SlideShare a Scribd company logo
Unit 1
Basic of computer graphics
By: Medhavi Pandey
Outline
▪ Numerical on types of Transformation
▪ SheRotation aring
▪ Scaling
▪
X-Shear
• The transformation matrix for X-Shear can be represented as:-
• Xsh = 1 Shx 0
0 1 0
0 0 1
• X' = X + ShX . Y
• Y’ = Y
Y-Shear
• The Y-Shear can be represented in matrix from as −
• Ysh = 1 0 0
Shy 1 0
0 0 1
• Y' = Y + Shy . X
• X’ = X
Numerical Practice
2D SCALING
• The scaling factor SX, SY scales the object in X and Y direction
respectively. The above equations can also be represented in matrix
form as below −
• (X′Y′)= (XY) Sx 0
0 Sy
[X' = X . SX and Y' = Y . SY ]
OR P’ = P . S
2D ROTATION
• Representing the above equation in matrix form,
• [X′Y′]=[XY] cosθ sinθ
-sinθ cosθ
OR, P’ = P . R
2D ROTATION
• The rotation angle can be positive and negative.
• For positive rotation angle, we can use the above rotation matrix. However, for
negative angle rotation, the matrix will change as shown below −
• R= cos(−θ) sin(−θ)
− sin(−θ) cos(−θ)
cosθ −Sinθ (∵cos(−θ)=cosθand sin(−θ)=−sinθ)
R=
Sinθ cosθ
THANK YOU

More Related Content

Similar to PPT_17.pptx

2 d geometric transformations
2 d geometric transformations2 d geometric transformations
2 d geometric transformationsMohd Arif
 
Chapter 3 - Part 1 [Autosaved].pptx
Chapter 3 - Part 1 [Autosaved].pptxChapter 3 - Part 1 [Autosaved].pptx
Chapter 3 - Part 1 [Autosaved].pptx
Kokebe2
 
seminar on 2D transformation
seminar on 2D transformationseminar on 2D transformation
seminar on 2D transformation
9784
 
Three dimensional transformations
Three dimensional transformationsThree dimensional transformations
Three dimensional transformations
Nareek
 
3d transformation computer graphics
3d transformation computer graphics 3d transformation computer graphics
3d transformation computer graphics
University of Potsdam
 
transformation IT.ppt
transformation IT.ppttransformation IT.ppt
transformation IT.ppt
ShubhamBatwani
 
1533 game mathematics
1533 game mathematics1533 game mathematics
1533 game mathematics
Dr Fereidoun Dejahang
 
Mid-Point Cirle Drawing Algorithm
Mid-Point Cirle Drawing AlgorithmMid-Point Cirle Drawing Algorithm
Mid-Point Cirle Drawing AlgorithmNeha Kaurav
 
Computer Graphics - transformations in 2d
Computer Graphics - transformations in 2dComputer Graphics - transformations in 2d
Computer Graphics - transformations in 2d
Hisham Al Kurdi, EAVA, DMC-D-4K, HCCA-P, HCAA-D
 
Computer Graphic - Transformations in 2D
Computer Graphic - Transformations in 2DComputer Graphic - Transformations in 2D
Computer Graphic - Transformations in 2D
2013901097
 
mid point algorithm.pdf
mid point algorithm.pdfmid point algorithm.pdf
mid point algorithm.pdf
MehulMunshi3
 
2d-transformation
2d-transformation2d-transformation
2d-transformation
Pooja Dixit
 
3D transformation in computer graphics
3D transformation in computer graphics3D transformation in computer graphics
3D transformation in computer graphics
SHIVANI SONI
 
2D Transformation.pdf
2D Transformation.pdf2D Transformation.pdf
2D Transformation.pdf
maheshshinde762539
 
slopweeeeeeeeeeeeeeeeeeeeeeeeeee43333.pptx
slopweeeeeeeeeeeeeeeeeeeeeeeeeee43333.pptxslopweeeeeeeeeeeeeeeeeeeeeeeeeee43333.pptx
slopweeeeeeeeeeeeeeeeeeeeeeeeeee43333.pptx
kristinebua
 
slopeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
slopeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeslopeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
slopeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
kristinebua
 
Computer graphics basic transformation
Computer graphics basic transformationComputer graphics basic transformation
Computer graphics basic transformation
Selvakumar Gna
 
Transforms UNIt 2
Transforms UNIt 2 Transforms UNIt 2
Transforms UNIt 2
sandeep kumbhkar
 
3 d transformations
3 d transformations3 d transformations
3 d transformations
Ankit Garg
 

Similar to PPT_17.pptx (20)

2 d geometric transformations
2 d geometric transformations2 d geometric transformations
2 d geometric transformations
 
Chapter 3 - Part 1 [Autosaved].pptx
Chapter 3 - Part 1 [Autosaved].pptxChapter 3 - Part 1 [Autosaved].pptx
Chapter 3 - Part 1 [Autosaved].pptx
 
