Unit-IV Windowing and Clipping.pdf
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The document provides an overview of windowing and clipping in computer graphics, detailing transformations from world coordinates to device coordinates and the various algorithms for clipping lines and points. It explains concepts such as windows, viewports, and the processes involved in clipping objects within specified regions. Various clipping algorithms, including Cohen-Sutherland, mid-point subdivision, and Liang-Barsky, are described along with their steps and applications.
![Cyrus Beck Line Clipping Algorithm
P1
P2
f
n
n
n
n.[ P(t) - f ] > 0
n.[ P(t) - f ] = 0
n.[ P(t) - f ] < 0
Clipping edge
(clipping boundary )
x
y
f
0
n
R-conves region
Convex region, boundary point
and inner normal](https://image.slidesharecdn.com/unit-ivwindowingandclipping-230316142407-744dde0c/85/Unit-IV-Windowing-and-Clipping-pdf-45-320.jpg)
![Cyrus Beck Line Clipping Algorithm
Consider a convex clipping region R, f is a boundary point of the convex region R
and n is an inner normal for one of its boundaries as shown in above figure
Then we can distinguish (decide) in which region a point lie by looking at the
value of the dot product, n.[P(t) – f ], as shown in Fig.
If dot product is negative i.e.,
n.[P(t) – f ] < 0 ... (2)
then the vector [P(t) – f ] is pointed away from the interior of R.
If dot product is zero i.e.,
n.[P(t) – f ] = 0 ... (3)
then the vector [P(t) – f ] is pointed parallel to the plane containing f and
perpendicular (90 degree) to the normal](https://image.slidesharecdn.com/unit-ivwindowingandclipping-230316142407-744dde0c/85/Unit-IV-Windowing-and-Clipping-pdf-46-320.jpg)
![Cyrus Beck Line Clipping Algorithm
If dot product is positive i.e.,
n.[P(t) – f ] > 0 ... (4)
then the vector [P(t) – f ] is pointed towards the interior of R.
As shown in Fig. if the point f lies in the boundary plane or edge for which n is
the inner normal, then that point t on the line P(t) which satisfies,
n.[P(t) – f ] = 0 condition is the intersection of the line with the boundary edge
To get the formal statement of the Cyrus-Beck algorithm we substitute value of
P(t) in equation 3
n . [P(t) – f ] = n . [P1 + (P2 – P1)t – f ] = 0 ... (5)
The relation should be applied for each boundary plane or edge of the window
to get the intersection points](https://image.slidesharecdn.com/unit-ivwindowingandclipping-230316142407-744dde0c/85/Unit-IV-Windowing-and-Clipping-pdf-47-320.jpg)
![Cyrus Beck Line Clipping Algorithm
Thus in general form equation (5) can be written as,
ni . [P1 + (P2 – P1)t – fi ] = 0 ... (6)
where, i is edge number
Solving equation (6) we get,
ni . [P1 – fi ] + ni . (P2 –P1)t = 0 ... (7)
Here the vector P2 – P1 defines the direction of the line, the direction of the line
is important to correctly identify the visibility of the line
The vector P1 - fi is proportional to the distance from the end point of the line
to the boundary point
Let us define,
D = P2 – P1 as the direction of a line and
Wi = P1 – fi as weighting factor](https://image.slidesharecdn.com/unit-ivwindowingandclipping-230316142407-744dde0c/85/Unit-IV-Windowing-and-Clipping-pdf-48-320.jpg)
Unit-IV Windowing and Clipping.pdf
- 1. COMPUTER GRAPHICS by Amol S. Gaikwad Lecturer Government Polytechnic Gadchiroli Maharashtra
- 3. Welcome! Are you excited for a fun learning session? Hi
- 4. Unit Outcomes Apply window to viewport transformation on the given object Write a program using given line clipping algorithm Apply the given line clipping algorithm to clip the line Apply text clipping on given tex Write a program using given polygon clipping algorithm
- 5. Introduction To Windowing A computer graphics package (graphics software) allows user to select which part of the picture to show on the display device and where that part to be placed on the display device A Cartesian co-ordinate system (world co-ordinate system) is used to define the picture In a two-dimensional picture , a view is selected by deciding a subarea of total picture are A user can select single area or multiple areas for display The picture part within the selected areas are then mapped (converted) onto the specific areas of the device coordinates
