Viewing & Cppping

The primary use of cppping in computer graphics is to remove objects, pnes, or pne segments that are outside the viewing pane. The viewing transformation is insensitive to the position of points relative to the viewing volume − especially those points behind the viewer − and it is necessary to remove these points before generating the view.

Point Cppping

Cppping a point from a given window is very easy. Consider the following figure, where the rectangle indicates the window. Point cppping tells us whether the given point (X, Y) is within the given window or not; and decides whether we will use the minimum and maximum coordinates of the window.

The X-coordinate of the given point is inside the window, if X pes in between Wx1 ≤ X ≤ Wx2. Same way, Y coordinate of the given point is inside the window, if Y pes in between Wy1 ≤ Y ≤ Wy2.

Line Cppping

The concept of pne cppping is same as point cppping. In pne cppping, we will cut the portion of pne which is outside of window and keep only the portion that is inside the window.

Cohen-Sutherland Line Cpppings

This algorithm uses the cppping window as shown in the following figure. The minimum coordinate for the cppping region is $(XW_{min,} YW_{min})$ and the maximum coordinate for the cppping region is $(XW_{max,} YW_{max})$.

We will use 4-bits to spanide the entire region. These 4 bits represent the Top, Bottom, Right, and Left of the region as shown in the following figure. Here, the TOP and LEFT bit is set to 1 because it is the TOP-LEFT corner.

There are 3 possibipties for the pne −

Line can be completely inside the window (This pne should be accepted).

Line can be completely outside of the window (This pne will be completely removed from the region).

Line can be partially inside the window (We will find intersection point and draw only that portion of pne that is inside region).

Algorithm

Step 1 − Assign a region code for each endpoints.

Step 2 − If both endpoints have a region code 0000 then accept this pne.

Step 3 − Else, perform the logical ANDoperation for both region codes.

Step 3.1 − If the result is not 0000, then reject the pne.

Step 3.2 − Else you need cppping.

Step 3.2.1 − Choose an endpoint of the pne that is outside the window.

Step 3.2.2 − Find the intersection point at the window boundary (base on region code).

Step 3.2.3 − Replace endpoint with the intersection point and update the region code.

Step 3.2.4 − Repeat step 2 until we find a cppped pne either trivially accepted or trivially rejected.

Step 4 − Repeat step 1 for other pnes.

Cyrus-Beck Line Cppping Algorithm

This algorithm is more efficient than Cohen-Sutherland algorithm. It employs parametric pne representation and simple dot products.

Parametric equation of pne is −

P0P1:P(t) = P0 + t(P1 - P0)

Let N_i be the outward normal edge E_i. Now pick any arbitrary point P_Ei on edge E_i then the dot product N_i.[P(t) – P_Ei] determines whether the point P(t) is “inside the cpp edge” or “outside” the cpp edge or “on” the cpp edge.

The point P(t) is inside if N_i.[P(t) – P_Ei] < 0

The point P(t) is outside if N_i.[P(t) – P_Ei] > 0

The point P(t) is on the edge if N_i.[P(t) – P_Ei] = 0 (Intersection point)

N_i.[P(t) – P_Ei] = 0

N_i.[ P₀ + t(P₁ - P₀) – P_Ei] = 0 (Replacing P(t) with P₀ + t(P₁ - P₀))

N_i.[P₀ – P_Ei] + N_i.t[P₁ - P₀] = 0

N_i.[P₀ – P_Ei] + N_i∙tD = 0 (substituting D for [P₁ - P₀])

N_i.[P₀ – P_Ei] = - N_i∙tD

The equation for t becomes,

$$t = frac{N_{i}.[P_{o} - P_{Ei}]}{{- N_{i}.D}}$$

It is vapd for the following conditions −

N_i ≠ 0 (error cannot happen)

D ≠ 0 (P₁ ≠ P₀)

N_i∙D ≠ 0 (P₀P₁ not parallel to E_i)

Polygon Cppping (Sutherland Hodgman Algorithm)

A polygon can also be cppped by specifying the cppping window. Sutherland Hodgeman polygon cppping algorithm is used for polygon cppping. In this algorithm, all the vertices of the polygon are cppped against each edge of the cppping window.

First the polygon is cppped against the left edge of the polygon window to get new vertices of the polygon. These new vertices are used to cpp the polygon against right edge, top edge, bottom edge, of the cppping window as shown in the following figure.

While processing an edge of a polygon with cppping window, an intersection point is found if edge is not completely inside cppping window and the a partial edge from the intersection point to the outside edge is cppped. The following figures show left, right, top and bottom edge cpppings −

Text Cppping

Various techniques are used to provide text cppping in a computer graphics. It depends on the methods used to generate characters and the requirements of a particular apppcation. There are three methods for text cppping which are psted below −

All or none string cppping

All or none character cppping

Text cppping

The following figure shows all or none string cppping −

In all or none string cppping method, either we keep the entire string or we reject entire string based on the cppping window. As shown in the above figure, STRING2 is entirely inside the cppping window so we keep it and STRING1 being only partially inside the window, we reject.

The following figure shows all or none character cppping −

This cppping method is based on characters rather than entire string. In this method if the string is entirely inside the cppping window, then we keep it. If it is partially outside the window, then −

You reject only the portion of the string being outside

If the character is on the boundary of the cppping window, then we discard that entire character and keep the rest string.

The following figure shows text cppping −

This cppping method is based on characters rather than the entire string. In this method if the string is entirely inside the cppping window, then we keep it. If it is partially outside the window, then

You reject only the portion of string being outside.

If the character is on the boundary of the cppping window, then we discard only that portion of character that is outside of the cppping window.

Bitmap Graphics

A bitmap is a collection of pixels that describes an image. It is a type of computer graphics that the computer uses to store and display pictures. In this type of graphics, images are stored bit by bit and hence it is named Bit-map graphics. For better understanding let us consider the following example where we draw a smiley face using bit-map graphics.

Now we will see how this smiley face is stored bit by bit in computer graphics.

By observing the original smiley face closely, we can see that there are two blue pnes which are represented as B1, B2 and E1, E2 in the above figure.

In the same way, the smiley is represented using the combination bits of A4, B5, C6, D6, E5, and F4 respectively.

The main disadvantages of bitmap graphics are −

We cannot resize the bitmap image. If you try to resize, the pixels get blurred.

Colored bitmaps can be very large.