Department of Architectural Representation
Descriptive Geometry 2
2015 spring semester
3rd drawing
In graphite pencil or ink: 420x594 mm
Submission deadline: May 4, 2015
Titles:
HYPRBOLIC PARABOLOID IN PERSPECTIVE, CIRCULAR CONOID SHADE IN
PERSPECTIVE, HELICAL SURFACE, EARTH WORKS, COMPOSITE SURFACE OF
HYPRBOLIC PARABOLOIDS IN AXONOMETRY
1. Let a saddle surface be defined by the skew quadrilateral frame, The top view is a rhombus
of the side length of 9 cm and the angles are 60°/120°. Round the vertices at obtuse angles by
the arcs of the inscribed circle. Represent the saddle surface with the top view of the
“rounded rhombus” in perspective such that a pair of opposite vertices of the skew
quadrilateral are of the height of 9 cm. Construct shadows and shades.
2. Represent a right circular conoid shade in perspective. The director semi-circle lies in the
picture plane higher than the horizon and the dirctrix is parallel to the horizon. Construct the
generators, the contour points, draw the contour. Show the visibility if the generators. With a
proper direction of lighting not parallel to the picture plane construct all shadows.
3. Construct one pitch of a helix on the surface of a horizontal cylinder lying on the first image
plane. Reflect the helix for the axis and draw 13 rulings of the helicoid that is defined by the
transversals of the two helixes. Construct contour points, draw the contour curve and show
the visibility of the rulings. Chose a generator and construct the first tracing lines of the
tangent planes of the surface at the endpoint and a quarter point of the ruling.
4. The Figure represents a topographical map with a road and platform. The scale is M 1:200,
the slope of the road is 10 %, the slope of cut is R b =4/4, the slope of fill is Rf=6/4. Construct
the neutral lines, the surfaces of cuts and fills with contour lines and the lines of the top of the
cut and the toe of the fill with the topmost and lowest points. Construct sections at the meter
levels of the road. (Color code: earth surface – light brown, cut – dark brown, fill – green,
road and platform – gray.)
5. Construct a cube in orthogonal axonometry, Define two skew quadrilaterals such that the
quadrilaterals have an edge in common, connecting the centre of the top face and the vertex
of the base square closest to the observer. Two more vertices are the midpoints of the edges
of the base square starting from the vertex mentioned above. The midpoints of edges of the
top square above the previous points are also vertices of the skew quadrilaterals. Represent
the two hyperbolic paraboloids defined by the quadrilaterals, find the saddle points and the
principal sections. Construct the projected shadow of one on the other at a proper direction of
lighting.
March 30, 2015, Budapest
dr. Pál Ledneczki
associate professor
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