Problem with Understanding Oblique and Orthographic Projection

Discussion in 'Homework Help' started by zulfi100, Apr 12, 2015.

  1. zulfi100

    Thread Starter Member

    Jun 7, 2012
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    Hi,
    Can some body please tell me the geometrical difference between orthographic and oblique projection?
    In the book, it says that :
    "When the projection is perpendicular to the view plane, we have an orthographic parallel projection. Otherwise we have an oblique parallel projection."
    I cannot understand this difference in their diagrams. In the slide related to orthographic projection, it says: if the view plane is placed at position Zvp, I cannot understand this. orthographic projection.png
    oblique projection.png
    Somebody please guide me.

    Zulfi.
     
  2. MrChips

    Moderator

    Oct 2, 2009
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    Orthogonal means at 90-degrees.
    So if it is not orthogonal it must be oblique.
     
  3. zulfi100

    Thread Starter Member

    Jun 7, 2012
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    Hi,
    Thanks for your reply. Please explain me through diagram that projectors are perpendicular to projection plane in case of orthogonal projection and are not perpendicular in case of Oblique projection.

    Zulfi.
     
  4. MrChips

    Moderator

    Oct 2, 2009
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    [​IMG]

    Picture hand shadows on the wall. If the light source is at 90-degrees to the wall, that is orthographic projection.
    If the light source is not at 90-degrees, that is oblique projection.

    [​IMG]
     
  5. zulfi100

    Thread Starter Member

    Jun 7, 2012
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    Hi,
    I got some understanding. Actually i was talking about the figures which i posted. I would come to your posted figures later on. In the figures, i thing we are concerned with two points: (x, y, z) & (x,y). In orthographic projection, the line (x, y,z) to (x, y) intersects the plane at (x,y) and it makes a 90 degree angle. In oblique project the line (x, y, z) to (x, y) is not at 90 degrees with the view plane. Its oblique. Is this correct?

    However, I cant understand what is (xp, yp) in oblique projection. We dont have (xp, yp) in orthographic projection because xp =x and yp =y;

    Please guide me.


    Zulfi.
     
  6. MrChips

    Moderator

    Oct 2, 2009
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    If you are projecting the point (x, y, z) on to the (x, y) plane then the orthographic projection is (x, y, 0) which becomes (x, y) on a 2-D plane.

    If the projection is not (x, y) then it is an oblique projection.

    A point (x, y, 0) is already on the (x, y) plane. Hence the oblique projection is the same as the orthographic projection, i.e. (x, y).
     
  7. zulfi100

    Thread Starter Member

    Jun 7, 2012
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    0
    Hi,
    Thanks for your reply. But if you look at the diagram (xp, yp) is also the intersection of projectors with the view plane. What is the difference between (x,y) and (xp, yp)? (Asking Again) In the diagram of oblique projection (posted by me), it shows two lines intersecting the view plane: one is (x, y, z) to (x, y) and the other is from (x, y, z) to (xp, yp). What is the difference between these two lines? What is the difference between (x,y) and (xp, yp)?
    I dont think so because in case of projection we move from n-domain to n-1 domain.
    Zulfi.
     
  8. MrChips

    Moderator

    Oct 2, 2009
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    (x, y, z) is an arbitrary point on 3-D space.
    (x, y, 0) is the orthographic projection on the (x-y) plane.
    (xp, yp, 0) is an oblique projection of (x, y, z) on the (x-y) plane.

    What is the difference? (xp, yp, 0) is not coincident with (x, y, 0) and hence it is an oblique projection on the (x-y) plane.
    If xp ≠ x or yp ≠ y then (xp, xp) is not coincident with (x, y). Both are the projections on the (x-y) plane.

    Do not confuse the point (x, y, 0) and hence the point (x, y) with the plane (x-y).

    I include the z = 0 coordinate to make it perfectly clear that (x, y) is the same point (x, y, 0) on the (x-y) plane.
    Otherwise (x, y) alone is a straight line that is orthogonal to the (x-y) plane and intercepts the point (x, y, 0).
    In other words (x, y) is the locus of all points with value (x, y) and all possible values of z.

    Let's review:

    (z) is a plane.
    (x, y) is a line.
    (x, y, z) is a point.
     
    Last edited: Apr 14, 2015
  9. MrChips

    Moderator

    Oct 2, 2009
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    Imagine you are my friend R!f@@ in the Maldives standing in the sun at midday on June 20.
    The orthographic projection of the shadow of your head would fall at your feet.
    If your head's shadow does not fall at your feet it is now an oblique projection because the sun has moved away from being exactly overhead.
     
  10. zulfi100

    Thread Starter Member

    Jun 7, 2012
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    oblique proj equations.png
    Hi,
    Thanks for removing most of the problems. I like your example. I was also thinking in that way but not confident.
    Now we try to discuss the equations. I am able to understand these equations. I got solution from some other forum but i have one another problem in the oblique triangle whose image i have posted above. The oblique triangle consists of points (x,y,z), (xp, yp) and (x,y) and has an internal angle alpha (α). But in the equations they have used the angle phi (∅) instead of alpha where phi is an external angle. I cant understand this thing. The equations are given above.

    Some body please guide me.

    Zulfi.
     
    Last edited: Apr 15, 2015
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