Multiview orthographic projection

Symbols used to dene whether a projection is either First Angle(left) or Third Angle (right).

In technical drawing and computer graphics, amultivieworthographic projection is an illustration technique inwhich up to six pictures of an object are produced, witheach projection plane parallel to one of the coordinateaxes of the object.[1]

The views are positioned relative to each other accordingto either of two schemes: rst-angle or third-angle pro-jection. In each, the appearances of viewsmay be thoughtof as being projected onto planes that form a 6-sided boxaround the object.

1 First-angle projectionIn rst-angle projection, the object is conceptually lo-cated in quadrant I, i.e. it oats above and before theviewing planes, the planes are opaque, and each view ispushed through the object onto the plane furthest fromit. (Mnemonic: an actor on a stage.) Extending to the6-sided box, each view of the object is projected in thedirection (sense) of sight of the object, onto the (opaque)interior walls of the box; that is, each view of the object isdrawn on the opposite side of the box. A two-dimensionalrepresentation of the object is then created by unfoldingthe box, to view all of the interior walls. This producestwo plans and four elevations. A simpler way to visualizethis is to place the object on top of an upside-down bowl.Sliding the object down the right edge of the bowl revealsthe right side view.

Image of object in box, with views of object pro-jected in the direction of sight onto walls using rst-angle projection.

Similar image showing the box unfolding fromaround the object.

Image showing orthographic views located relativeto each other in accordance with rst-angle projec-tion.

2 Third-angle projection

An example of a multiview orthographic drawing from a USPatent (1913), showing two views of the same object. Third an-gle projection is used.

In third-angle projection, the object is conceptually lo-cated in quadrant III, i.e. it is positioned below andbehind the viewing planes, the planes are transparent,and each view is pulled onto the plane closest to it.(Mnemonic: a shark in a tank, esp. that is sunken intothe oor.) Using the 6-sided viewing box, each view ofthe object is projected opposite to the direction (sense)of sight, onto the (transparent) exterior walls of the box;that is, each view of the object is drawn on the same sideof the box. The box is then unfolded to view all of itsexterior walls. A simpler way to visualize this is to placethe object in the bottom of a bowl. Sliding the object upthe right edge of the bowl reveals the right side view.Here is the construction of third angle projections of thesame object as above. Note that the individual views arethe same, just arranged dierently.

1

2 4 MULTIVIEWS WITHOUT ROTATION

3 Additional informationFirst-angle projection is as if the object were sitting onthe paper and, from the face (front) view, it is rolled tothe right to show the left side or rolled up to show its bot-tom. It is standard throughout Europe and Asia (exclud-ing Japan). First-angle projection was widely used in theUK, but during World War II, British drawings sent to bemanufactured in the USA, had to be drawn in third-angleprojection. This historical position of the UK means thatsome British companies completely adopted third angleprojection. BS 308 (Part 1) Engineering Drawing Prac-tice, gave the option of using both projections, but gen-erally every illustration (other than the ones explainingthe dierence between rst and third-angle) was done inrst-angle. After the withdrawal of BS 308 in 1999, BS8888 oered the same choice since it referred directly toISO 5456-2, Technical drawings Projection methods Part 2: Orthographic representations.Third-angle is as if the object were a box to be unfolded.If we unfold the box so that the front view is in the centerof the two arms, then the top view is above it, the bottomview is below it, the left view is to the left, and the rightview is to the right. It is standard in the USA (ASMEY14.3-2003 species it as the default projection system),Japan (JIS B 0001:2010 species it as the default projec-tion system), Canada, and Australia.Both rst-angle and third-angle projections result in thesame 6 views; the dierence between them is the arrange-ment of these views around the box.A great deal of confusion has ensued in drafting roomsand engineering departments when drawings are trans-ferred from one convention to another. On engineeringdrawings, the projection angle is denoted by an interna-tional symbol consisting of a truncated cone, respectivelyfor rst-angle and third-angle:http://www3.ul.ie/~{}rynnet/orthographic_projection_fyp/images/projection_symbols.pngThe 3D interpretation of the symbol can be deduced byenvisioning a solid truncated cone, standing upright withits large end on the oor and the small end upward. Thetop view is therefore two concentric circles (donut). Inparticular, the fact that the inner circle is drawn with asolid line instead of dashed identies this view as the topview, not the bottom view.

