New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI...
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![Page 1: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/1.jpg)
New Methods of the Computer Aided Design of Roofs in
Descriptive Geometry
Edwin KOŹNIEWSKI
Białystok University of Technology
Poland
![Page 2: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/2.jpg)
Roofs shape the landscape
Dachy kształtują krajobraz
Roofs shape the lansdcape
![Page 3: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/3.jpg)
Roofs and their skeletons
Roofs shape the lansdcape
![Page 4: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/4.jpg)
The roof which has a planar base
Roofs shape the lansdcape
![Page 5: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/5.jpg)
The roof which does not have a planar base
Roofs shape the lansdcape
![Page 6: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/6.jpg)
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:
![Page 7: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/7.jpg)
Student’s works – 2003.
Civil Engineering Faculty, I semester
Bialystok University of Technology
Roofs shape the lansdcape
![Page 8: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/8.jpg)
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
![Page 9: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/9.jpg)
The determined roof and four projections of it
![Page 10: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/10.jpg)
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
![Page 11: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/11.jpg)
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
![Page 12: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/12.jpg)
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
![Page 13: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/13.jpg)
The determination of a roof with complete constraints
the base of a roof with 5 downspout
points
5 infinitesimal
eaves
and
five downspout points
![Page 14: New Methods of the Computer Aided Design of Roofs in Descriptive Geometry Edwin KOŹNIEWSKI Białystok University of Technology Poland edwikozn@pb.bialystok.pl.](https://reader036.fdocuments.in/reader036/viewer/2022062806/56649f135503460f94c278df/html5/thumbnails/14.jpg)
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 partsa) let us consider a generalized 3-connected polygon
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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)
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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)
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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)
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Thank you very much
Roofs shape the lansdcape