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New Methods of the Computer Aided Design of Roofs in
Descriptive Geometry
Edwin KOŹNIEWSKI
Białystok University of Technology
Poland
Roofs shape the landscape
Dachy kształtują krajobraz
Roofs shape the lansdcape
Roofs and their skeletons
Roofs shape the lansdcape
The roof which has a planar base
Roofs shape the lansdcape
The roof which does not have a planar base
Roofs shape the lansdcape
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:
Student’s works – 2003.
Civil Engineering Faculty, I semester
Bialystok University of Technology
Roofs shape the lansdcape
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
The determined roof and four projections of it
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
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
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
The determination of a roof with complete constraints
the base of a roof with 5 downspout
points
5 infinitesimal
eaves
and
five downspout points
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
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)
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)
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)
Thank you very much
Roofs shape the lansdcape
