New Methods of the Computer Aided Design of Roofs in Descriptive Geometry

1. New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl

2. Roofs shape the landscape Roofs shape the lansdcape Dachy kształtują krajobraz

3. Roofs and their skeletons Roofs shape the lansdcape

4. The roof which has a planar base Roofs shape the lansdcape

5. The roof which does not have a planar base Roofs shape the lansdcape

6. Roofs shape the lansdcape The part regular roof (with court-yard) of the building of the Białystok University and the block of atrial buildings of the Theological Seminary:

7. Roofs shape the lansdcape Student’s works – 2003. Civil Engineering Faculty, I semester Bialystok University of Technology

8. Roof with constraints (the case from first class) we construct as follows: A) Let the base of a roof with constraints (double lines) is given, A1) we embed thisbaseto be a simply connected polygon. A2) we determine a roof generated by thispolygon, A3) we cut out the roof with constraints by means of a boolean operation

9. The determined roof and four projections of it

10. The construction of a roof with constraints (a roof with a niche) a) the base of a roof a1) the indication of the points of additional eaves a3) the determination of a roof generated by thispolygon a2) the polygon of a auxiliary extended base of a roof a5) the roof obtained by of a boolean operation a4) the roof embedded in a regular roof generated by a simple connected polygon a6) the roof obtained after removing the parts of two ridges

11. The construction of a roof with constraints (the case from third class) with two downspout points b) the base of a roof with constraints and downspout points b1) the extended polygon as the base of a roof with two downspout points the eaves with aninfinitesimal length b2) the polygon as the simply connected base of a roof b3) the determination of the roof embedded in a regular roof and boolean operation (intersection) b4) the roof with constraints and two downspout points this eaves must beinfinitesimal

12. Other roof with constraints and downspout this eaves must beinfinitesimal needed correction of a hipped roof end c6) the roof with constraints and one downspout point

13. The determination of a roof with complete constraints the base of a roof with 5 downspout points and five downspout points 5 infinitesimal eaves

14. The construction of an atrial roof (building with court-yards) building with coust-yards a) let us consider a generalized 3-connected polygon a1) we divide this polygon into three parts a2) we decompose the polygon into three parts

15. The construction of atrial roof (building with coust-yards) (continuation) building with coust-yards a3) we extend and complete each part of the polygon to three polygons a4) we determine the roofs generated by each of three polygons

16. The construction of atrial roof (building with coust-yards) (continuation) building with coust-yards a5) we cut out (boolean operations: subtraction or intersection) parts of roofs a6) and prepare the parts of roofs to joining to one object

17. The construction of atrial roof (building with coust-yards) (continuation) Dachy z podwórkami a7) we connect (boolean operations: union) parts of roofs a8, a9) and obtain the inquired roof

18. Roofs shape the lansdcape Thank you very much