Assorted Brain Teasers by Kundan Pangtey - HTML preview

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TEASER - 15

TELESCOPIC EFFECT

On a local scale, compare an aerial photograph (seen from top) of a mountain with contour map of same mountain or an aerial photograph   of   a   tall   building   with   contour   map   of   same building.

The shape of the mountain, or the tall building would be exactly same in both aerial photograph and contour map:

(a) Falls

(b) True

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THE EXPLANATION:

The aerial photograph is a method of creating 2D image of relief of an undulating surface by means of variations of light and shade. The contour maps are systematized form of showing same variations of light  and  shade  by  means  of  lines  connecting  equal  elevation  or depth.

The  most  important  thing  in  determining  shape  and  size  of  3D objects  in  contour  map  or  aerial  photograph  is  whether  relative position  of  each  point,  with  respect  to  each  other,  have  been maintained  taking  into  account  the  element  of  height,  length  and width.

The contour map (especially on a local scale) maintains the relative position of each points with respect to each other as seen in ground at  all  level.  However,  even  though  aerial  photographs  do  not  hide anything, it deforms the feature and distorts the relative position of points seen in ground. The nearer objects appear bigger and farther one  becomes  smaller  telescopically.  The  objects  seen  within  the ‘view   finder’   have   to   be   adjusted   for   depth   element   because photographs or image in 2D formats lack depth.

One  scale  would  not  be  applicable  for  all  the  objects  seen  within same  photo-frame  and  shall  vary  according  to  depth.  Therefore shape of object get distorted proportionately with depth in an aerial photograph.

Take  for  example  a  pyramid  shaped  structure  with  staircase  type slopes as shown in figure below (A).

•     In  the  map  view  (contour  map)  of  the  structure  (B),  the relationship between each step with respect to their size and position  remain  constant  irrespective  of  relative  distance  of each step from top to bottom. The ratio of an area between top step and bottom step would remain same as would be in reality.

•     Single   map   scale   would   be   applicable   for   each   step, irrespective  of  their  depth  or  height  from  reference  level (datum level) on which map is made.

•     In an aerial photograph (C), taken from very close range from top, the step closer to the viewer  would appear bigger than the   step   away  from   viewer   (towards   bottom).  The  ratio between  top  and  bottom  steps  with  respect  to  size  and position would not be same as would be in reality. The ratio would depend on how close the photograph is taken from.

•     Single scale would not be applicable for all steps in the aerial photograph (C). Each step shall have to have its own scale depending upon its depth from the level on which photograph is referenced.

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SHADED CONTOURS (B) & PHOTOGRPH (C) OF A PYRAMID (A) SEEN FROM TOP

•     In an extreme case (D), only the top stair would be visible in the aerial photograph and all below would be hidden behind. It  may  appear  like  an  inverted  pyramid,  like  a  tall  building seen from above (E).

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D: A PYRAMID SEEN FROM TOP AT CLOSE RANGE

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E;   TALL BUILDING SEEN FROM ABOVE ROOF IS MUCH BIGGER THAN BASE

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