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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 http://ocw.mit.edu
4.105 Geometric Disciplines and Architecture Skills: Reciprocal Methodologies Fall 2012
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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 http://ocw.mit.edu
4.105 Geometric Disciplines and Architecture Skills: Reciprocal Methodologies Fall 2012
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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