GG303 Lecture 3 8/24/03 1

ORTHOGRAPHIC PROJECTIONS

I Main Topics AIntroduction to orthographic projections B Three rules C Examples II Introduction to orthographic projections A Provide two-dimensional representations of objects B Points are projected such that lines of projection are all parallel and hence are all perpendicular to a single plane C Points project as points DA line projects as a point only if viewed parallel to its length EA plane projects as a line only if viewed edge-on (parallel to the plane) F Principal views 1 Portray object most simply 2 Plane figures appear in true size and shape 3 Lines appear in true length 4 Principal view directions are perpendicular to each other 5 Three principal views needed to describe objects IIIThree rules A The lines of sight for any two adjacent views of an object must be perpendicular. Two adjacent views share a common edge. B Every point on an object in one view must be aligned on a parallel directly opposite the corresponding point in an adjacent view (in other words, all tie lines connecting points in adjacent views are parallel). CThe distance between any two points on an object as measured along one of the aforementioned parallels must be the same in all related views. All views that are adjacent to one particular view are called related views. IV Examples A Points B Lines C Planes

Stephen Martel 3 - 1 University of Hawaii GG303 Lecture 3 8/24/03 2

Orthographic Projections of a Point Fig. 3.1

PT zP PT x PR P T T R T F F F R zP xP PF PR PF The front and right views are both Here the right view is drawn adjacent to adjacent to the top view. The front view is the front view. The top and right views perpendicular to the top view, and the top are related. The top and right views are view is perpendicular to the right view ; both adjacent to the front view. Both the adjacent views are perpendicular to each top and right views give the distance other. The projection or tie lines (thin lines) xP of point P from the front. are viewing direction lines and are perpen- dicular to the fold lines (dashed ilnes). The front view (F) and right view (R) are related. Two adjacent views give enough information Note: In the figures here, the to construct a third view. For example, the distances here are labeled with top view and front view could be used to x being the distance from the construct the right view: Point P is on front view, y being the distance projection lines perpendicular to the fold from the left view, and z being lines, and the front view tells us that point P is the distance down from the top. a distance zP from the top. Similarly, the This is equivalent to putting front view could be created from the top view the coordinate origin where the and the right view. Both the front and right views top, front, and left views intersect. give the distance zP of point P from the top. This arrangement is right-handed.

z P P R

PT PT T A xP T T F F F B xP PB zP PF PF The front view and view "A" are related. The top and view "B" are related. Both are adjacent to the top view, and both Both are adjacent to the front view, and both give the distance zP of point P from the top. give the distance xP of point P from the front.

Stephen Martel 3 - 2 University of Hawaii GG303 Lecture 3 8/24/03 3

Orthographic Projections of a Line Fig. 3.2

B B z T T B BR AT AT z A AR x xB A T R T T F F zB zB z zA A BF BF

AF AF A line is defined by two points. Suppose This is how line AB projects into a right view we have with the information above. The adjacent to the top view. We just use the two views provide information on the procedure for projecting a single point twice, left-right, up-down, and front-back once for each point, and connect the dots. coordinates of the points, so that gives complete information on their positions. True length of line AB

AC Plunge BC C D zA ADBD zB rB C End-on view BT rB of line AB AT T BT AT x x xA BxA B T T

F F R F z x B B B R zA BF BF

xA AF AR AF This is how line AB would project into To find the length and plunge of AB we take a a right view adjacent to the front view. cross section parallel to the trend of the line (the trend is given in the top view). The length and plunge are in view C, adjacent to the top. A view "down the line" gives the end-on view of the line (view D) in which the line appears as a point.

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Orthographic Projection of a Plane Fig. 3.3

(4) Three points define a plane. N BT The two adjacent views here give complete information on (3) AT the positions of three points CT defining plane ABC. This (1) information might come from T 5 B a cross section or a map. 4 F F 3 Suppose we want to know the 2 AF strike and dip of plane ABC. Elevation 1 C We first need to find the strike 0 F of the plane. The line of strike is a horizontal line in plane ABC. (4) N BT We find the line of strike Line of strike (3) D by intersecting a horizontal (3) T AT plane with plane ABC. CT We start with a vertical view (1) (here that is the front view F) and T 5 B then project the line of strike into 4 F F the top view T. The strike of the 3 DF plane is measured in the top view 2 AF by finding the direction of the Elevation 1 0 CF (horizontal) line of strike. The Horizontal plane numbers in parentheses in the top

view are elevations, taken from the A

front view. T

A

B

z

A

B (4) ,D

N BT A

Take an auxiliary view cross section A

(3) A z

perpendicular to the line of strike D A T C

line A (3) C to get the dip of the plane. The z T Dip

CT

of strike will be viewed end-on and 0

1

2

Elevation

(1) 3

4 horizontally, and it will appear as a 5 T point. The plane will appear edge-on 5 z zA F BF B zA as a line. The inclination of the plane 4 D z below the horizontal is the dip; it is 3 F C 2 AF measured here in view A. Because Elevation 1 the top plane T is horizontal, the 0 CF intersection of T and A is horizontal. Horizontal plane

Stephen Martel 3 - 4 University of Hawaii