Géométrie de l’espace 1

Course 01 :  Methods of projection & Representation of the point in space

1       Introduction :. 

2       Methods of projection :. 

2.1        Orthographic (parallel) projection. 

2.2        perspective projection. 

3       Geometric space :. 

4       Representation of the point. 

Course 02 :  Reflection On Octants & Point Representation…………………....... P16-22

1       Introduction :. 17

2       The coordinate of point in geometry descriptive :. 18

3       Octant and quadrant:. 18

3.1        Quadrant :. 18

3.2        Octant. 20

Course 03 : The Line And Notable Lines…………………………………………. P 23-30

1       LINE : 24

2 Line projecting on the three projection planes :. 25

3       Remarkable Lines:. 26

v     THE VERTICAL LINE.. 27

v     THE UPRIGHT( standing) LINE :. 27

v     THE HORIZONTAL LINE. 28

v     FRONTAL LINE : 28

v     PROFIL LINE : 29

v     PARALLEL LINE to two planes of projection: 30

Course 04 : The piercing points of a line…………………………………………. P 31-39

1       PIERCING POINTS :. 31

2       Features of Points of Piercing:. 31

3       Horizontal and Frontal Traces in the Case of Two Projection Planes. 32

PH (x,0). 33

PF(0,y). 33

4       Horizontal, Frontal, and Profile Traces in the Case of Three Projection Planes: 35

PH (x,y,0). 35

PF (0,y,Z). 35

Pp (X, 0, Z). 36

Course 05 : Parallel and intersect lines…………………………………………… P 40-44

1       Position of line in space:. 40

.1.1       Parallel lines:. 40

.1.2       intersect lines:. 42

.1.3       Skew lines:. 43

Course 06: A plane and remarkable planes………………………………………. P45-58

1 Determination of plane:. 45

.1.1       Plane traces:. 47

.1.2       Remarkable planes. 49

Course 07:  Drawing transformation in geometry………………………………… P59-73

1       Introduction. 59

2       Changing the projection plane (or ground-line) / (Auxiliary View Method) :. 60

3       Methods of rotation. 66

4       Rabbatement:. 69

5       Rotation around plane traces (or coinciding method). 71

Course 08: plane surfaces (polyhedrons) and representation of circle / cone / cylinder / sphere……………………………………………………………………………… P 74-87

1       Defenition polyhedrons:. 74

2       Prisms, Prismoids, and Pyramids :. 75

3       Representation of cone / cylinder / sphere. 78

4       Intersecting polyhedron and plane:. 81

5       Intersecting polyhedron and line:. 82

6       Intersecting of two polyhedrons:. 83

Course 09 :  introduction to tree-dimensions geometry and axonometric projection………………………………………………………………………….. P98-99

1       Understanding Three-Dimensional Space:. 89

2       Demonstrating how to represent three-dimensional objects on a two-dimensional plane using projection techniques. 93

3       solid modeling techniques for representing complex 3D objects :. 96

Course 10:  generalities about perspective……………………………………....... P 100-114

1       Introduction:. 102

Course 11:  application of the theory of shadows in monge projection perspective and axonometry………………………………………………………………………... P115-129

1       Introduction :. 119

2       Definition of Shadows :. 119

3       Laws of light and shadow projection :. 119

4       Projection of a Shadow of Point A (Application of the theory of shadow in monge projection):  121

5       Properties of Shadows :. 126