A simple type of graphicalprojection Used for producing pictorial, 2d images of 3d objects.
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)
Types of parallel projection When a=b=0, the projection is said to be orthographic or orthogonal If not the projection is oblique
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.
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
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
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
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