21-12-2012, 05:33 PM
3D Projection Transformations
[attachment=44817]
Principal Axes
Man-made objects often have “cube-like” shape. These objects have 3 principal axes.
One point, two point, three point perspective
Depends on how many principal axes intersect with view plane.
Parallel lines not parallel to view plane have the same vanishing point.
Orthographic Parallel Projection Matrix
Transform each vertex from Viewing Coordinates into Normalized Coordinates using orthographic projection
Suppose that a point is (x,y,z) in Viewing Coordinates, what’s the transformation necessary to transform it to (x’,y’,z’) in Normalized Coordinates?
Given: the dimensions of the view window: xwmin, xwmax, ywmin, ywmax
Orthogonal Projection Matrix on p. 362.
Basically Translate center of view to origin and then Scale to (-1,1) cube
Translate by -(min+max)/2, then scale by 2/(max-min).
[attachment=44817]
Principal Axes
Man-made objects often have “cube-like” shape. These objects have 3 principal axes.
One point, two point, three point perspective
Depends on how many principal axes intersect with view plane.
Parallel lines not parallel to view plane have the same vanishing point.
Orthographic Parallel Projection Matrix
Transform each vertex from Viewing Coordinates into Normalized Coordinates using orthographic projection
Suppose that a point is (x,y,z) in Viewing Coordinates, what’s the transformation necessary to transform it to (x’,y’,z’) in Normalized Coordinates?
Given: the dimensions of the view window: xwmin, xwmax, ywmin, ywmax
Orthogonal Projection Matrix on p. 362.
Basically Translate center of view to origin and then Scale to (-1,1) cube
Translate by -(min+max)/2, then scale by 2/(max-min).