- 6. Transformations from world coordinates (cartesian coordinates) to device coordinates involves translation, rotation and scaling operations Transformations from world coordinates (cartesian coordinates) to device coordinates also involves deleting those parts of the picture that are outside the boundaries of selected display area Introduction To Windowing Window - A world coordinate area selected for display is called as window Viewport - An area on the display device to which a window is mapped is called as a viewport
- 7. Windowing - mapping a part of a world coordinate scene to device coordinates is referred to as windowing transformation Introduction To Windowing Windowing transformation is also called as viewing transformation or window- to-viewport transformation Window is also considered as an area of picture that is selected for viewing (display)
- 8. Introduction To Windowing Fig: Window-to-viewport transformation (viewing transformation)
- 9. The Two Dimensional Viewing-Transformation Pipeline Step-1 : First, we construct scene in world coordinates using basics figures and attributes Step-2 : Convert world coordinates to Viewing coordinates. (Viewing coordinate system is used to set up arbitrary orientation (direction) for rectangular windows) Step-3 : Map Viewing coordinates to Normalized View coordinates ( Normalized coordinates are in the range of 0 to 1) Step-4 : At final step all parts of picture that lie outside the viewport are clipped (removed) and contents of the viewport are transferred to device coordinates
- 10. The Two Dimensional Viewing-Transformation Pipeline Fig : Setting up a rotated world window in viewing coordiates and then transferring it to normalized-coordinate viewport
- 11. Window -To-Viewport Coordinate Transformation XWmin XWmax XVmax XVmin YVmin YVmax YWmin YWmax ( XW, YW ) ( XV, YV ) Fig : Window to viewport mapping
- 12. XV - XVmin Window -To-Viewport Coordinate Transformation To maintain the same relative position in viewport and window, we use following equation : XVmax - XVmin XW - XWmin XWmax - XWmin and YV -YVmin YVmax - YVmin YW - YWmin YWmax - YWmin = = ........ eqn-1 where (XW, YW) = window coordinates of point (XV, YV) = viewport coordinates of point
- 13. Window -To-Viewport Coordinate Transformation Solving eqn-1 we can calculate values of viewport position (XV,YV) as follow : XV = XVmin + (XW - XWmin)Sx YV = YVmin + (YW - YWmin)Sy ........ eqn-2 Where values of scaling factor Sx and Sy are XVmax - XVmin XWmax - XWmin YVmax - YVmin YWmax - YWmin = Sy Sx = and ..... eqn-3
- 14. Window -To-Viewport Coordinate Transformation Fig : Mapping selected parts of a scene in normalized coordinates to different video monitors
- 15. Clipping Any procedure that identifies which portion of a picture is inside or outside of a specified region (area) is called as 'clipping algorithm) The region (area) which is used to clip an object is called as 'clip window' There are various applications of clipping like - extracting part of a scene - creating objects using solid -modelling procedures - displaying multi-window environment - drawing and painting operations - selecting picture for copying
- 16. Clipping Classification of Clipping Algorithms Point Clipping Algorithm Line Clipping Algorithm ( Straight lines ) Polygon Clipping Algorithm ( Area clipping ) Curve Clipping Algorithm Text Clipping Algorithm
- 17. Point Clipping In point clipping we decide whether a point is inside or outside a region (area) Consider we have a rectangular window and we have to decide whether point P = (X,Y) is inside or outside the region Point P (X,Y) is inside the window if it satisfies following equation XWmin <= X <= XWmax YWmin <= Y <= YWmax Where ( XWmin, XWmax, YWmin, YWmax ) are edges of clip window Clip window can be world coordinate window or viewport boundaries
- 18. Solved Example - Point Clipping Check the points M(13,20) and K(17,65) for clipping. Soln :- Given : XWmin = 10, XWmax = 60 YWmin = 15 , YWmax = 40 XWmax XWmin YWmin 60 10 15 M (13,20 ) YWmax 40 P (X,Y) K (17,65 )