In third-angle projection, the top view is pusheddown to the oor, and the front view is pushedback to the rear wall; the intersection line betweenthese two planes is therefore closest to the large endof the cone, hence the third-angle symbol shows thecone with its large end open toward the donut.

In rst-angle projection, the top view is pulled upto the ceiling, and the front view is pulled forwardto the front wall; the intersection line between the

two planes is thus closest to the small end of thecone, hence the rst-angle symbol shows the conewith its large end away from the donut.

4 Multiviews without rotationOrthographic multiview projection is derived from theprinciples of descriptive geometry and may produce animage of a specied, imaginary object as viewed fromany direction of space. Orthographic projection is distin-guished by parallel projectors emanating from all pointsof the imaged object and which intersect of projectionat right angles. Above, a technique is described that ob-tains varying views by projecting images after the objectis rotated to a desired position.Descriptive geometry customarily relies on obtaining var-ious views by imagining an object to be stationary, andchanging the direction of projection (viewing) in orderto obtain the desired view.See Figure 1. Using the rotation technique above, notethat no orthographic view is available looking perpendic-ularly at any of the inclined surfaces. Suppose a tech-nician desired such a view to, say, look through a holeto be drilled perpendicularly to the surface. Such a viewmight be desired for calculating clearances or for dimen-sioning purposes. To obtain this view without multiplerotations requires the principles of Descriptive Geome-try. The steps below describe the use of these principlesin third angle projection.

Figures one through nine.

Fig.1: Pictorial of imaginary object that the techni-cian wishes to image.

Fig.2: The object is imagined behind a vertical planeof projection. The angled corner of the plane of pro-jection is addressed later.

Fig.3: Projectors emanate parallel from all points ofthe object, perpendicular to the plane of projection.

Fig.4: An image is created thereby.

Fig.5: A second, horizontal plane of projection isadded, perpendicular to the rst.

5.2 Elevation 3

Fig.6: Projectors emanate parallel from all pointsof the object perpendicular to the second plane ofprojection.

Fig.7: An image is created thereby. Fig.8: A third plane of projection is added, perpen-dicular to the previous two.

Fig.9: Projectors emanate parallel from all points ofthe object perpendicular to the third plane of pro-jection.

Figures ten through seventeen.

Fig.10: An image is created thereby. Fig.11: A fourth plane of projection is added par-allel to the chosen inclined surface, and per force,perpendicular to the rst (Frontal) plane of projec-tion.

Fig.12: Projectors emanate parallel from all pointsof the object perpendicularly from the inclined sur-face, and per force, perpendicular to the fourth(Auxiliary) plane of projection.

Fig.13: An image is created thereby. Fig.14-16: The various planes of projection are un-folded to be planar with the Frontal plane of projec-tion.

Fig.17: The nal appearance of an orthographicmultiview projection and which includes an"Auxiliary view" showing the true shape of aninclined surface.

5 Views

5.1 SectionSee also: Cross section (geometry)

A section, or cross-section, is a view of a 3-dimensionalobject from the position of a plane through the object.

A cross section is a common method of depicting the in-ternal arrangement of a 3-dimensional object in two di-mensions. It is often used in technical drawing and istraditionally crosshatched. The style of crosshatching in-dicates the type of material the section passes through.With computed axial tomography, computers constructcross-sections from x-ray data.

A 3-D view of a beverage-can stove with a cross-section in yellow.

