Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Spatial
Transformations
BY : EHSAN HAMZEI - 810392121
Geometric transformations
 Geometric transformations will map points in one
space to points in another: (x',y',z') = f(x,...
Linear Transformation
 A 2 x 2 linear transformation matrix allows:
 Scaling
 Rotation
 Reflection
 Shearing
2
Affine Transformation 3
 Definition:
 P(Px, Py) is transformed into Q(Qx , Qy ) as follows:
 Qx = aPx + cPy + Tx
 Qy =...
Affine Properties 4
 Preserves parallelism of lines, but not lengths and
angles.
 Lines are preserved.
 Proportional di...
An Affine Application 4
 Computer graphic
Projective Geometry 4
 Euclidean geometry describes shapes “as they are”.
 Projective geometry describes objects “as the...
Projective Transformation 4
 Definition:
Projective Properties 4
 With projective geometry, two lines always meet in a
single point, and two points always lie on ...
Cross Ratio 4
A Projective Application 4
 Robot Recognition
Review 4
Thanks 26
Upcoming SlideShare
Loading in …5
×

Spatial Transformation

969 views

Published on

Geospatial Transformation

Published in: Engineering
  • If you’re looking for a great essay service then you should check out ⇒ www.WritePaper.info ⇐. A friend of mine asked them to write a whole dissertation for him and he said it turned out great! Afterwards I also ordered an essay from them and I was very happy with the work I got too.
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • ⇒ www.HelpWriting.net ⇐ is a good website if you’re looking to get your essay written for you. You can also request things like research papers or dissertations. It’s really convenient and helpful.
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here

Spatial Transformation

  1. 1. Spatial Transformations BY : EHSAN HAMZEI - 810392121
  2. 2. Geometric transformations  Geometric transformations will map points in one space to points in another: (x',y',z') = f(x, y, z).  These transformations can be very simple, such as scaling each coordinate, or complex, such as nonlinear twists and bends. 1
  3. 3. Linear Transformation  A 2 x 2 linear transformation matrix allows:  Scaling  Rotation  Reflection  Shearing 2
  4. 4. Affine Transformation 3  Definition:  P(Px, Py) is transformed into Q(Qx , Qy ) as follows:  Qx = aPx + cPy + Tx  Qy = bPx + dPy + Ty
  5. 5. Affine Properties 4  Preserves parallelism of lines, but not lengths and angles.  Lines are preserved.  Proportional distances are preserved (Midpoints map to midpoints).
  6. 6. An Affine Application 4  Computer graphic
  7. 7. Projective Geometry 4  Euclidean geometry describes shapes “as they are”.  Projective geometry describes objects “as they appear”. (Ex: Railroad…)  Lengths, angles, parallelism become “distorted” when we look at objects
  8. 8. Projective Transformation 4  Definition:
  9. 9. Projective Properties 4  With projective geometry, two lines always meet in a single point, and two points always lie on a single line.  Mapping from points in plane to points in plane  3 aligned points are mapped to 3 aligned points  Cross Ratio
  10. 10. Cross Ratio 4
  11. 11. A Projective Application 4  Robot Recognition
  12. 12. Review 4
  13. 13. Thanks 26

×