- 19. Solved Example - Point Clipping Point P (X,Y) is inside the window if it satisfies the both following equation : XWmin <= X <= XWmax, and YWmin <= Y <= YWmax For point M (13,20) , 10 <= 13 <= 60 and 15 <= 20 <= 40 Hence both equation are satisfied so point M(13,20) is inside the window Soln :- For point K (17,65 ) , 10 <= 65 > 60 and 15 <= 17 <= 40 only second equation is satisfied and first equation is not satisfied so, point K(17,65) is outside the window
- 20. Line Clipping Line clipping means identifying which portion of the line is inside or outside the clipping window Line clipping algorithm has to check three conditions as below 1) If line is completely inside the clipping window 2) If line is completely outside the clipping window 3) If the line both inside and outside the window
- 21. Line Clipping In the given figure line P1P2 is completely outside the clipping window P1 P2 P3 P4 P5 P6 clipping window Line P3P4 is completely inside the window Line P5P6 is partially inside and partially outside the window
- 22. Line Clipping After clipping ( removing ) the line, line P1P2 is completely removed because it was outside the window P3 P4 P7 P6 clipping window Line P3P4 is completely inside the window, so it will remain as it is inside the window For line P5P6, we have to calculate new intersection point P7 with window boundary and draw only portion P7P6 which is inside the window
- 23. Line Clipping Algorithms Various line clipping algorithm are as follow : Cohen-Sutherland Line Clipping Algorithm Cyrus-Beck Line Clipping Algorithm Liang Barsky Line Clipping Algorithm Mid-point subdivision Line Clipping Algorithm
- 24. Cohen -Sutherland Line Clipping Algorithms 1000 1001 1010 0001 0101 0100 0010 0110 0000 Window In Cohen-sutherland line clipping algorithm, a four-digit binary code is assigned (given) to each two both end points of a all the lines. This four digit binary code is called as 'region code', ex: 1010 Region code identifies the location of the point as compared to rectangular clipping window. Each bit gives information about the location of point with respect to clipping window
- 25. Cohen -Sutherland Line Clipping Algorithms 0000 If a point is on the left side of the window then its first bit is 1 or when X < XWmin If a point is on the right side of the window then its second bit is 1 or when XWmax < X If a point is below the window then its third bit is 1 or when Y < YWmin If a point is above the window then its fourth bit is 1 or when YWmax < Y bit 1: left bit bit 2: right bit bit 3: below bit bit 4: above bit If a point is inside the window then all four bits of that point are 0
- 26. Cohen-Sutherland Line Clipping Algorithms Cohen-Sutherland line clipping algorithm can be divided into two parts PART-1 : In part-1 we decide the category of lines as below Category 1: Lines which are completely inside the window Category 2: Lines which are completely outside the window Category 3: Lines which are partially inside and partially outside the window We give four bit code or region code to each end points of all the lines We give four bit code or region code to each end points of all the lines If a point is on the left side of the window or when X < XWmin then set first bit to 1
- 27. Cohen-Sutherland Line Clipping Algorithms PART-1 : If a point is on the left side of the window or when X < XWmin then set first bit to 1 If a point is on the right side of window or when XWmax < X then set second bit to 1 If a point is below the window or when Y < Y Wmin then set the third bit to 1 If a point is above the window or when YWmax< Y then set the fourth bit to 1 If a point is inside the window then all four bits of that point are 0
- 28. Cohen-Sutherland Line Clipping Algorithms PART-1 : If the region codes of both end points of line 0000 then that line completely lies inside the window and belongs to category-1 Select the line for displaying If the bitwise logical AND operation of region codes of the both end points of line is NOT 0000, then the line is completely outside the window and belongs to category-2 Reject this line and don't display it If the bitwise logical AND operation of region codes of the both end points of line is equal to 0000, then the line intersects the boundaries of window and we need to clip the line, such lines belong to category-3
