This document discusses oblique parallel projection, which is a type of graphical projection that uses parallel rays to project a 3D image onto a 2D plane at an oblique angle. It notes that parallel lines in the 3D object remain parallel in the 2D projection. The document outlines different types of parallel projections, including orthogonal projection where a and b are both 0, and oblique projection where they are not both 0. It also discusses specific types of oblique parallel projections like cavalier and cabinet projection, and provides a mathematical formula to calculate projected point coordinates.

1. Oblique Parallel
projection
CHANDAN GUPTA BHAGAT
067BCT512

2. A simple type of graphical
projection
 Used for producing pictorial, 2d images of 3d objects.

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. Types of parallel projection
 When a=b=0, the projection is said to be orthographic or orthogonal
 If not the projection is oblique

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. 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. 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. 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. 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. sources
 Wikipedia.com