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 Dachy kształtują krajobraz Roofs shape the lansdcape

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

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 this base to be a simply connected polygon. A2) we determine a roof generated by this polygon, 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 a2) the polygon of a auxiliary extended base of a roof a3) the determination of a roof generated by this polygon a4) the roof embedded in a regular roof generated by a simple connected polygon a5) the roof obtained by of a boolean operation 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 b3) the determination of the roof embedded in a regular roof and boolean operation (intersection) b1) the extended polygon as the base of a roof with two downspout points b2) the polygon as the simply connected base of a roof b4) the roof with constraints and two downspout points b) the base of a roof with constraints and downspout points the eaves with an infinitesimal length this eaves must be infinitesimal

12. Other roof with constraints and downspout needed correction of a hipped roof end this eaves must be infinitesimal 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 5 infinitesimal eaves and five downspout points

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

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

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

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

18. Thank you very much Roofs shape the lansdcape