertical edge - With two horizontal edges. 7.2.6. Shadows 7.2.7. Problems 7.3 HEXAEDRON 7.3.1. Definition and description 7.3.2. Properties 7.3.3. Principal section 7.3.4. Plane sections 7.3.5. Representation: - With one face in the horizontal plane - With two horizontal edges - With a vertical main diagonal 7.3.6. Shadows 7.3.7. Problems 7.4 OCTAEDRON 7.4.1. Definition and description 7.4.2. Properties 7.4.3. Principal section 7.4.4. Planar sections 7.4.5. Representation: - With one face in the horizontal plane - With two horizontal edges - With a vertical main diagonal 7.4.6. Shadows 7.4.7. Problems 7.5 DODECAHEDRON AND ICOSAHEDRON 7.5.1. Definition, description. 7.5.2. Properties 7.5.3. Principal sections. 7.5.4. Representation. 7.6. Generation of Geodesic Domes

Dedication

8.1. Projections of the sphere. 8.2. Section of a sphere by a horizontal plane and a vertical plane. 8.3. Projections of points located on the sphere. 8.4. Intersection of a horizontal line with a sphere. 8.5. Intersection of a line with a sphere. 8.6. Section of a sphere by a vertical plane. 8.7. Section of a sphere by a plane of edge. 8.8. Tangent plane to a sphere by a point on the surface. 8.9. Tangent plane to a sphere and passing through LT 8.10. Tangent plane to a sphere with a given direction. 8.11. Tangent planes to a sphere that contain an outer line. 8.12. Intersection of a sphere by an oblique plane (any) that passes through the center of the sphere. 8.13. Proper and cast shadow of a sphere on the projection planes. 8.14. problems S8-2. Problems and exercises

Dedication

9.1. Developable 9.1.1. Definition and classification. 9.2. Prism. 9.2.1. Representation. 9.2.2. Situation of a point on the prism. 9.2.3. Intersection of the prism with a line. 9.2.4. Intersection of the prism with a plane. 9.2.5. Prism development. 9.2.6. Problems and exercises 9.3. Pyramid. 9.3.1. Representation. 9.3.2. Location of a point on the pyramid. 9.3.3. Intersection of the pyramid with a line. 9.3.4. Intersection of the pyramid with a plane. 9.3.5. Development of the pyramid. 9.3.7. Problems and exercises. 9.4. Cone. 9.4.1 Representation. 9.4.2 Location of a point on the cone. 9.4.3 Intersection of the cone with a line. 9.4.4 Development of the cone. 9.4.5 Plane sections and true magnitude: - Circumference, ellipse, parabola and hyperbola 9.4.6 Tangent planes to the cone: - By a point on the surface. - By a point outside the surface. - Tangent planes to a given direction. 9.4.7. Problems and exercises 9.5. Cylinder. 9.5.1 Representation. 9.5.2 Location of a point on the cylinder. 9.5.3 Intersection of the cylinder with a line. 9.5.4 Cylinder development. 9.5.5 Flat sections and true magnitude: - Circumference. - Ellipse. 9.5.6 Tangent planes to the cylinder: - By a point on the surface. - By a point outside the surface. - Tangent planes to a given direction. 9.5.7. Problems and exercises

Dedication

10. Intersection of radiated and revolution surfaces. 10.1. Intersection of two surfaces, whose bases are contained in the same projection plane: - Two pyramids, two prisms, two cones, two cylinders. - Cone - pyramid, cone - cylinder, cone - prism. - Cylinder - pyramid, Cylinder - prism and pyramid - prism. - Problems and exercises 10.2. Intersection of two surfaces, whose bases are contained in different projection planes. 10.3. Intersection of two surfaces where one of them is defined by horizontal edges / generatrices. - Problems and exercises 10.4. Intersection of two surfaces of revolution 10.5. problems - Problems and exercises