Linear equations 2-2 a graphing and x-y intercepts
Linear equations   2-2 a graphing and x-y interceptsLinear equations   2-2 a graphing and x-y intercepts
Linear equations 2-2 a graphing and x-y intercepts
 
seminar on 2D transformation
seminar on 2D transformationseminar on 2D transformation
seminar on 2D transformation
 
Three dimensional transformations
Three dimensional transformationsThree dimensional transformations
Three dimensional transformations
 
3d transformation computer graphics
3d transformation computer graphics 3d transformation computer graphics
3d transformation computer graphics
 
transformation IT.ppt
transformation IT.ppttransformation IT.ppt
transformation IT.ppt
 
1533 game mathematics
1533 game mathematics1533 game mathematics
1533 game mathematics
 
Mid-Point Cirle Drawing Algorithm
Mid-Point Cirle Drawing AlgorithmMid-Point Cirle Drawing Algorithm
Mid-Point Cirle Drawing Algorithm
 
Computer Graphics - transformations in 2d
Computer Graphics - transformations in 2dComputer Graphics - transformations in 2d
Computer Graphics - transformations in 2d
 
Computer Graphic - Transformations in 2D
Computer Graphic - Transformations in 2DComputer Graphic - Transformations in 2D
Computer Graphic - Transformations in 2D
 
mid point algorithm.pdf
mid point algorithm.pdfmid point algorithm.pdf
mid point algorithm.pdf
 
2d-transformation
2d-transformation2d-transformation
2d-transformation
 
3D transformation in computer graphics
3D transformation in computer graphics3D transformation in computer graphics
3D transformation in computer graphics
 
2D Transformation.pdf
2D Transformation.pdf2D Transformation.pdf
2D Transformation.pdf
 
slopweeeeeeeeeeeeeeeeeeeeeeeeeee43333.pptx
slopweeeeeeeeeeeeeeeeeeeeeeeeeee43333.pptxslopweeeeeeeeeeeeeeeeeeeeeeeeeee43333.pptx
slopweeeeeeeeeeeeeeeeeeeeeeeeeee43333.pptx
 
slopeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
slopeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeslopeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
slopeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
 
Computer graphics basic transformation
Computer graphics basic transformationComputer graphics basic transformation
Computer graphics basic transformation
 
Transforms UNIt 2
Transforms UNIt 2 Transforms UNIt 2
Transforms UNIt 2
 
3 d transformations
3 d transformations3 d transformations
3 d transformations
 

More from SanandMishra

New_title.pptx
New_title.pptxNew_title.pptx
New_title.pptx
SanandMishra
 
AI.pptx
AI.pptxAI.pptx
AI.pptx
SanandMishra
 
Graphis_AI_Desiggn.pptx
Graphis_AI_Desiggn.pptxGraphis_AI_Desiggn.pptx
Graphis_AI_Desiggn.pptx
SanandMishra
 
new ai techniques.pptx
new ai techniques.pptxnew ai techniques.pptx
new ai techniques.pptx
SanandMishra
 
PPT_14.pptx
PPT_14.pptxPPT_14.pptx
PPT_14.pptx
SanandMishra
 
PPT_1.pptx
PPT_1.pptxPPT_1.pptx
PPT_1.pptx
SanandMishra
 

More from SanandMishra (6)

New_title.pptx
New_title.pptxNew_title.pptx
New_title.pptx
 
AI.pptx
AI.pptxAI.pptx
AI.pptx
 
Graphis_AI_Desiggn.pptx
Graphis_AI_Desiggn.pptxGraphis_AI_Desiggn.pptx
Graphis_AI_Desiggn.pptx
 
new ai techniques.pptx
new ai techniques.pptxnew ai techniques.pptx
new ai techniques.pptx
 
PPT_14.pptx
PPT_14.pptxPPT_14.pptx
PPT_14.pptx
 
PPT_1.pptx
PPT_1.pptxPPT_1.pptx
PPT_1.pptx
 

Recently uploaded

Empowering Data Analytics Ecosystem.pptx
Empowering Data Analytics Ecosystem.pptxEmpowering Data Analytics Ecosystem.pptx
Empowering Data Analytics Ecosystem.pptx
benishzehra469
 
Ch03-Managing the Object-Oriented Information Systems Project a.pdf
Ch03-Managing the Object-Oriented Information Systems Project a.pdfCh03-Managing the Object-Oriented Information Systems Project a.pdf
Ch03-Managing the Object-Oriented Information Systems Project a.pdf
haila53
 
