This document discusses different algorithms for line and polygon clipping. It describes 4 cases for line clipping depending on where the endpoints are located relative to the clipping area. For polygon clipping, it explains the Sutherland-Hodgeman algorithm and 4 cases for processing vertices and adding them to the output list. It also introduces the midpoint subdivision algorithm for line clipping which uses binary search to iteratively subdivide lines into smaller segments for clipping.
Sutherland hodgman polygon clipping algorithmTawfiq Ahmed
Sutherland Hodgman polygon clipping algorithm is a very simple clipping algorithm to understand. I hope my slide will help you guys.
-Thanks
Tawfiq Ahmed
The Lian-Barsky algorithm is a line clipping algorithm. This algorithm is more efficient than Cohen–Sutherland line clipping algorithm and can be extended to 3-Dimensional clipping. This algorithm is considered to be the faster parametric line-clipping algorithm. The following concepts are used in this clipping:
The parametric equation of the line.
The inequalities describing the range of the clipping window which is used to determine the intersections between the line and the clip window.
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In the heart of Singapore, where tradition meets modernity, He embarks on a culinary adventure that transcends borders. His mission? Ang Chong Yi Exploring the Cultural Heritage and Identity in Singaporean Cuisine. To explore the rich tapestry of flavours that define Singaporean cuisine while embracing innovative plant-based approaches. Join us as we follow his footsteps through bustling markets, hidden hawker stalls, and vibrant street corners.
Sutherland hodgman polygon clipping algorithmTawfiq Ahmed
Sutherland Hodgman polygon clipping algorithm is a very simple clipping algorithm to understand. I hope my slide will help you guys.
-Thanks
Tawfiq Ahmed
The Lian-Barsky algorithm is a line clipping algorithm. This algorithm is more efficient than Cohen–Sutherland line clipping algorithm and can be extended to 3-Dimensional clipping. This algorithm is considered to be the faster parametric line-clipping algorithm. The following concepts are used in this clipping:
The parametric equation of the line.
The inequalities describing the range of the clipping window which is used to determine the intersections between the line and the clip window.
Ang Chong Yi Navigating Singaporean Flavors: A Journey from Cultural Heritage...Ang Chong Yi
In the heart of Singapore, where tradition meets modernity, He embarks on a culinary adventure that transcends borders. His mission? Ang Chong Yi Exploring the Cultural Heritage and Identity in Singaporean Cuisine. To explore the rich tapestry of flavours that define Singaporean cuisine while embracing innovative plant-based approaches. Join us as we follow his footsteps through bustling markets, hidden hawker stalls, and vibrant street corners.
Hamdard Laboratories (India), is a Unani pharmaceutical company in India (following the independence of India from Britain, "Hamdard" Unani branches were established in Bangladesh (erstwhile East Pakistan) and Pakistan). It was established in 1906 by Hakeem Hafiz Abdul Majeed in Delhi, and became
a waqf (non-profitable trust) in 1948. It is associated with Hamdard Foundation, a charitable educational trust.
Hamdard' is a compound word derived from Persian, which combines the words 'hum' (used in the sense of 'companion') and 'dard' (meaning 'pain'). 'Hamdard' thus means 'a companion in pain' and 'sympathizer in suffering'.
The goals of Hamdard were lofty; easing the suffering of the sick with healing herbs. With a simple tenet that no one has ever become poor by giving, Hakeem Abdul Majeed let the whole world find compassion in him.
They had always maintained that working in old, traditional ways would not be entirely fruitful. A broader outlook was essential for a continued and meaningful existence. their effective team at Hamdard helped the system gain its pride of place and thus they made an entry into an expansive world of discovery and research.
Hamdard Laboratories was founded in 1906 in Delhi by Hakeem Hafiz Abdul Majeed and Ansarullah Tabani, a Unani practitioner. The name Hamdard means "companion in suffering" in Urdu language.(itself borrowed from Persian) Hakim Hafiz Abdul Majeed was born in Pilibhit City UP, India in 1883 to Sheikh Rahim Bakhsh. He is said to have learnt the complete Quran Sharif by heart. He also studied the origin of Urdu and Persian languages. Subsequently, he acquired the highest degree in the unani system of medicine.
Hakim Hafiz Abdul Majeed got in touch with Hakim Zamal Khan, who had a keen interest in herbs and was famous for identifying medicinal plants. Having consulted with his wife, Abdul Majeed set up a herbal shop at Hauz Qazi in Delhi in 1906 and started to produce herbal medicine there. In 1920 the small herbal shop turned into a full-fledged production house.
Hamdard Foundation was created in 1964 to disburse the profits of the company to promote the interests of the society. All the profits of the company go to the foundation.
After Abdul Majeed's death, his son Hakeem Abdul Hameed took over the administration of Hamdard Laboratories at the age of fourteen.
Even with humble beginnings, the goals of Hamdard were lofty; easing the suffering of the sick with healing herbs. With a simple tenet that no one has ever become poor by giving, Hakeem Abdul Majeed let the whole world find compassion in him. Unfortunately, he passed away quite early but his wife, Rabia Begum, with the support of her son, Hakeem Abdul Hameed, not only kept the institution in existence but also expanded it. As he grew up, Hakeem Abdul Hameed took on all responsibilities. After helping with his younger brother's upbringing and education, he included him in running the institution. Both brothers Hakeem Abdul Hameed and Hakim Mohammed
Vietnam Mushroom Market Growth, Demand and Challenges of the Key Industry Pla...IMARC Group
The Vietnam mushroom market size is projected to exhibit a growth rate (CAGR) of 6.52% during 2024-2032.
