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PROJECTIONS
              Sanu Philip
              No:47




                            1
Transform 3D objects on to a 2D plane using
projections

2 types of projections
Perspective
Parallel

In parallel projection, coordinate positions are
transformed to the view plane along parallel lines.
In perspective projection, object position are
transformed to the view plane along lines that
converge to a point called projection reference point
(center of projection)


                                                        2
Perspective Projection




                         3
Parallel Projection




                      4
PROJECTIONS



PARALLEL
                                                                                PERSPECTIVE
(parallel projectors)
                                                                                (converging projectors)

                                                                                                   One point
Orthographic                                         Oblique
                                                                                                   (one principal
(projectors perpendicular                            (projectors not perpendicular to              vanishing point)
to view plane)                                       view plane)

                                                                                                    Two point
                                                                  General                           (Two principal
Multiview                     Axonometric                                                           vanishing point)

(view plane parallel          (view plane not parallel to                       Cavalier
to principal planes)          principal planes)
                                                                                                     Three point
                                                                                                     (Three principal
                                                                                                     vanishing point)
                                                                                    Cabinet
    Isometric               Dimetric               Trimetric

                                                                                                                        5
Perspective v Parallel

• Perspective:
    – visual effect is similar to human visual system...
    – has 'perspective foreshortening'
        • size of object varies inversely with distance from the center of
          projection. Projection of a distant object are smaller than the
          projection of objects of the same size that are closer to the
          projection plane.
• Parallel:
     It preserves relative proportion of object.
    – less realistic view because of no foreshortening
    – however, parallel lines remain parallel.


                                                                             6
Perspective Projections

• Characteristics:

• Center of Projection (CP) is a finite distance from object
• Projectors are rays (i.e., non-parallel)
• Vanishing points
• Objects appear smaller as distance from CP (eye of observer)
  increases
• Difficult to determine exact size and shape of object
• Most realistic, difficult to execute

                                                                 7
• When a 3D object is projected onto view plane using
  perspective transformation equations, any set of parallel lines
  in the object that are not parallel to the projection plane,
  converge at a vanishing point.
   – There are an infinite number of vanishing points,
     depending on how many set of parallel lines there are in
     the scene.
• If a set of lines are parallel to one of the three principle axes,
  the vanishing point is called an principal vanishing point.
   – There are at most 3 such points, corresponding to the
     number of axes cut by the projection plane.


                                                                       8
Vanishing points

• Certain set of parallel lines appear to meet at a different point
   – The Vanishing point for this direction
• Principal vanishing points are formed by the apparent
  intersection of lines parallel to one of the three principal x, y, z
  axes.
• The number of principal vanishing points is determined by the
  number of principal axes intersected by the view plane.
• Sets of parallel lines on the same plane lead to collinear
  vanishing points.
   – The line is called the horizon for that plane

                                                                     9
Classes of Perspective Projection
•    One-Point Perspective
•    Two-Point Perspective
•    Three-Point Perspective




                                        10
One-Point Perspective




                        11
Two-point perspective projection:

– This is often used in architectural, engineering and
  industrial design drawings.
–




                                                     12
Three-point perspective projection
• Three-point perspective projection is used less
  frequently as it adds little extra realism to that
  offered by two-point perspective projection




                                                   13
Parallel Projections
• We can define a parallel projection with a projection vector that
   defines the direction for the projection lines.
2 types:
• Orthographic : when the projection is perpendicular to the view
   plane. In short,
   – direction of projection = normal to the projection plane.
   – the projection is perpendicular to the view plane.
• Oblique : when the projection is not perpendicular to the view
  plane. In short,
   – direction of projection normal to the projection plane.
   – Not perpendicular.


                                                                   14
• Orthographic projection     Oblique projection




  when the projection is      when the projection is not
  perpendicular to the view   perpendicular to the view
  plane                       plane




                                                           15
Orthographic (or orthogonal) projections:

    – Front, side and rear orthographic projection of an object are
      called elevations and the top orthographic projection is called
      plan view.
    – all have projection plane perpendicular to a principle axes.
    – Here length and angles are accurately depicted and measured
      from the drawing, so engineering and architectural drawings
      commonly employee this.
• However, As only one face of an object is shown, it can be hard to
  create a mental image of the object, even when several views are
  available.

                                                                        16
Orthogonal projections:




                          17
Axonometric orthographic projections

• Orthographic projections that show more than one face of an
  object are called axonometric orthographic projections.
•
 The most common axonometric
projection is an isometric
projection where the projection
plane intersects each coordinate
axis in the model coordinate
system at an equal distance.