- 29. Cohen-Sutherland Line Clipping Algorithms PART-2 : In part-2 we calculate the itersection points of lines which are in category-3 If first bit is 1, then the line intersects the left vertical boundary of the rectangle window, the intersection point (X,Y) is calculated as : Y = Y1 + m(XWmin - X1) If second bit is 1, then the line intersects the right vertical boundary of the rectangle window, the intersection point (X,Y) is calculated as : Y = Y1 + m(XWmax - X1) If third bit is 1, then the line intersects the bottom horizontal boundary of the rectangle window, the intersection point (X,Y) is calculated as : X = X1 + (YWmin - Y1)/m
- 30. Cohen-Sutherland Line Clipping Algorithms PART-2 : If fourth bit is 1, then the line intersects the top horizontal boundary of the rectangle window, the intersection point (X,Y) is calculated as : X = X1 + (YWmax - Y1)/m Where (X1, Y1) and (X2, Y2) = end points of line (X, Y) = intersection points of the line with rectangular window XWmin and XWmax = minimum and maximum X co-ordinate of window m = (Y2 - Y1)/ (X2 - X1) = slope of line YWmin and YWmax = minimum and maximum Y co-ordinate of window
- 31. Cohen-Sutherland Line Clipping Algorithms PART-2 : After calculating the intersection point join these intersection point to each other and draw the line, or Join the intersection point with the point which is already inside the window and draw the line Stop
- 32. Cohen-Sutherland Line Clipping Algorithms Cohen - Sutherland line clipping algorithm is written in short as below : Step-1 : Read the two end points of a line P1( X1, Y1) and P2 (X2, Y2) Step-2 : Read the lower left and upper left co-ordinates of clipping window Step-3 : Assign 4-bit region codes to P1 and P2 Step-4: Check category of line for its visibility Step-5 : If category-1 line then, accept line, display line and exit If category-2 line then, reject line and exit If category-3 line then, continue next steps Step-6 : Find out intersecting boundaries of clipping window
- 33. Cohen-Sutherland Line Clipping Algorithms Step-7 : Find out point of intersection of line with window boundary Step -8 : Replace end point with intersection point form the new line, accept this new line and discard (reject) others Step-9 : Display this new line Step-10 : Stop
- 34. Mid-Point Subdivision Line Clipping Algorithms Mid-Point Subdivision line clipping algorithm can be divided into two parts PART-1 : In part-1 we decide the category of lines as below Category 1: Lines which are completely inside the window Category 2: Lines which are completely outside the window Category 3: Lines which are partially inside and partially outside the window We give four bit code or region code to each end points of all the lines We give four bit code or region code to each end points of all the lines If a point is on the left side of the window or when X < XWmin then set first bit to 1
- 35. Mid-Point Subdivision Line Clipping Algorithms PART-1 : If a point is on the left side of the window or when X < XWmin then set first bit to 1 If a point is on the right side of window or when XWmax < X then set second bit to 1 If a point is below the window or when Y < Y Wmin then set the third bit to 1 If a point is above the window or when YWmax< Y then set the fourth bit to 1 If a point is inside the window then all four bits of that point are 0
- 36. PART-1 : If the region codes of both end points of line 0000 then that line completely lies inside the window and belongs to category-1 Select the line for displaying If the bitwise logical AND operation of region codes of the both end points of line is NOT 0000, then the line is completely outside the window and belongs to category-2 Reject this line and don't display it If the bitwise logical AND operation of region codes of the both end points of line is equal to 0000, then the line intersects the boundaries of window and we need to clip the line, such lines belong to category-3 Mid-Point Subdivision Line Clipping Algorithms
