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5. Relief Displacement

Figure C-9 is an overhead picture of nine vertical cylinders on a flat surface. Cylinders A-D are the same size; J-N are 25% wider and taller. The picture was taken centered on cylinder A and approximately 30 inches above.

 
Figure C-9
Overhead Photo of Cylinders
 

On the picture we see that:

  • Cylinder A is the only one whose top is directly over its bottom, the other cylinders lean away from A with their tops displaced outward.
  • Cylinders J and L are approximately the same distance from A; their tops shift the same amount but in opposite directions; cylinders K and M behave the same.
  • Cylinder N is twice the distance from A as M; its top shifts about twice M's.
  • Cylinders B and N are the same distance from A; B is shorter and its top shift is slightly less than N's.

Relief displacement is the radial offset from the principal point due to object height, Figure C-10. The amount of displacement is a function of an object's height and where it appears on the image.

 
Figure C-10
Relief Displacement

Relief displacement can be used to determine object heights, Figure C-11. The top and bottom of the object must be visible on the photo and the top must be vertically above the bottom.

   
(a) Object (b) Measurements 
Figure C-11
Height from Relief Displacement

Height is determined using Equation C-5

  Equation C-5 

h - object height above ground 
hb - elevation at base of object
H - Camera height above datum
H' - Camera height above base of object
rb - radial distance from principal point to object base
rt - radial distance from principal point to object top

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