A 2-D cross-sectional view of a compression seal. Half-section of a Porsche 996

5.2 Elevation

Principal faade of the Panthon, Paris, by Jacques-GermainSouot.

An elevation is a view of a 3-dimensional object fromthe position of a vertical plane beside an object. In otherwords, an elevation is a side-view as viewed from thefront, back, left or right (and referred to as a front ele-vation, [left/ right] side elevation, and a rear elevation).It is the corollary to the concept of a view (which is al-ways overhead and is therefore referred to as an overheadview).An elevation is a common method of depicting the exter-nal conguration and detailing of a 3-dimensional objectin two dimensions. Building faades are shown as eleva-tions in architectural drawings and technical drawings.Elevations are the most common orthographic projectionfor conveying the appearance of a building from the ex-terior. Perspectives are also commonly used for this pur-pose. A building elevation is typically labeled in rela-tion to the compass direction it faces; the direction from

4 8 EXTERNAL LINKS

which a person views it. E.g. the North Elevation of abuilding is the side that most closely faces true north onthe compass.[2]

Interior elevations are used to show detailing such asmillwork and trim congurations.In the building industry elevations are a non-perspectiveview of the structure. These are drawn to scale so thatmeasurements can be taken for any aspect necessary.Drawing sets include front, rear and both side elevations.The elevations specify the composition of the dierentfacades of the building, including ridge heights, the posi-tioning of the nal fall of the land, exterior nishes, roofpitches and other architectural details.

5.2.1 Developed Elevation

A developed elevation is a variant of a regular elevationview in which several adjacent non-parallel sides may beshown together, as if they have been unfolded. For exam-ple, the north and west views may be shown side-by-side,sharing an edge, even though this does not represent aproper orthographic projection.

5.3 Plan

See also: Floor plan

A plan is a view of a 3-dimensional object from the po-sition of a horizontal plane through, above, or below theobject. In such views, the portion of the object in frontof the plane is omitted to reveal what lies beyond. In thecase of a oor plan, the roof and upper portion of thewalls may be omitted. Elevations, top (roof) plans, andbottom plans are orthographic projections, but they arenot sections as their viewing plane is outside of the ob-ject.A plan is a common method of depicting the internal ar-rangement of a 3-dimensional object in two dimensions.It is often used in technical drawing and is traditionallycross-hatched. The style of crosshatching indicates thetype of material the section passes through.

5.4 Auxiliary view

An auxiliary view is a view taken from an angle that isnot one of the primary views.[3][4] An auxiliary view isa view at an angle used to give deeper insight into theactual shape of the object. An auxiliary view is used toshow a slanted surface in true size and shape. This is ac-complished by providing a view that is perpendicular tothe slanted surface.

An auxiliary view next to three primary views.

Another example of an auxiliary view (rather than aprimary view from an orthographic projection).

These allow the true shape/dimension of features at anyangle relative to the main views to be shown .

6 See also Architectural drawing Cross section (geometry) Engineering drawing Graphical projection Plans (drawings)

7 References[1] Ingrid Carlbom, Joseph Paciorek (1978), Planar

Geometric Projections and Viewing Transforma-tions, ACM Computing Surveys 10 (4): 465502,doi:10.1145/356744.356750

[2] Ching, Frank (1985),Architectural Graphics - Second Edi-tion, New York: Van Norstrand Reinhold, ISBN 0-442-21862-1

[3] Illustrator Draftsman 3& 2 - Volume 2 Standard Practicesand Theory, pages 3/49-3/50, from tpub.com

[4] Dorn, Dennis; Mark Shanda (1992), Drafting for the the-atre, SIU Press, p. 90, ISBN 0-8093-1508-4

BS 308 (Part 1) Engineering Drawing Practice BS 8888Technical product documentation and specication ISO5456-2 Technical drawings Projection methods Part2: Orthographic Representations (includes the truncatedcone symbol)

