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# Oblique parallel projection

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### Oblique parallel projection

1. 1. Oblique ParallelprojectionCHANDAN GUPTA BHAGAT067BCT512
2. 2. A simple type of graphicalprojection  Used for producing pictorial, 2d images of 3d objects.
3. 3. Oblique projection  A parallel projection  Projects a 3d image by the intersection of the parallel rays which is known as projectors.  Parallel lines of the source object produces a parallel lines in the projected images.  the projectors intersects the projection in oblique angle to produce the projected image. Parallel projection of the point(x,y,z) on the xy plane is (x+az,y+bz,0)
4. 4. Types of parallel projection  When a=b=0, the projection is said to be orthographic or orthogonal  If not the projection is oblique
5. 5. More about the parallel projection  Crudest 3d drawing but easy to master.  Oblique is not really 3d system but 2d view of an object with ‘forced depth’.  Oblique is rarely used as it is unconvincing to the eye.
6. 6. Oblique peojection  Angles displayed among the axes  Foreshortening factors or scales are arbitrary  Length along the x and y direction are preserved  Length along the z axis are drawn at an angle using a reduction factor
7. 7. Cavalier projection  Also known as high view point  Length along the z axis remain unscaled  Easy to draw  Y axis is drawn diagonally making an angle of 30 or 45 degree with x axis.  X and z are perpendicular and length on these axes are 1:1 scaled
8. 8. Cabinet projection  Used by furniture industry  One face of the object is parallel to the viewing plane  Third axis is projected at angle 30 or 45 degree  The projection length of the receding lines are half
9. 9. Mathematical formula A projected point has the following transformation formula X = X + 0.5 * Z * cos() Y = Y + 0.5 * Z * sin() Z=0  is the mentioned angle
10. 10. sources  Wikipedia.com