- 37. PART-2 : Mid-Point Subdivision Line Clipping Algorithms In part-2 we divide the line into eul parts by calculate the middle points of lines which are in category-3 P1 P2 If P1(X1,Y1) and P2(X2,Y2) are end points of line then mid-points are calculated as Xm = (X1 +X2)/2 Ym = (Y1+Y2)/2 P1 P2 P3 For both the divided line segments check whether they are completey inside or outside
- 38. PART-2 : Mid-Point Subdivision Line Clipping Algorithms If the line segments are not completely inside or side then again divide the line segments into two equal parts by calculating Xm and Ym values P1 P2 P4 P5 P3 Repeatedly divide the line till we get those lines which are completely inside or outside Draw the line which are completely inside and reject the line which are completely outside Stop P4 P5 P3
- 39. Mid-Point Subdivision Line Clipping Algorithms Mid-Point Subdivision line clipping algorithm is written in short as below : Step-1 : Read two end points of line P1 (X1, Y1) and P2 (X2, Y2) Step-2 : Read lower left and upper right co-ordinates of clipping window Step-3 : Assign 4-bit region codes to points P1 and P2 Step-4 : Check category of line for visibility Step-5 : If category-1 line then, accept line, display line and exit If category-2 line then, reject line and exit If category-3 line then, continue next steps
- 40. Mid-Point Subdivision Line Clipping Algorithms Step-6 : For category-3 line, find out its mid-point and divide it into two equal line segments Step-7 : For both divided line segments, repeat step-3 to step-6 till we get completely inside (visible ) and completely outside (invisible) line segments i.e category-1 and category-2 lines Step-8 : Stop
- 41. Liang-Barsky Line Clipping Algorithms Step-1 : Accept the end points A (X1, Y1) and B (X2, Y2) of line and window co-ordinates XWmin , YWmin, YWmax as input Step-2: Calculate pk and qk for k = 1, 2, 3, 4 as follow p1 = - X q1 = X1 - XWmin p2 = X q2 = XWmax - X1 p3 = - Y q3 = Y1 - YWmin p4 = Y q4 = YWmax - Y1 = delta symbol, X = X2-X1 and Y = Y2 - Y1
- 42. Liang-Barsky Line Clipping Algorithms Step-3 : If pk = 0, then line is parallel to kth boundary if qk < 0, then line is outside the boundary and discard (reject) the line and stop if qk >= 0, then line is inside the parallel boundary, calculate intersection points if pk not equal to 0, then go to step-4 Step-4 : calculate : rk = qk / pk, for k =1, 2, 3, 4 Step-5 : Determine (decide) u1 for pk < 0 by selecting relative rk as u1 = max(0, rk) u2 for pk > 0 by selecting rk as u2 = min(rk, 1)
- 43. Liang-Barsky Line Clipping Algorithms Step-6 : If u1 > u2 then line is totally outside discard (reject) the line and stop X' = X1 + u1 X and Y' = Y1 + u1 Y Step-7 : If u1 < u2 then calculate end points of clipped line as below : Step-8 : Display the new line segment X'' = X1 + u2 X and Y'' = Y1 + u2 Y
- 44. Cyrus Beck Line Clipping Algorithm Cyrus Beck line clipping algorithm is used to clip 2D/3D lines against convex polygon / polyhedron It is a parametric line clipping algorithm The term parametric means that we require finding the value of the parameter t in the parametric representation of the line segment for the point where the segment intersects the clipping edge Consider the line segment P1P2, the parametric equation of line segment P1P2 is : P(t) = P1 + t(P2 – P1) Where, t value defines a point on the line going through P1 and P2. 0 <= t <= 1 defines line segment between P1 and P2. If t = 0 then P(0) = P1 and If t = 1 then P(1) = P2
- 45. Cyrus Beck Line Clipping Algorithm P1 P2 f n n n n.[ P(t) - f ] > 0 n.[ P(t) - f ] = 0 n.[ P(t) - f ] < 0 Clipping edge (clipping boundary ) x y f 0 n R-conves region Convex region, boundary point and inner normal
- 46. Cyrus Beck Line Clipping Algorithm Consider a convex clipping region R, f is a boundary point of the convex region R and n is an inner normal for one of its boundaries as shown in above figure Then we can distinguish (decide) in which region a point lie by looking at the value of the dot product, n.[P(t) – f ], as shown in Fig. If dot product is negative i.e., n.[P(t) – f ] < 0 ... (2) then the vector [P(t) – f ] is pointed away from the interior of R. If dot product is zero i.e., n.[P(t) – f ] = 0 ... (3) then the vector [P(t) – f ] is pointed parallel to the plane containing f and perpendicular (90 degree) to the normal
