Exercise 1Plane Figures

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Descriptive Geometry and Projectionparallel orthographic projection with planes of projection normal to object edges

parallel orthographic projection with planes of projection normal to object edges

descriptive geometry and projection

parallel orthographic projection with planes of projection plumb to one another, but not normal to all object edges

descriptive geometry and projection

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parallel orthographic projection with planes of projection normal to object edges

descriptive geometry and projection

parallel orthographic projection with planes of projection plumb to one another, but not normal to all object edges

descriptive geometry and projection

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Descriptive Geometry and Projectionparallel orthographic projection with planes of projection plumb to one another, but not normal to all objects

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Descriptive Geometry and Projectionparallel orthographic projection with planes of projection oblique to one another, and oblique to most object edgesparallel orthographic projection with planes of projection oblique to one another,

and oblique to most object edges

descriptive geometry and projection

vertical projection

horizontal projection

conventions and terminology

descriptive geometry and projection

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parallel orthographic projection with planes of projection oblique to one another, and oblique to most object edges

descriptive geometry and projection

vertical projection

horizontal projection

conventions and terminology

descriptive geometry and projection

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Descriptive Geometry and Projectionconventions and termonology

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pin-up: tuesday, sept. 13

exercise 1a: projections of oblique planes

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.

arrange 4 trace points in vertical projection

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ARRANGE 4 TRACE POINTS IN VERTICAL PROJECTION

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connect the points and extend projector lines

projector lines are always perpendicular to the axis

define a plane through the horizontal trace

any three non-colinear points define a plane

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CONNECT THE POINTS AND EXTEND PROJECTOR LINESprojector lines are always perpendicular to the axis

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connect the points and extend projector lines

projector lines are always perpendicular to the axis

define a plane through the horizontal trace

any three non-colinear points define a plane

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DEFINE A PLANE THROUGH THE HORIZONTAL TRACEany three non-colinear points define a plane

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find fourth point using crossing lines

the marionette method acts to ensure planarity of the surface through lines inscribed on its face

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

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FIND FOURTH POINT USING CROSSING LINESthe marionette method acts to ensure planarity of the surface through lines inscribed on its face

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find fourth point using crossing lines

the marionette method acts to ensure planarity of the surface through lines inscribed on its face

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

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COMPLETE FIGURE IN HORIZONTAL PROJECTIONthe composite of both projections now describe a unique plane figure; the next step is to find the true shape

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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

find the level line in the horizontal projection

a projector line from l in the vertical projection meets l in the horizontal projection

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INSCRIBE A LEVEL LINE ON THE PLANEa 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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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

find the level line in the horizontal projection

a projector line from l in the vertical projection meets l in the horizontal projection

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FIND THE LEVEL LINE IN THE HORIZONTAL PROJECTIONa projector line from l in the vertical projection meets l in the horizontal projection

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establish a new vertical plane of projection

make this plane perpendicular to the level line in the horizontal projection

transfer traces to new projection

use a divider to duplicate distances from the original vertical projection

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ESTABLISH A NEW VERTICAL PLANE PROJECTIONmake this plane perpendicular to the level line in the horizontal projection

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establish a new vertical plane of projection

make this plane perpendicular to the level line in the horizontal projection

transfer traces to new projection

use a divider to duplicate distances from the original vertical projection

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TRANSFER TRACES TO NEW PROJECTIONuse a divider to duplicate distances from the original vertical projection

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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

establish a new plane of projection

create an axis parallel to the edge view of the oblique plane

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TRANSFER REMAINING TRACES TO REVEAL EDGE VIEW OF PLANEby chosing a projection plane perpendicular to the level line, we have assured an edge view

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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

establish a new plane of projection

create an axis parallel to the edge view of the oblique plane

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ESTABLISH A NEW PLANE OF PROJECTIONcreate an axis parallel to the edge view of the oblique plane

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transfer traces to new projection plane

again transfer measurements from the previous projection using a divider

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

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TRANSFER TRACES TO NEW PROJECTION PLANEagain transfer measurements from the previous projection using a divider

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transfer traces to new projection plane

again transfer measurements from the previous projection using a divider

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

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THE COMPLETE FIGURE IS THE TRUE SHAPE OF THE OBLIQUEthe true shape is the only cut piece that can be oriented to form the plane figure described

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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.

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.

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REPEAT THIS PROCESS FOR 3 ADJOINING FACESstart 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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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.

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.

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BUILD A MODEL OF THE COMPLETED FORMusing 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.

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01 Introduction