                                                            18
• 2 common oblique parallel projections:
   Cavalier and Cabinet

Cavalier projection:
All lines perpendicular to the projection plane are projected with
   no change in length.




                                                                     19
Cabinet projection:
   – Lines which are perpendicular to the projection plane
     (viewing surface) are projected at 1 / 2 the length .
   – This results in foreshortening of the z axis, and
     provides a more “realistic” view.




                                                             20
THANK YOU
            21

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Projection In Computer Graphics

  • 1. PROJECTIONS Sanu Philip No:47 1
  • 2. Transform 3D objects on to a 2D plane using projections 2 types of projections Perspective Parallel In parallel projection, coordinate positions are transformed to the view plane along parallel lines. In perspective projection, object position are transformed to the view plane along lines that converge to a point called projection reference point (center of projection) 2
  • 5. PROJECTIONS PARALLEL PERSPECTIVE (parallel projectors) (converging projectors) One point Orthographic Oblique (one principal (projectors perpendicular (projectors not perpendicular to vanishing point) to view plane) view plane) Two point General (Two principal Multiview Axonometric vanishing point) (view plane parallel (view plane not parallel to Cavalier to principal planes) principal planes) Three point (Three principal vanishing point) Cabinet Isometric Dimetric Trimetric 5
  • 6. Perspective v Parallel • Perspective: – visual effect is similar to human visual system... – has 'perspective foreshortening' • size of object varies inversely with distance from the center of projection. Projection of a distant object are smaller than the projection of objects of the same size that are closer to the projection plane. • Parallel: It preserves relative proportion of object. – less realistic view because of no foreshortening – however, parallel lines remain parallel. 6
  • 7. Perspective Projections • Characteristics: • Center of Projection (CP) is a finite distance from object • Projectors are rays (i.e., non-parallel) • Vanishing points • Objects appear smaller as distance from CP (eye of observer) increases • Difficult to determine exact size and shape of object • Most realistic, difficult to execute 7
  • 8. • When a 3D object is projected onto view plane using perspective transformation equations, any set of parallel lines in the object that are not parallel to the projection plane, converge at a vanishing point. – There are an infinite number of vanishing points, depending on how many set of parallel lines there are in the scene. • If a set of lines are parallel to one of the three principle axes, the vanishing point is called an principal vanishing point. – There are at most 3 such points, corresponding to the number of axes cut by the projection plane. 8
  • 9. Vanishing points • Certain set of parallel lines appear to meet at a different point – The Vanishing point for this direction • Principal vanishing points are formed by the apparent intersection of lines parallel to one of the three principal x, y, z axes. • The number of principal vanishing points is determined by the number of principal axes intersected by the view plane. • Sets of parallel lines on the same plane lead to collinear vanishing points. – The line is called the horizon for that plane 9
  • 10. Classes of Perspective Projection • One-Point Perspective • Two-Point Perspective • Three-Point Perspective 10
  • 12. Two-point perspective projection: – This is often used in architectural, engineering and industrial design drawings. – 12
  • 13. Three-point perspective projection • Three-point perspective projection is used less frequently as it adds little extra realism to that offered by two-point perspective projection 13
  • 14. Parallel Projections • We can define a parallel projection with a projection vector that defines the direction for the projection lines. 2 types: • Orthographic : when the projection is perpendicular to the view plane. In short, – direction of projection = normal to the projection plane. – the projection is perpendicular to the view plane. • Oblique : when the projection is not perpendicular to the view plane. In short, – direction of projection normal to the projection plane. – Not perpendicular. 14
  • 15. • Orthographic projection Oblique projection when the projection is when the projection is not perpendicular to the view perpendicular to the view plane plane 15
  • 16. Orthographic (or orthogonal) projections: – Front, side and rear orthographic projection of an object are called elevations and the top orthographic projection is called plan view. – all have projection plane perpendicular to a principle axes. – Here length and angles are accurately depicted and measured from the drawing, so engineering and architectural drawings commonly employee this. • However, As only one face of an object is shown, it can be hard to create a mental image of the object, even when several views are available. 16
  • 18. Axonometric orthographic projections • Orthographic projections that show more than one face of an object are called axonometric orthographic projections. •  The most common axonometric projection is an isometric projection where the projection plane intersects each coordinate axis in the model coordinate system at an equal distance. 18
  • 19. • 2 common oblique parallel projections: Cavalier and Cabinet Cavalier projection: All lines perpendicular to the projection plane are projected with no change in length. 19
  • 20. Cabinet projection: – Lines which are perpendicular to the projection plane (viewing surface) are projected at 1 / 2 the length . – This results in foreshortening of the z axis, and provides a more “realistic” view. 20
  • 21. THANK YOU 21