Exercise 1 Plane Figures
1 Descriptive Geometrydescriptive and Projection 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 1
descriptive geometry and projection
parallel orthographic projection with planes of projection plumb to one another, but not normal to all object edges
2 descriptive geometry and projection
parallel orthographic projection with planes of projection normal to object edges
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Descriptive Geometry and Projection parallel orthographic projection with planes of projection plumb to one another, but not normal to all objectsdescriptive geometry and projection
parallel orthographic projection with planes of projection plumb to one another, but not normal to all object edges
2 3 Descriptive Geometrydescriptive and Projection geometry and projection parallel orthographic projection with planes of projection oblique to one another, and oblique to mostparallel object edges orthographic projection with planes of projection oblique to one another, and oblique to most object edges
4 3
descriptive geometry and projection
conventions and terminology
vertical projection
horizontal projection
4 descriptive geometry and projection
parallel orthographic projection with planes of projection oblique to one another, and oblique to most object edges
3
descriptive geometry and projection Descriptive Geometry and Projection conventions andconventions termonology and terminology
vertical projection
horizontal projection
5 4 exercise 1a: projections of oblique planes
pin-up: tuesday, sept. 13
Using several methods associated with descriptive geometry, students will generate oblique plane figures, then rotate the planes of projection to find the “true” shape of each oblique. The exercise will begin with an ambiguous set of 4 traces, from which students will construct a figure and a second set of traces, thereby defining a plane in space. After this plane is defined, and projected from edge and frontal positions, students will carefully graft additional plane figures to the first. The result will be a composite drawing that describes the genesis of a faceted surface.
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ARRANGE 4 TRACEarrange POINTS 4 trace IN VERTICAL points in PROJECTION vertical projection
6 6 CONNECT THE POINTSconnect AND the EXTENDpoints andPROJECTOR extend projector LINES lines projector lines are always perpendicular to the axis projector lines are always perpendicular to the axis
7 7
define a plane through the horizontal trace
any three non-colinear points define a plane
8 connect the points and extend projector lines
projector lines are always perpendicular to the axis
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DEFINE A PLANEdefine THROUGH a plane THE throughHORIZONTAL the horizontalTRACE trace any three non-colinear points define a plane any three non-colinear points define a plane
8 8 FIND FOURTH POINTfind fourth USING CROSSINGpoint using LINES crossing lines the ‘marionette’ method acts to ensure planarity of the surface through lines inscribed on its facethe “marionette” method acts to ensure planarity of the surface through lines inscribed on its face
9 9
complete figure in horizontal projection
the composite of both projections now describes a unique plane figure; the next step is to find the “true shape”
10 find fourth point using crossing lines
the “marionette” method acts to ensure planarity of the surface through lines inscribed on its face
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COMPLETE FIGUREcomplete IN HORIZONTAL figure in PROJECTIONhorizontal projection the composite of both projections now describe a unique plane figure; the next step is to find the ‘truethe shape composite’ of both projections now describes a unique plane figure; the next step is to find the “true shape”
10 10 INSCRIBE A LEVELinscribe LINE ONa level THE PLANE line on the plane a level line is horizontal in the vertical projection; it traces the intersection of the oblique plane witha level a second line horizontal is horizontal plane in the vertical projection; it traces the intersection of the oblique plane with a second horizontal plane
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find the level line in the horizontal projection
a projector line from l in the vertical projection meets l in the horizontal projection
12 inscribe a level line on the plane
a level line is horizontal in the vertical projection; it traces the intersection of the oblique plane with a second horizontal plane
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FIND THE LEVELfind LINE the IN THElevel HORIZONTAL line in the PROJECTION horizontal projection 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 NEWestablish VERTICAL a new PLANE vertical PROJECTION plane of 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
use a divider to duplicate distances from the original vertical projection
14 establish a new vertical plane of projection
make this plane perpendicular to the level line in the horizontal projection
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TRANSFER TRACEStransfer TO NEW traces PROJECTION 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 TRANSFER REMAININGtransfer TRACES remaining TO REVEALtraces toEDGE reveal VIEW edge OF PLANEview 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 a new plane of projection
create an axis parallel to the edge view of the oblique plane
16 transfer remaining traces to reveal edge view of plane
by choosing a projection plane perpendicular to the level line, we have assured an edge view
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ESTABLISH A NEWestablish PLANE a OF new PROJECTION plane of 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 TRACEStransfer TO NEWtraces PROJECTION 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
the completed figure is the true shape of the oblique
the true shape is the only cut piece that can be oriented to form the plane figure described
18 transfer traces to new projection plane
again transfer measurements from the previous projection using a divider
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THE COMPLETEthe FIGURE completed IS THE figure TRUE SHAPE is the OF true THE shape OBLIQUE of the 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 PROCESSrepeat this FOR process3 ADJOINING for 3FACES adjoining faces start on one edge in the original projection, add 2 new traces, and describe a new quadrilateral planestart figure on . one edge in the original projection, add 2 new traces, and describe a 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 2 more quadrilateraladd 2 planes more to quadrilateral the open vertices to planes close the to overall the open vertices to close the overall figure. figure.
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build a model of the completed form
using the true shapes of all 4 faces (copied, and scaled if necessary), construct the object from bristol board
make markings to indicate the orientation of the model in relation to the drawing.
20 repeat this process for 3 adjoining faces
start on one edge in the original projection, add 2 new traces, and describe a new quadrilateral plane figure.
repeat all processes necessary to fully define this second plane and find its true shape.
add 2 more quadrilateral planes to the open vertices to close the overall figure.
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BUILD A MODELbuild OF THE a model COMPLETED of the FORMcompleted form using the true shapes of all 4 faces (copied, and scaled if necessary), construct the object from bristolusing board the 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 http://ocw.mit.edu
4.105 Geometric Disciplines and Architecture Skills: Reciprocal Methodologies Fall 2012
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