This publication is written by Engineer, Mr. Manoj Karagudri. In reference to understanding of photogrammetry which is a part of B-TECH or BE in Civil Engineering.
Research papers publications by Engineer Mr. Manoj Karagudri.
Determination of Relative Positions of Points Without Establishing Physical Contact With The Object By Concept Of Photogrammetry.
Download PDF. Scopus index publication.
http://www.ijitee.org/wp-content/uploads/papers/v9i2/B6272129219.pdf
List of PDF Download Scopus index publication.
https://www.ijitee.org/download/volume-9-issue-2/
Here is the link to:
Introduction of Photogrammetry. Written by Mr. Manoj Karagudri.
Here is the
bitly short url link to this page.
Shown is the Terrestrial Photograph.
Objective: Calculation of
Horizontal Angles (Ha, Hb) &
Vertical Angles (Va, Vb)
With horizontal Camera axis.
(Click the Image to Enlarge.)
Here is the link to
YouTube video created by Engineer, Mr. Manoj Karagudri.
Figure shows two object points (a) and (b). Photographed with camera axis horizontal. Picture plane is vertical.
The projections of objects on the horizon line (X axis) are a' and b' respectively. Y axis called as the principal line.
Distances Xa, Ya, Xb, Yb, are measured from the photograph.
Focal length f = ok This is the know quantity focal length of the camera lens.
Ha: Horizontal angle of A
Va: Vertical angle of A.
Hb and Vb are for B.
Calculation of Horizontal angles.
Tan Ha = Perpendicular/Base = k a’ / f and
Tan Hb = k b’ / f
Note that k a’= Xa, k b’= Xb, and f are known values, thus Ha and Hb can be calculated.
Horizontal angle between a' and b' is difference between Ha ± Hb.
Here is the link to
the sentence, to interpret the Trigonometric values.
Calculation of Vertical Angles.
Tan Va = a a’ / o a’ and Tan Vb = b b’ / o b’ - equation (1)
Note that the values of o a’ and o b’ are not known. aa', bb' are know values measured from the photograph.
Cos Ha = f / o a’ Therefore
o a’ = f / Cos Ha OR o a’ = f (Sec Ha)
Similarly o b’ = f (Sec Hb)
Substituting the values of o a’ and o b’ in equations (1)
Tan Va = a a’ / f (Sec Ha) and
Tan Vb = b b’ / f (Sec Hb)
Note that these are known values of
(aa’ = Ya), (bb’ = Yb), Ha, Hb and f are already known. From photograph.
Thus value of Va and Vb can be calculated after substitution.
Shown below is Terrestrial Photograph
Objective: Calculation of
Horizontal Position
With Horizontal Camera Axis
Using Plane Table Method.
(Click to enlarge image). Note that:
Distance between Camera stations P and Q are already known.
Focal Length of Camera Lens is known.
Thus to calculate Horizontal Position of objects A and B Draw P and Q positions of reduced scales on Plane Table.
Draw photo horizontal planes (x axis of photo) from P and Q with the known focal lengths.
Point k1 and k2 is fixed on the plane table with known azimuth angle from North Direction.
Then point a1 is drawn from k1 on the table.
Point a2 is similarly draw from point Q with the known azimuth angle from North Direction.
With the help of photographs draw straight lines of A and B.
Then measure the Horizontal distances of A and B from Q and P.
Terrestrial Photograph
Azimuth of a line from Photographic Measurement:
Azimuth is defined as the clockwise horizontal angle made by the line from the Magnetic North Direction.
Azimuth is always measured clockwise.
(Click to enlarge image).
Terrestrial Photogrammetry
Elevation of a point:
Note that: the distance (D) from Object to Camera is already known.
Determination of Elevation with respect to camera axis, applying trigonometry.
(Click to enlarge the image). Tan Ah = x / f - use this equation to calculate horizontal angle Ah
Note that x and f are already known.
SPH, CBH, TPB (some people have, curly brown hair, till painted black.)
Sin=Perpendicular / Hypotenuse, Cos=Base / Hypotenuse, Tan=Perpendicular / Base.
Tan Av = y / o,a1 Note that o,a1 is not known, thus o,a1 = √(x ^2 + f ^2 )
Another way is, Cos Ah = f / (o,a1) therefore o,a1 = f (Sec Ah)
Therefore, Tan Av = y / √(x^(2 )+〖 f〗^2 ) or Tan Av = y / f (Sec Ah) - Use this equation to calculate Av
Note that y, x, f and Ah are already known.
Consider Similar Triangles o,a1,a and o,A1,A
a,a1 / o,a1 = A,A1 / o,A1
y / o,a1 = Vh / D Note that D is already known and we need to find Vh
Vh = D (y) / (o,a1) Note that o,a1 = √(x^(2 )+〖 f〗^2 ) or o,a1 = f (Sec Ah)
Vh = D (y) / √(x^(2 )+〖 f〗^2 ) or Vh = D (y) / f (Sec Ah) - Use this equation to calculate Height Vh
Terrestrial Photogrammetry
Focal Length determination:
(Click on the image to enlarge)
Tan Ha = Xa / f and Tan Hb = Xb / f
Considering the entire angle (Ha + Hb) to determine value of (f)
Tan Hab = tan (Ha + Hb) = (tan Ha + tan Hb) / (1 – tan Ha tan Hb)
Tan Hab = ( Xa / f + Xb / f ) / (1 - (Xa / f) (Xb / f) )
Tan Hab = ( Xa / f + Xb / f ) / (1 - (Xa ) (Xb) / f2 )
Tan Hab = ( (Xa + Xb) / f ) / ( (f2 - (Xa ) (Xb) ) / f2 )
Tan Hab ( f2 - (Xa ) (Xb) ) / f2 = ( (Xa + Xb) / f )
Tan Hab ( f2 - (Xa ) (Xb) ) = ( (Xa + Xb) / f ) (f2)
Tan Hab ( f2 - (Xa ) (Xb) ) = (f) (Xa + Xb)
( f2 - (Xa ) (Xb) ) - (f) (Xa + Xb) / Tan Hab = 0
f2 - ( (f (Xa + Xb ) ) / Tan Hab ) - ( (Xa ) (Xb) ) = 0
Therefore f = ( (Xa+Xb) / 2 Tan Hab ) + Sqrt ( (( Xa+Xb)2 / 4 tan2 Hab ) + ( Xa.Xb ) )
Here is the link to few 3D videos on PhotoGrammetry:
https://m.youtube.com/user/prayersofhope/videos
http://www.youtube.com/user/sam131141510#g/c/71E0E326EC496BAC
Sites for PhotoGramMetry:
http://www.photogrammetry.com/
http://en.wikipedia.org/wiki/Photogrammetry
http://www.geodetic.com/whatis.htm
Photographic Intersection
http://www.hugha.co.uk/PhotoInt/PhotoIntTechnical.htm
Wiki on Theodolite:
http://en.wikipedia.org/wiki/Theodolite
Image of PHOTO-THEODOLITE
http://www.gmat.unsw.edu.au/currentstudents/ug/projects/f_pall/html/t13.html
*
Images on Google Search.
Vernier Reading.
Horizontal and Vertical Angle in Surveying.
Calculation of degrees minutes and seconds.
Understanding Time Zones.
How w to prepare a manuscript for international journals
https://www.elsevier.com/connect/11-steps-to-structuring-a-science-paper-editors-will-take-seriously
