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Unformatted text preview: 8/25/11 3. ORTHOGRAPHIC PROJECTIONS I Main Topics A IntroducBon to orthographic projecBons B Three rules C Examples 8/25/11 GG303 1 3. ORTHOGRAPHIC PROJECTIONS II IntroducBon to orthographic projecBons A Provide two
dimensional representaBons of objects B Points are projected such that lines of projecBon are all parallel and hence are all perpendicular to a single plane C Points project as points D A line projects as a point only if viewed parallel to its length E A plane projects as a line only if viewed edge
on
(parallel to the plane) 8/25/11 GG303 2 1 8/25/11 3. ORTHOGRAPHIC PROJECTIONS 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 direcBons are perpendicular to each other 5 Three principal views needed to describe objects 8/25/11 GG303 3 3. ORTHOGRAPHIC PROJECTIONS III Three 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 Be lines connecBng points in adjacent views are parallel). C The distance between any two points on an object as measured along one of the aforemenBoned parallels must be the same in all related views. All views that are adjacent to one parBcular view are called related views. 8/25/11 GG303 4 2 8/25/11 3. ORTHOGRAPHIC PROJECTIONS IVExamples A Points B Lines C Planes 8/25/11 GG303 5 8/25/11 GG303 6 3 8/25/11 Orthographic ProjecBons of a Point Fig. 3.1.a The front and right views are both adjacent to the top view. The front view is perpendicular to the top view, and the top view is perpendicular to the right view ; adjacent views are perpendicular to each other. The projecBon or Be lines (thin lines) are viewing direcBon lines and are perpendicular to the fold lines (dashed lines). The front view (F) and right view (R) are related. Two adjacent views give enough informaBon to construct a third view. For example, the top view and front view could be used to construct the right view: Point P is on projecBon lines perpendicular to the fold lines, and the front view tells us that point P is a distance zP from the top. Similarly, the front view could be created from the top view and the right view. Both the front and right views give the distance zP of point P from the top. 8/25/11 x =distance from the front view, y =distance from the lea view, z =distance down from the top. Right
handed coordinate origin where the top, front, and lea views intersect. GG303 7 Orthographic ProjecBons of a Point Fig. 3.1.b Here the right view is drawn adjacent to the front view. The top and right views are related. The top and right views are both adjacent to the front view. Both the top and right views give the distance xP of point P from the front. 8/25/11 GG303 8 4 8/25/11 Orthographic ProjecBons of a Point Fig. 3.1.c The front view and view "A" are related. Both are adjacent to the top view, and both give the distance zP of point P from the top. 8/25/11 GG303 9 Orthographic ProjecBons of a Point Fig. 3.1.d The top and view "B" are related. Both are adjacent to the front view, and both give the distance xP of point P from the front. 8/25/11 GG303 10 5 8/25/11 Orthographic ProjecBons of a Line Fig. 3.2.a A line is deﬁned by two points. Suppose we have with the informaBon above. The two views provide informaBon on the lea
right, up
down, and front
back coordinates of the points, so that gives complete informaBon on their posiBons. 8/25/11 GG303 11 Orthographic ProjecBons of a Line Fig. 3.2.b This is how line AB projects into a right view adjacent to the top view. We just use the procedure for projecBng a single point twice, once for each point, and connect the dots. 8/25/11 GG303 12 6 8/25/11 Orthographic ProjecBons of a Line Fig. 3.2.c This is how line AB would project into a right view adjacent to the front view. 8/25/11 GG303 13 Orthographic ProjecBons of a Line Fig. 3.2.d To ﬁnd the length and plunge of AB we take a cross secBon 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. 8/25/11 GG303 14 7 8/25/11 Orthographic ProjecBons of a Plane Fig. 3.3.a Three points deﬁne a plane. The two adjacent views here give complete informaBon on the posiBons of three points deﬁning plane ABC. This informaBon might come from a cross secBon or a map. Suppose we want to know the strike and dip of plane ABC. We ﬁrst need to ﬁnd the strike of the plane. The line of strike is a horizontal line in plane ABC. 8/25/11 GG303 15 Orthographic ProjecBons of a Plane Fig. 3.3.b We ﬁnd the line of strike by intersecBng a horizontal plane with plane ABC. We start with a verBcal view (here that is the front view F) and then project the line of strike into the top view T. The strike of the plane is measured in the top view by ﬁnding the direcBon of the (horizontal) line of strike. The numbers in parentheses in the top view are elevaBons, taken from the front view. 8/25/11 GG303 16 8 8/25/11 Orthographic ProjecBons of a Plane Fig. 3.3.c Take an auxiliary view cross secBon perpendicular to the line of strike to get the dip of the plane. The line of strike will be viewed end
on and horizontally, and it will appear as a point. The plane will appear edge
on as a line. The inclinaBon of the plane below the horizontal is the dip; it is measured here in view A. Because the top plane T is horizontal, the intersecBon of T and A is horizontal. 8/25/11 GG303 17 9 ...
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This note was uploaded on 12/05/2011 for the course GEOLOGY 300 taught by Professor Stephenmartel during the Fall '11 term at University of Hawaii, Manoa.
 Fall '11
 StephenMartel

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