8 External links Educational website describing the principles of rstand third angle projectionUniversity of Limerick

Educational website describing the principles of rstand third angle projection

Images tagged Elevation on Flickr.com

59 Text and image sources, contributors, and licenses9.1 Text

Multiview orthographic projection Source: http://en.wikipedia.org/wiki/Multiview%20orthographic%20projection?oldid=655799988Contributors: Rich Farmbrough, Mdd, Grutness, Firien, Rjwilmsi, Bgwhite, NawlinWiki, DVD R W, SmackBot, GoodDay, Peter Horn,PKT, Epbr123, Maximilian Schnherr, 1Rabid Monkey, PhilKnight, John85710, Rickterp, Hasanisawi, SharkD, Robprain, Lears Fool,DesmondW, Sfan00 IMG, The Thing That Should Not Be, Robert Skyhawk, Stepheng3, Versus22, Addbot, Some jerk on the Internet,Luckas-bot, Fraggle81, AnomieBOT, KDS4444, Bussard, Neptune5000, MegaPedant, GenQuest, Miym, BenzolBot, Citation bot 1, Vre-nator, Clarkcj12, Ripchip Bot, John of Reading, Orphan Wiki, Penom, Wikipelli, F, Wkollar, Jay-Sebastos, Pun, ClueBot NG, Widr,Helpful Pixie Bot, BG19bot, ElphiBot, Malik6040, Mdann52, Mark viking, Jodosma, Skr15081997, Mike crowfone, RecordPlayerUSA,Amanlamalayu and Anonymous: 47

9.2 Images File:Axonometric_projection.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/48/Axonometric_projection.svg License:

Public domain Contributors: This vector image was created with Inkscape. Original artist: Yuri Raysper File:Convention_placement_vues_dessin_technique.svg Source: http://upload.wikimedia.org/wikipedia/commons/4/4d/Convention_

placement_vues_dessin_technique.svg License: CC-BY-SA-3.0 Contributors: Vector version of Image:Convention placement vues dessintechnique.png. Original artist: Fvasconcellos (talk contribs), original drawing by Christophe Dang Ngoc Chan

File:One_thru_Nine_Step_by_Step_Orthographic_Auxiliary_Projection2.png Source: http://upload.wikimedia.org/wikipedia/en/2/23/One_thru_Nine_Step_by_Step_Orthographic_Auxiliary_Projection2.png License: Cc-by-sa-3.0 Contributors: ? Original artist: ?

File:Orthographic_example.gif Source: http://upload.wikimedia.org/wikipedia/en/8/8c/Orthographic_example.gif License: PD Con-tributors: ? Original artist: ?

File:Panthon_Soufflot_-_levation_principale.png Source: http://upload.wikimedia.org/wikipedia/commons/1/14/Panth%C3%A9on_Soufflot_-_%C3%A9levation_principale.png License: Public domain Contributors: Paris BNF, cabinet des estampes Originalartist: Jacques-Germain Souot

File:Question_book-new.svg Source: http://upload.wikimedia.org/wikipedia/en/9/99/Question_book-new.svg License: Cc-by-sa-3.0Contributors:Created from scratch in Adobe Illustrator. Based on Image:Question book.png created by User:Equazcion Original artist:Tkgd2007

File:Ten_through_Seventeen_Step_by_Step_Orthographic_Auxiliary_Projection.png Source: http://upload.wikimedia.org/wikipedia/en/1/15/Ten_through_Seventeen_Step_by_Step_Orthographic_Auxiliary_Projection.png License: Cc-by-sa-3.0 Contributors:? Original artist: ?

9.3 Content license Creative Commons Attribution-Share Alike 3.0

First-angle projectionThird-angle projectionAdditional informationMultiviews without rotationViewsSectionElevationDeveloped Elevation

PlanAuxiliary view

See alsoReferencesExternal links Text and image sources, contributors, and licensesTextImagesContent license