Dedication

During this practical part of the course, concepts and methodologies typical of BIM design will be introduced and the use of basic construction elements will be taught that will allow the student to create structures and surfaces typical of civil engineering and architecture. It will be taught to add topographic surfaces, modeling with masses and parametric elements, to later document the Project, which will allow the student to create projects. The course includes practical exercises aimed at consolidating student's use of this software. - Presentation of the BIM Revit software - Project in revir: organization, visualization, links, import-export of files and location and location. - Creation and edition of constructive elements. - Project Documentation: Surfaces, tables, details, Annotation, labels, legends, preparation of plans and boxes. - Topography and platforms. - Modeling of masses: conceptual and "in situ" - Creation and edition of families - Creation of advanced masses and components in situ: Curtain wall, surface pattern, adaptive component, spatial and adaptive structures. ------------------------------- Starting from the basic concepts and the handling of the BIM software, we will see its design application to geometric surfaces typical of Descriptive Geometry used in engineering and architecture: S2-3. CAD_BIM S3-3. CAD_BIM S4-3. CAD_BIM S5-3. CAD_BIM S6-3. CAD_BIM S7-3. CAD_BIM S8-3. CAD_BIM S9-3. CAD_BIM ------------------------------- 11. Application of BIM to the study of geometric surfaces typical of Descriptive Geometry through the generation of masses and adaptive components. 11.1. Developable surfaces: 11.1.1. Geodesic - Icosahedral - Dodecahedral domes 11.1.2. Folds - Linear - On curved surfaces - Bidirectional - Discontinuous - Radial - Combinations and groupings - Vault and Domes 11.1.3. Flat double-layer spatial lattice structures - Triangular, square and hexagonal equipartitions. 11.2. Simple curvature surfaces: 11.2.1. General concepts 11.2.2. Cylindrical surfaces and sections 11.2.3. Conical surfaces and sections 11.2.4. Intersections between surfaces of simple curvature - Conical lunettes - Cylindrical lunettes - Vaults by edge and cloister corner - Intersections between conical and cylindrical surfaces. 11.3. Elliptical Quadrics and their applications 11.3.1. General concepts - elliptical quadrics and scales 11.3.2. Vaulted Domes and Vaults with straight and inclined planes - Triangular base - Square base - Pentagonal Base - Hexagonal Base 11.3.3. Elliptical domes of revolution and spherical caps. 11.5. Ruled ruled surfaces - Concept and classification 11.5.1. Triaxial ruled surfaces - Concept - Ruled and revolution hyperboloid - Hyperbolic paraboloid - Combinations - Traction surface using paraboloids - Vaults by parabolic edge 11.5.2. Biaxial ruled surfaces - Concept and types - Straight and oblique circular cone - straight elliptical conoid - Double straight cone - Combination of conoids 11.5.3. Axial ruled surfaces - Concept - General cylinder and master plane - Ordinary and oblique pitch cap - Straight cylindrical helical 11.5.4. Anaxial ruled surfaces - oblique cylindrical helical.

Specific Objectives

- Preparation of students for the use of computer instruments using BIM software as a projecting tool and for solving geometric problems. - Identify and represent through the system of multiple, dihedral, axonometric and conical views, the characteristics of bodies, surfaces and objects, according to their location in space. - Know, identify, represent and use the known surfaces and volumes in descriptive geometry using BIM software applied to projects. - Application of current computer tools (BIM software) to graphic representation in the field of Civil Engineering through the use of parametric-type assisted design programs. - Introduction of the student in the rational use of computer science as a work base, under the "interface" of the operating systems, and the application of the specific BIM software as a 2D and 3D project drawing tool. Always under the conceptual guideline of the geometric structuring of the projects to be represented and the help of informatics in the field of descriptive geometry and technical drawing.

Dedication

It will consist of two evaluable tests during the four-month period, framed in the evaluation weeks planned by the Escola de Camins.

Dedication