OVERVIEW OF GRAPHICS
SYSTEMS
L7
Clipping
Plan
Review of rendering pipeline
Clipping
The Graphics Pipeline
Modeling
Transformations
Illumination
(Shading)
Viewing
Transformation
(Perspective /
Orthographic)
Clipping
Projection
(to Screen Space)
Scan Conversion
(Rasterization)
Visibility / Display
Clipping
Clipping is the process of extracting identifying element of a
scene or picture inside or outside a special region, called the
clipping region. ‫عملية استخراج اجزاء معينة من مشهد او صورة‬
Clipping: Remove points outside a region of interest – clip
‫حذف النقاط اللي تكون خارج املنطقة اللي نبيها‬
window.
Clipping is useful for copying, moving or deleting a portion
: ‫استعماالته‬
of a scene or picture
Windowing I
A scene is made up of a collection of objects specified in
world coordinates ‫يتكون املشهد من مجموعة من الكائنات املحددة في إحداثيات العالم‬
World Coordinates
Windowing II
.‫ يتم عرض تلك الكائنات فقط داخل نافذة معينة‬، ‫عندما نعرض مشهًدا‬
When we display a scene only those objects within a particular window are displayed.
clipping Window
wxmax
‫ألن جميع أجزاء املشهد خارج القسم املحدد يتم قطعها‬
A section of a two dimensional scene that is selected for display is called a clipping
window, because all parts of the scene outside the selected section are clipped off
wymax
wymin
wxmin
World Coordinates
Windowing III
‫ألن رسم األشياء على شاشة العرض يستغرق وقتًا نقطع كل شيء خارج النافذة‬
viewport
wxmax
Because drawing things to a display takes time we clip
everything outside the window
wymax
wymin
wxmin
World Coordinates
Clipping
(‫عشان نتجنب نرسم اشياء خارج النافذة)الجزء اللي نبيه‬
‫ نحدد الجزء اللي نبي نعرضه‬١‫ نرسم بدائل هندسية داخل النافذة‬٢-
Avoid Drawing Parts of Primitives Outside Window
Window defines part of scene being viewed
Must draw geometric primitives only inside window
World Coordinates
Viewport Transformation
Image
Transform 2D Geometric Primitives from Screen Coordinate
System (Projection Coordinates) to Image Coordinate
System (Device Coordinates)
Screen
Viewport
Window
‫إحداثيات العالم)الحقيقي( املحدد للعرض‬
Window vs. Viewport
‫الجزء اللي حددناه‬
‫حددناه مع‬-‫الصورة الكاملة‬
World-coordinate area selected for display
What is to be viewed
‫املساحة املوجودة على جهاز العرض الذي تم تعيني نافذة فيه‬
Area on the display device to which a window is mapped
Where it is to be displayed
Viewport
‫الجزء بعد‬
‫ماسوينا له قص‬
-‫ على جهاز العرض‬-
Clipping
All-or-none clipping: If any part of object outside clip
window then the whole object is rejected.
Point clipping: Only keep the points that are inside
clip window.
Line clipping: Only keep segment of line inside clip
window.
Polygon clipping: Only keep segment of polygon
inside clip window.
Text clipping.
Types of clipping:
1.
2.
3.
4.
5.
Why Clip?
Bad idea to rasterize outside of framebuffer bounds
Also, don’t waste time scan converting pixels outside
‫ما نضيع وقت بأننا نحول االشياء اللي خارج النافذة لبكسل‬
window
Clipping
P3
P7
P4
P5
P9
Window
P6
P10
P1
wxmax
P8
P2
For the image below consider which lines and points should
be kept and which ones should be clipped.
wymax
wymin
wxmin
Point Clipping
P
P1
P Clipped
4
Window
Clipped
P9
P10
P8
P2
Clipped
wxmax
Points Within the Window
are Not Clipped
5
Easy - a point (x,y) is not clipped if:
wxmin≤ x ≤ wxmaxAND wymin≤ y ≤ wymax
P7
Clipped
otherwise it is clipped
wymax
wymin
wxmin
((30 ,30)) ‫قيمة امليمنوم عندي‬
((110 ,130)) ‫قيمة املاكس عندي‬
‫ هي‬: ‫النقاط اللي مارح تنقص‬
‫اللي تكون بينهم )اكبر من املن‬
(‫واصغر من املاكس‬
P1= (10,20), P2= (30,50), P3= (60,90), and P4=
(130,150). Suppose that the coordinates of the two
opposite corners of the clip window are (xwmin, ywmin) =
(30, 30) and (xwmax, ywmax) = (130, 110). Which of the
above points will be clipped?
