Q. Describe different types of parallel and perspective projection used in computer graphics.

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Explain projection, type of projection, view plane vanishing point in detail.

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Write short note on parallel projection.

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Describe different types of parallel projections used in computer graphics.

Ans. Projection: Once world coordinate descriptions of the objects in a scene are converted to viewing coordinate, we can project the three- dimensional object onto the two- dimensional view plane. There are two basic projections methods- parallel and Perspective projection. (i) Parallel projection: In a parallel projection, parallel lines in the world coordinate scene project into parallel lines on the two dimensional display plane. This technique is used in engineering and architectural drawings to represent an object with a set of views that maintain relative proportions of the object. By selecting different viewing positions, we can project visible points on the object onto the display plane to obtain different - dimensional views of the object. When the projection is perpendicular to the view plane, we have an orthographic parallel projection. Three basic types of orthographic parallel projections are: (a) Top view( plan view): The projection of the object as seen from the top. (b) side view (side elevation): The projection of the object on a display plane as seen from a side of the object. The display plane is always on the side just opposite to the viewing position. (c) Front view (front elevation) The projection of the object as seen from the front side of the object. Orthographic projection are those that display more than one face of an object which can also be drawn. Such views are called 'axonometric' orthographic projection. The most commonly used axonometric projection is the Isometric projection. An isometric projection can be generated by aligning the projection plane so that it intersects each coordinate axis in which the object is defined (called the principal axis) at the same distance from the origin. Oblique projection: An oblique projection is obtained by projection points along parallel lines that are not perpendicular to the projection plane. The oblique projection vector is specified with two angles a and o. Common choices for angle o are 30­₀ and 45₀ which display a combination view of the front, side and top of an object. Commonly used values for a are those which tan a = 1 and tan a = 2. For the first case, a = 45₀ and the views obtained are called Cavalier projection. All lines perpendicular to the projection plane are projection with no change in length. When the projection angle a is chosen so that tan a = 2, the resulting view is called a cabinet projection. For this angle (=63.4₀), lines perpendicular to the viewing surface are projection at one- half their length. Cabinet projection appears more realistic then cavalier projection because of the reduction in the length of perpendiculars. (ii) Perspective projection: To obtain a perspective projection of a three- dimensional object, we transform points along projection lines that meet at the projection reference point. Suppose we set the projection reference point at position Z _prp along the Z _v axis, and we place the view plane the view plane at Z _{v p},. We can write equations describing coordinate position along this perspective projection line in parametric from as x' = x- x u y' = y- y u z' = z- (z- z _prp)u parameter u takes values from 0 to 1, and coordinate position (x', y', z') represents any point along the projection line. When u=0, we are at position P= (x, y, z). At the other end of the line, u=1 and we have the projection reference point coordinate (0, 0, z _prp). On the view plane, z'=z_vp and we can solve the z' equation of parameter u at this position along the projection line: u = 0, we are at position P = (x, y, z). At the other end of the line, u = 1 and we have the projection reference point coordinates (0, 0, z ). On the view plane z = z and we can solve the z equation of parameter u at this position along the projection line: View Plane A view plane, or projection plane is the set up perpendicular to the viewing z_y axis. The view plane as the film plane in a camera that has been positioned and oriented for a particular shot of the scene. World coordinate positions in the scene are transformed to viewing coordinates. Then viewing coordinates are projected on to the view plane.