- 47. Cyrus Beck Line Clipping Algorithm If dot product is positive i.e., n.[P(t) – f ] > 0 ... (4) then the vector [P(t) – f ] is pointed towards the interior of R. As shown in Fig. if the point f lies in the boundary plane or edge for which n is the inner normal, then that point t on the line P(t) which satisfies, n.[P(t) – f ] = 0 condition is the intersection of the line with the boundary edge To get the formal statement of the Cyrus-Beck algorithm we substitute value of P(t) in equation 3 n . [P(t) – f ] = n . [P1 + (P2 – P1)t – f ] = 0 ... (5) The relation should be applied for each boundary plane or edge of the window to get the intersection points
- 48. Cyrus Beck Line Clipping Algorithm Thus in general form equation (5) can be written as, ni . [P1 + (P2 – P1)t – fi ] = 0 ... (6) where, i is edge number Solving equation (6) we get, ni . [P1 – fi ] + ni . (P2 –P1)t = 0 ... (7) Here the vector P2 – P1 defines the direction of the line, the direction of the line is important to correctly identify the visibility of the line The vector P1 - fi is proportional to the distance from the end point of the line to the boundary point Let us define, D = P2 – P1 as the direction of a line and Wi = P1 – fi as weighting factor
- 49. Cyrus Beck Line Clipping Algorithm Substituting newly defined variable D and Wi in Equation (7) we get, ni.Wi + (ni . D)t = 0 ... (8) t = – (ni.Wi) /(ni.D) ... (9) where, D ≠ 0 and i = 1, 2, 3 ..... The equation (9) is used to obtain the value of t for the intersection of the line with each edge of the clipping window. We must select the proper value for t using following tips : 1. If t is outside the range 0<= t <= 1, then it can be ignored 2. We know that, the line can intersect the convex window in at most two points , i.e. at two values of t. With equation (9) , there can be several values of t in the range of 0<= t<= 1 . We have to choose the largest lower limit and the smallest upper limit 3. If (ni . Di) > 0 then equation (9) gives lower limit value for t and if (ni. Di) < 0 then equation (9) gives upper limit value for t
- 50. Cyrus Beck Line Clipping Algorithm Cyrus Beck line clipping algorithm is written in short as below : Step 1 : Read end points of line P1 and P2 Step 2 : Read vertex coordinates of clipping window Step 3 : Calculate D = P2 – P1 Step 4 : Assign boundary point b with particular edge Step 5 : Find inner normal vector for corresponding edge Step 6 : Calculate D.n and W = P1 – b
- 51. Cyrus Beck Line Clipping Algorithm Step 12 : Draw line segment P(tL) to P(tU) Step 13 : Stop
- 52. Polygon Clipping Polygon clipping means removing that portion of polygon which is outside the window Fig : Correctly clipped polygon
- 53. Polygon Clipping Various polygon clipping algorithm Sutherland - Hodgeman Polygon Clipping Algorithm Weiler - Atherton Polygon Clipping Algorithm
- 54. Sutherland - Hodgeman Polygon Clipping Algorithm We can clip a polygon by processing the whole polygon boundary against the window boundary (edge) First clip the polygon against the left rectangle boundary, after doing this we will get new set of polyon vertices or polygon points These new set of polygon points (vertices) are successively passed to the right boundary clipper, bottom boundary clipper and top boundary clipper After clipping the polygon at each rectangle boundary, we will get a new set of polygon points (vertices)
- 55. Sutherland - Hodgeman Polygon Clipping Algorithm Fig : Clipping a polygon against successive window boundaries
- 56. Sutherland - Hodgeman Polygon Clipping Algorithm There are four possible cases when processing polygon vertices in sequence around the perimeter of a polygon Case-1 : If the first vertex is outside the window boundary and the second vertex is inside the window boundary, then the intersection point with the window boundary and polygon vertex which is inside are added to the output vertex list Case-2 : If both the input vertices are inside the window boundary, then only second vertex is added to the output vertex list Case-3 : If the first vertex is inside the window boundary and second vertex is outside, then only the intersection point is added to the output vertex list