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...
John Andrews
 
一比一原版(TWU毕业证)西三一大学毕业证成绩单
一比一原版(TWU毕业证)西三一大学毕业证成绩单一比一原版(TWU毕业证)西三一大学毕业证成绩单
一比一原版(TWU毕业证)西三一大学毕业证成绩单
ocavb
 
standardisation of garbhpala offhgfffghh
standardisation of garbhpala offhgfffghhstandardisation of garbhpala offhgfffghh
standardisation of garbhpala offhgfffghh
ArpitMalhotra16
 
社内勉強会資料_LLM Agents                              .
社内勉強会資料_LLM Agents                              .社内勉強会資料_LLM Agents                              .
社内勉強会資料_LLM Agents                              .
NABLAS株式会社
 
【社内勉強会資料_Octo: An Open-Source Generalist Robot Policy】
【社内勉強会資料_Octo: An Open-Source Generalist Robot Policy】【社内勉強会資料_Octo: An Open-Source Generalist Robot Policy】
【社内勉強会資料_Octo: An Open-Source Generalist Robot Policy】
NABLAS株式会社
 
FP Growth Algorithm and its Applications
FP Growth Algorithm and its ApplicationsFP Growth Algorithm and its Applications
FP Growth Algorithm and its Applications
MaleehaSheikh2
 
Criminal IP - Threat Hunting Webinar.pdf
Criminal IP - Threat Hunting Webinar.pdfCriminal IP - Threat Hunting Webinar.pdf
Criminal IP - Threat Hunting Webinar.pdf
Criminal IP
 
tapal brand analysis PPT slide for comptetive data
tapal brand analysis PPT slide for comptetive datatapal brand analysis PPT slide for comptetive data
tapal brand analysis PPT slide for comptetive data
theahmadsaood
 
一比一原版(UPenn毕业证)宾夕法尼亚大学毕业证成绩单
一比一原版(UPenn毕业证)宾夕法尼亚大学毕业证成绩单一比一原版(UPenn毕业证)宾夕法尼亚大学毕业证成绩单
一比一原版(UPenn毕业证)宾夕法尼亚大学毕业证成绩单
ewymefz
 
Business update Q1 2024 Lar España Real Estate SOCIMI
Business update Q1 2024 Lar España Real Estate SOCIMIBusiness update Q1 2024 Lar España Real Estate SOCIMI
Business update Q1 2024 Lar España Real Estate SOCIMI
AlejandraGmez176757
 
Criminal IP - Threat Hunting Webinar.pdf
Criminal IP - Threat Hunting Webinar.pdfCriminal IP - Threat Hunting Webinar.pdf
Criminal IP - Threat Hunting Webinar.pdf
Criminal IP
 
1.Seydhcuxhxyxhccuuxuxyxyxmisolids 2019.pptx
1.Seydhcuxhxyxhccuuxuxyxyxmisolids 2019.pptx1.Seydhcuxhxyxhccuuxuxyxyxmisolids 2019.pptx
1.Seydhcuxhxyxhccuuxuxyxyxmisolids 2019.pptx
Tiktokethiodaily
 
Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...
Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...
Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...
Subhajit Sahu
 
Q1’2024 Update: MYCI’s Leap Year Rebound
Q1’2024 Update: MYCI’s Leap Year ReboundQ1’2024 Update: MYCI’s Leap Year Rebound
Q1’2024 Update: MYCI’s Leap Year Rebound
Oppotus
 
一比一原版(QU毕业证)皇后大学毕业证成绩单
一比一原版(QU毕业证)皇后大学毕业证成绩单一比一原版(QU毕业证)皇后大学毕业证成绩单
一比一原版(QU毕业证)皇后大学毕业证成绩单
enxupq
 
Opendatabay - Open Data Marketplace.pptx
Opendatabay - Open Data Marketplace.pptxOpendatabay - Open Data Marketplace.pptx
Opendatabay - Open Data Marketplace.pptx
Opendatabay
 
一比一原版(ArtEZ毕业证)ArtEZ艺术学院毕业证成绩单
一比一原版(ArtEZ毕业证)ArtEZ艺术学院毕业证成绩单一比一原版(ArtEZ毕业证)ArtEZ艺术学院毕业证成绩单
一比一原版(ArtEZ毕业证)ArtEZ艺术学院毕业证成绩单
vcaxypu
 
一比一原版(CBU毕业证)卡普顿大学毕业证成绩单
一比一原版(CBU毕业证)卡普顿大学毕业证成绩单一比一原版(CBU毕业证)卡普顿大学毕业证成绩单
一比一原版(CBU毕业证)卡普顿大学毕业证成绩单
nscud
 

Recently uploaded (20)

Empowering Data Analytics Ecosystem.pptx
Empowering Data Analytics Ecosystem.pptxEmpowering Data Analytics Ecosystem.pptx
Empowering Data Analytics Ecosystem.pptx
 
Ch03-Managing the Object-Oriented Information Systems Project a.pdf
Ch03-Managing the Object-Oriented Information Systems Project a.pdfCh03-Managing the Object-Oriented Information Systems Project a.pdf
Ch03-Managing the Object-Oriented Information Systems Project a.pdf
 
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...
Chatty Kathy - UNC Bootcamp Final Project Presentation - Final Version - 5.23...
 