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Roti Bank Hyderabad: A Beacon of Hope and NourishmentRoti Bank
One of the top cities of India, Hyderabad is the capital of Telangana and home to some of the biggest companies. But the other aspect of the city is a huge chunk of population that is even deprived of the food and shelter. There are many people in Hyderabad that are not having access to
Roti Bank Hyderabad: A Beacon of Hope and Nourishment
ytdty.pptx
1. Different cases for Line Clipping
1. Both endpoints of the line lie with in the clipping area. This means that the
line is included completely in the clipping area, so that the whole line must be
drawn.
Clip
rectangle
B
A
B
A
1
2. Conti….
3. Both end points are located outside the clipping area and the line do not intersect the
clipping area. In the case , the line lies completely outside the clipping area and can be
neglected for the scene.
4. Both endpoints are located outside the clipping area and the line intersect the clipping
area. The two intersection points of the line with the clipping are must be determined.
Only the part of the line between these two intersection points should be drawn.
C
D’
B
A
G’
H'
Clip
rectangle
B
A
D
D’
C
G’
H'
G
H
I’
I
J’
J
E
F
2
3. Mid point subdivision algorithm
This method divide the line into three category:
I. Category 1: Visible line
II. Category 2: not visible line
III. Category 3: candidate for Clipping.
An alternative way to process a line in category 3 is based on binary
search.The line is divided at its midpointsinto two shorter line segments.
Each line in a category three is divided again into shorter segments and
categorized.This bisection and categorization process continue until eavh
line segment that spans across a window boundary reaches a threshold for
line size and all other segments are either in a category 1 (visible) or in
category 2 (Not visible.)
3
6. Comparison b/w Cohen-Sutherland and Mid-point subdivision clipping Algorithm
• Midpoint subdivision algorithm is a special case of Cohen-sutherland algorithm,
where the intersection is not computed by equation solving. It is computed by a
midpoint approximation method, which is suitable for hardware and it is very
fast and efficient.
• The maximum time is consume in the clipping process is to do intersection calculation
with the window boundaries.
• The Cohen-sutherland algorithm reduces these calculation by first discarding that lines
those can be trivially accepted or rejected.
6
7. Polygon Clipping
The simplest curve is a line segment or simply a line. A sequence of line where the
following line starts where the previous one ends is called a polyline. If the last line
segment of the polyline ends where the first line segment started, the polyline is called
a polygon. A polygon is defined by n number of sides in the polygon. We can divide
polygon into two classes.
A convex polygon is a polygon such that for any two points inside the polygon , all
the point of the line segment connecting them are also inside the polygon. A triangle
is always a convex one.
Polygon
Convex
Polygon
Concave
Polygon
P
Q
7
8. Conti…
A Concave polygon is one which is not convex.. A polygon is said to be a concave
if the line joining any two interior points of the polygon does not lies completely
inside the polygon.
There are four possible cases when processes vertices in sequence around the
parameter of the polygon. As each pair of adjacent polygon vertices is passed to a
window boundary clipper. We make the following test.
P
Q
8
9. Conti…
Case 1: If the first vertex is outside the window boundary and second vertex
is inside the window boundary then both the intersection point of a polygon
edge with the window boundary and second vertex are added to the output
vertex list.
Case 2: If both input vertices are inside the window boundary. Only the
second vertex is added to the Vertex list
Case3: If the first vertex is inside the window boundary and the second
vertex is outside the window boundary then only the edge intersection with the
window boundary is added to the output vertex list.
Case 4: If both the input vertices are outside the window boundary then
nothing is save to the output list.
9
10. SUTHERLAND AND HODGEMAN
ALGORITHM(Polygon clipping)
Polygon clipping is a process of clipping a polygon by considering
the edge of that as different line segments. If a polygon is clipped
against a rectangular window then it is possible that we get various
unconnected edges of a polygon. To get a closed polygon of unconnected
edges we connect theses edges along the side of a clipping window to
form a closed polygon.
The Sutherland –Hodgeman polygon clipping algorithm clips polygon
against convex clipping windows. The Sutherland Hodgeman Polygon
clipping algorithm may produce connecting lines that were not in the
original polygon. When the subject polygon is concave theses connecting
lines may be undesirable artifacts.
There are four situation to save vertices in output vertex list.
10
11. Conti……
1. If the first vertex is outside the window boundary and second vertex is inside the
window boundary then both the intersection point of a polygon edge with the
window boundary and second vertex are added to the output vertex list.Ex:save v1’,v2.
POLYGON
WINDOW(W)
2. If both input vertices are inside the window boundary. Only the second vertex is
added to the Vertex list
POLYGON
WINDOW(w)
V1
V1’
V2
V1
V2
11
12. Cont…..
3. If the first vertex is inside the window boundary and the second vertex is
outside the window boundary then only the edge intersection with the
window boundary is added to the output vertex list.Ex: v1’, v1.
POLYGON
WINDOW(W)
4. If both the input vertices are outside the window boundary then nothing is
save to the output list.
POLYGON
WINDOW(W)
’
V2
V1
V2
V1’
V1
12