- 57. Sutherland - Hodgeman Polygon Clipping Algorithm Case-4 : If both polygon vertices are outside the window, then nothing is added to the output vertex list Fig : Successive processing of polygon vertices against left window boundary
- 58. Sutherland - Hodgeman Polygon Clipping Algorithm As we can see in the above first figure, vertex V2 inside the window, V1 is outside the window and vertex V1' is intersection point with the left boundary of window, so both V1' and V2 are added to the output vertex list In second figure, vertices V1 and V2 both are inside the window, but add only second vertex V2 in the output vertex list In third figure, vertex V1 is inside the window, V2 is outside the window and V1' is the intersection point with left boundary of window, so add only intersection point V1' in the output vertex list In fourth figure vertex V1 and V2 are both outside the window so nothing is added to the output vertex list
- 59. Sutherland - Hodgeman Polygon Clipping Algorithm The Sutherland - Hodgeman algorithm can be written in short as below Step-1 : Read the coordinates of all the vertices of a polygon Step-2 : Read the coordinates of clipping window Step-3 : Process the vertices of polygon with respect to boundary of window to get a set of output vertices Step-4 : Repeat step-3 for right, top and bottom edges (boundary) of polygon respectively to get the final set of output vertices Step-5 : Display (draw) the polygon by connecting all the vertices from the out vertices list (set) Step-6 : Stop
- 60. Text Clipping Text clipping means removing that portion of text (string) that is outside the clipping window and keeping that portion of text (string) that is inside the clipping window Various text clipping techniques All-or-none string clipping strategy All-or-none character clipping strategy Clipping individual characters
- 61. Al-Or-None String Clipping This is a simplest method for clipping character strings with respect to window boundary In this method, if the string is completely inside the window , then we select that string for drawing If the string is completely outside or partially outside the window then we reject that string and don't select the string for drawing In the given figure 'STRING 1' is partially outside and 'STRING 2' is completely inside the window, so we select 'STRING 2' and reject 'STRING 1' Fig : All-or-none string clipping
- 62. Al-Or-None Character Clipping In this method we discard (remove) only those characters which are completely outside the window We draw those characters which are completely inside the window Boundary limits of each character is compared to the window boundary Any character that is on the boundary or is outside the window boudary is clipper (removed) In the given figure character 'S' and 'N' are removed as they are on the window boundary Fig : All-or-none character clipping
- 63. Clipping Individual Characters In this method we don not remove entire character If the character is partially inside and partially outside then, we remove only that part of charcter which is outside and draw that part of character which is inside In this figure character 'S' and 'T' are on the boundary of the window, they are partially inside and partially outside the window So we draw only draw that portion of 'S' and 'N' character which is inside and remove that portion which is outside Fig : Clipping individual characters
- 66. Additional Resources https://www.tutorialspoint.com/computer_graphics https://nptel.ac.in/courses/106/102/106102065 Computer Graphics - Donald Hearn, Baker M Pauline, Pearson Education
- 67. Summary of Class Windowing and Clipping Lesson Recap 1 Line Clipping Algorithms Lesson Recap 2 Polygon Clipping Algorithm Lesson Recap 3 Text Clipping Lesson Recap 4
- 68. Thank you for attending!