Exercise 1
Plane Figures
1
Descriptive Geometry
and Projection
descriptive
geometry and projection
parallel orthographic projection with planes of projection normal to object edges
parallel orthographic projection with planes of projection normal to object edges
2
Descriptive Geometry and Projection
parallel orthographic projection with planes of projection plumb to one another,
but not normal to all objects
descriptive
geometry and projection
parallel orthographic projection with planes of projection plumb to one another,
but not normal to all object edges
2
3
descriptive
geometry and projection
Descriptive Geometry
and Projection
parallel orthographic projection with planes of projection oblique to one another,
parallel
orthographic
and oblique to most
object edges
projection with planes of projection oblique to one another,
and oblique to most object edges
4
descriptive geometry and projection
Descriptive Geometry and Projection
conventions and
termonology
conventions
and terminology
vertical projection
horizontal projection
5
arrange
4 trace
points in
vertical projection
ARRANGE 4 TRACE
POINTS
IN VERTICAL
PROJECTION
6
6
connectAND
the EXTEND
points and
extend projector
lines
CONNECT THE POINTS
PROJECTOR
LINES
projector lines are always perpendicular to the axis
projector lines are always perpendicular to the axis
7
7
define
a plane
the horizontal
trace
DEFINE A PLANE
THROUGH
THE through
HORIZONTAL
TRACE
any three non-colinear points define a plane
any three non-colinear points define a plane
8
8
find fourth
point using
crossing lines
FIND FOURTH POINT
USING CROSSING
LINES
the ‘marionette’ method acts to ensure planarity of the surface through lines
the “marionette” method acts to ensure planarity of the surface through lines
inscribed on its face
inscribed on its face
9
9
complete
figure in PROJECTION
horizontal projection
COMPLETE FIGURE
IN HORIZONTAL
the composite of both projections now describe a unique plane figure; the next
theshape
composite
step is to find the ‘true
’
of both projections now describes a unique plane figure; the next step is to find
the “true shape”
10
10
inscribe
a level
line on the plane
INSCRIBE A LEVEL
LINE ON
THE PLANE
a level line is horizontal in the vertical projection; it traces the intersection of
a level line is horizontal in the vertical projection;
it traces the intersection of the oblique plane with a second horizontal plane
the oblique plane with a second horizontal plane
11
11
find
the
level
line in thePROJECTION
horizontal projection
FIND THE LEVEL
LINE
IN THE
HORIZONTAL
a projector line from l in the vertical projection meets l in the horizontal
projection
a projector line from l in the vertical projection meets l in the horizontal projection
12
12
establish
a new
vertical
plane of projection
ESTABLISH A NEW
VERTICAL
PLANE
PROJECTION
make this plane perpendicular to the level line in the horizontal projection
make this plane perpendicular to the level line in the horizontal projection
13
13
transfer
traces
to new projection
TRANSFER TRACES
TO NEW
PROJECTION
use a divider to duplicate distances from the original vertical projection
use a divider to duplicate distances from the original vertical projection
14
14
transferTRACES
remaining
traces to
reveal
view of plane
TRANSFER REMAINING
TO REVEAL
EDGE
VIEWedge
OF PLANE
by chosing a projection plane perpendicular to the level line, we have assured an edge
view
by choosing a projection plane perpendicular to the level line, we have assured an edge view
15
15
establish
new
plane of projection
ESTABLISH A NEW
PLANEaOF
PROJECTION
create an axis parallel to the edge view of the oblique plane
create an axis parallel to the edge view of the oblique plane
16
16
transfer
traces
to new projection
TRANSFER TRACES
TO NEW
PROJECTION
PLANE plane
again transfer measurements from the previous projection using a divider
again transfer measurements from the previous projection using a divider
17
17
completed
is theOF
true
of the oblique
THE COMPLETEthe
FIGURE
IS THEfigure
TRUE SHAPE
THEshape
OBLIQUE
the true shape is the only cut piece that can be oriented to form the plane figure
described
the true shape is the only cut piece that can be oriented to form the plane figure described
18
18
repeat this
for 3FACES
adjoining faces
REPEAT THIS PROCESS
FOR process
3 ADJOINING
start on one edge in the original projection, add
2 new traces, and describe a
start on one edge in the original projection, add 2 new traces, and describe a new
quadrilateral plane figure.
new quadrilateral plane figure.
repeat all processes necessary to fully define this second plane and find its
true shape.
repeat all processes necessary to fully define this second plane and find its true shape.
add 2planes
moretoquadrilateral
the open vertices to close the overall figure.
2 more quadrilateral
the open vertices toplanes
close theto
overall
figure.
add
19
19
build
a model
of the FORM
completed form
BUILD A MODEL
OF THE
COMPLETED
using the true shapes of all
4 faces (copied, and scaled if necessary), construct
using
the
the object from bristol
board
true shapes of all 4 faces (copied, and scaled if necessary),
construct the object from bristol board
make marking to indicate the orientation of the model in relation to the drawing.
make markings to indicate the orientation of the model in relation to the drawing.
20
20
MIT OpenCourseWare
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4.105 Geometric Disciplines and Architecture Skills: Reciprocal Methodologies
Fall 2012
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