Simple imposter distortion estimation

W. Pasman, revised 23/10/1

d=distance between optimal viewpoint and imposter
dobj=distance between optimal viewpoint and frontside of object
ef=distance between imposter and front side of object
eb=distance between imposter and back side of object
r= radius of object (=ef+eb)
θ=distance (angle) from frontal view

Here distortion is the max angular displacement of pixels on the object's surface.

Front face Distortion

Back face Distortion

Plots

[Graphics:Images/impdist_gr_5.gif]
[Graphics:Images/impdist_gr_6.gif]

[Graphics:Images/impdist_gr_7.gif]

[Graphics:Images/impdist_gr_8.gif]
[Graphics:Images/impdist_gr_9.gif]

[Graphics:Images/impdist_gr_10.gif]

[Graphics:Images/impdist_gr_11.gif]
[Graphics:Images/impdist_gr_12.gif]

[Graphics:Images/impdist_gr_13.gif]

[Graphics:Images/impdist_gr_14.gif]

Note on this plot. Distance to front side of object is fixed dobj. So increasing distance to imposter d
shifts the imposter more towards the back face. Of cource distortion=0 when the imposter hits the back face.

[Graphics:Images/impdist_gr_15.gif]

Solve the equation of the two

Much simpler but rougher approximation

Linear approximation as an inbetween solution?

Yet another approach with some trigo


Converted by Mathematica      February 7, 2002