P2 and P3 will saved because:
For P2: 30 ≤ 30 ≤ 130 and 30 ≤ 50 ≤ 110.
For P3: 30 ≤ 60 ≤ 130 and 30 ≤ 90 ≤ 110.
Line Clipping
‫ فحص نقاط نهاية كل سطر ملعرفة ما إذا كانت في النافذة أم ال‬- ‫أصعب‬
Solution
Example
Harder - examine the end-points of each line to see if they
are in the window or not
Situation
Must clip
Don’t clip
• One end-point inside the
window, one outside
Don’t know!
• Both end-points inside the
window
• Both end-points outside
the window
Brute Force Line Clipping
Brute force line clipping can be
performed as follows: ‫ال تقم بقص الخطوط بنقطتي النهاية داخل النافذة‬
Don’t clip lines with both endpoints within the window
For lines with one end- point
inside the window and one endpoint outside, calculate the
intersection point (using the
equation of the line) and clip
from this point out.
‫للنقاط اللي بدايتها داخل ونهايتها برا‬
(‫ نحسب نقطة التقاطع )تقاطع الخط مع حدود النافذة‬، ‫باستخدام معادلة الخط‬
‫واللي بعد هالنقطة نحذفه‬
Brute Force Line Clipping (cont…)
For lines with both end-points outside the
window test the line for intersection with all
of the window boundaries, and clip
appropriately.
، ‫بالنسبة للخطوط ذات النهايتني الخارجيتني للنافذة‬
‫اختبر الخط للتقاطع مع كل حدود النافذة‬
.‫ وقم باملقطع بشكل مناسب‬،
However, calculating line intersections is
computationally expensive
Because a scene can contain so many lines,
the brute force approach to clipping is much
too slow
‫يعتبر مكلف وبطيء‬
Cohen-Sutherland Clipping
Algorithm
An efficient line clipping algorithm
The key advantage of the algorithm is that it vastly reduces the
number of line intersections that must be calculated
‫يقلل بشكل كبير من عدد التقاطعات الخط الذي يجب حسابه‬
Cohen-Sutherland : World Division
World space is divided into regions based on the window
boundaries.
Each region has a unique four bit region code
Region codes indicate the position of the regions with
respect to the window ‫تشير رموز املنطقة إلى موضع املناطق فيما يتعلق بالنافذة‬
Cohen-Sutherland: Labelling
P5 [0000]
P6 [0000]
Window
P4 [1000]
‫يتم تمييز كل نقطة نهاية برمز املنطقة املناسب‬
P3 [0001]
P7 [0001]
P9 [0000]
P [0100]
10
wxmax
P14 [0110]
P8 [0010]
P12 [0010]
P11 [1010]
Every end-point is labelled with the appropriate region code
wymax
wymin
P13 [0101]
wxmin
Cohen-Sutherland: Lines in The Window
Lines completely contained within the window
boundaries have region code [0000] for both end-points
so are not clipped
Cohen-Sutherland: Other Lines
Lines that cannot be identified as completely inside or
outside the window may or may not cross the window
interior ‫األسطر التي ال يمكن تحديدها تماًما داخل أو خارج النافذة قد تعبر أو ال تعبر النافذة الداخلية‬
These lines are processed as follows:
◦ Compare an end-point outside the window to a boundary
(choose any order in which to consider boundaries e.g.
left, right, bottom, top) and determine how much can be
discarded
◦ If the remainder of the line is entirely inside or outside the
window, retain it or clip it respectively
Cohen-Sutherland: Other Lines
(cont…)
◦ Otherwise, compare the remainder of the line against the other
window boundaries
◦ Continue until the line is either discarded or a segment inside
the window is found
We can use the region codes to determine which window
boundaries should be considered for intersection
◦ To check if a line crosses a particular boundary we compare the
appropriate bits in the region codes of its end-points
◦ If one of these is a 1 and the other is a 0 then the line crosses
the boundary
Cohen-Sutherland Examples
Consider the line P9 to P10below
◦ Start at P10
◦ From the region codes of the two
end-points we know the line doesn’t
cross the left or right boundary
◦ Calculate the intersection of the line
with the bottom boundary to generate
point P10
◦ The line P9 to P10’ is completely inside
the window so is retained
wymax
wymin
Window
P9 [0000]
P10’ [0000]
P10 [0100]
P8 [0010]
wxmax
P8’ [0000]
Window
P7’ [0000]
wxmin
P7 [0001]
Cohen-Sutherland Examples (cont…)
wymin
wymax
Consider the line P7 to P8below
◦ Start at P7
◦ From the two region
codes of the two
end-points we know
the line crosses the
left boundary so
calculate the
intersection point to
generate P ’
7
wymax
wymin
P7 [0001]
Cohen-Sutherland Examples (cont…)
Consider the line P7’ to P8
◦ Start at P8
◦ Calculate the
intersection with the
right boundary to
generate P 8’
◦ P’7 to P 8’ is inside
the window so is
retained
P8 [0010]
wxmax
P8’ [0000]
Window
P7’ [0000]
wxmin
Window
wxmax
Cohen-Sutherland Worked Example
wymax
wymin
wxmin
Intersection points with the window boundaries are
calculated using the line-equation parameters
◦ Consider a line with the end-points (x1, y1) and (x2, y2)
◦ The y-coordinate of an intersection with a vertical
window boundary can be calculated using:
y = y1 + m (xboundary - x1)
where xboundary can be set to either wxmin or wxmax
◦ The x-coordinate of an intersection with a horizontal
window boundary can be calculated using:
x = x1 + (yboundary - y1) / m
where yboundary can be set to either wymin or wymax
◦ m is the slope of the line in question and can be
calculated as m = (y2- y1) / (x2 - x1)
Suppose that the coordinates of opposite corners of the
clip window are (68,59) & (92,71). Use CohenSutherland clipping line algorithm to find region codes
of the line (72,65)-(90,68), and the line (74,93)-(85,100),
and the line (60,50)-(120, 93).
Solution:
1. Calculate differences between endpoint coordinates
and clipping boundaries.
2. Use the resultant sign bit of each difference
calculation to set the corresponding value in the
region code.
(68,59) & (92,71)
Line (72,65)-(90,68):
the region code of (72,65) is 0000
the region code of (90,68) is 0000
The line (72-65)-(90,68) is
completely inside
Line (74,93)-(85,100):
the region code of (74,93) is 1000
the region code of (85,100) is 1000
Since 1000 AND 1000 = 1000 (Non Zero), so the line
(74,93) – (85,100) lie completely outside the clipping
region. So we clip it.
Line (60,50)-(120,95):
the region code of (60,50) is 1010
the region code of (120,95) is 0101
The line is saved because the final region code is 0000.
Similarly to lines, areas must
be clipped to a window
boundary
Consideration must be taken
as to which portions of the
area must be clipped
Clip Left
Clip Right
Clip Top
Clip Bottom
A technique for clipping areas developed by
Sutherland & Hodgman
Put simply the polygon is clipped by comparing it
against each boundary in turn
Original Area
To clip an area against an individual boundary:
◦
◦
◦
◦
◦
Consider each vertex in turn against the boundary
Vertices inside the boundary are saved for clipping against
the next boundary
Vertices outside the boundary are clipped
If we proceed from a point inside the boundary to one
outside, the intersection of the line with the boundary is
saved
If we cross from the outside to the inside intersection point
and the vertex are saved
character
‫نستخدم مستطيل لكل‬
‫نستخدم مستطيل لكل سترينق‬
In general, methods depend on how characters are represented
However, three strategies can be followed:
all-or-none string clipping
use a bounding rectangle for the string
all-or-none character clipping
use a bounding rectangle for the character
individual character clipping or component clipping
like line/curve clipping (outlined char’s)
compare individual pixels (bit-mapped)