一比一原版(TWU毕业证)西三一大学毕业证成绩单
一比一原版(TWU毕业证)西三一大学毕业证成绩单一比一原版(TWU毕业证)西三一大学毕业证成绩单
一比一原版(TWU毕业证)西三一大学毕业证成绩单
 
standardisation of garbhpala offhgfffghh
standardisation of garbhpala offhgfffghhstandardisation of garbhpala offhgfffghh
standardisation of garbhpala offhgfffghh
 
社内勉強会資料_LLM Agents                              .
社内勉強会資料_LLM Agents                              .社内勉強会資料_LLM Agents                              .
社内勉強会資料_LLM Agents                              .
 
【社内勉強会資料_Octo: An Open-Source Generalist Robot Policy】
【社内勉強会資料_Octo: An Open-Source Generalist Robot Policy】【社内勉強会資料_Octo: An Open-Source Generalist Robot Policy】
【社内勉強会資料_Octo: An Open-Source Generalist Robot Policy】
 
FP Growth Algorithm and its Applications
FP Growth Algorithm and its ApplicationsFP Growth Algorithm and its Applications
FP Growth Algorithm and its Applications
 
Criminal IP - Threat Hunting Webinar.pdf
Criminal IP - Threat Hunting Webinar.pdfCriminal IP - Threat Hunting Webinar.pdf
Criminal IP - Threat Hunting Webinar.pdf
 
tapal brand analysis PPT slide for comptetive data
tapal brand analysis PPT slide for comptetive datatapal brand analysis PPT slide for comptetive data
tapal brand analysis PPT slide for comptetive data
 
一比一原版(UPenn毕业证)宾夕法尼亚大学毕业证成绩单
一比一原版(UPenn毕业证)宾夕法尼亚大学毕业证成绩单一比一原版(UPenn毕业证)宾夕法尼亚大学毕业证成绩单
一比一原版(UPenn毕业证)宾夕法尼亚大学毕业证成绩单
 
Business update Q1 2024 Lar España Real Estate SOCIMI
Business update Q1 2024 Lar España Real Estate SOCIMIBusiness update Q1 2024 Lar España Real Estate SOCIMI
Business update Q1 2024 Lar España Real Estate SOCIMI
 
Criminal IP - Threat Hunting Webinar.pdf
Criminal IP - Threat Hunting Webinar.pdfCriminal IP - Threat Hunting Webinar.pdf
Criminal IP - Threat Hunting Webinar.pdf
 
1.Seydhcuxhxyxhccuuxuxyxyxmisolids 2019.pptx
1.Seydhcuxhxyxhccuuxuxyxyxmisolids 2019.pptx1.Seydhcuxhxyxhccuuxuxyxyxmisolids 2019.pptx
1.Seydhcuxhxyxhccuuxuxyxyxmisolids 2019.pptx
 
Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...
Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...
Algorithmic optimizations for Dynamic Levelwise PageRank (from STICD) : SHORT...
 
Q1’2024 Update: MYCI’s Leap Year Rebound
Q1’2024 Update: MYCI’s Leap Year ReboundQ1’2024 Update: MYCI’s Leap Year Rebound
Q1’2024 Update: MYCI’s Leap Year Rebound
 
一比一原版(QU毕业证)皇后大学毕业证成绩单
一比一原版(QU毕业证)皇后大学毕业证成绩单一比一原版(QU毕业证)皇后大学毕业证成绩单
一比一原版(QU毕业证)皇后大学毕业证成绩单
 
Opendatabay - Open Data Marketplace.pptx
Opendatabay - Open Data Marketplace.pptxOpendatabay - Open Data Marketplace.pptx
Opendatabay - Open Data Marketplace.pptx
 
一比一原版(ArtEZ毕业证)ArtEZ艺术学院毕业证成绩单
一比一原版(ArtEZ毕业证)ArtEZ艺术学院毕业证成绩单一比一原版(ArtEZ毕业证)ArtEZ艺术学院毕业证成绩单
一比一原版(ArtEZ毕业证)ArtEZ艺术学院毕业证成绩单
 
一比一原版(CBU毕业证)卡普顿大学毕业证成绩单
一比一原版(CBU毕业证)卡普顿大学毕业证成绩单一比一原版(CBU毕业证)卡普顿大学毕业证成绩单
一比一原版(CBU毕业证)卡普顿大学毕业证成绩单
 

PPT_17.pptx

  • 1. Unit 1 Basic of computer graphics By: Medhavi Pandey
  • 2. Outline ▪ Numerical on types of Transformation ▪ SheRotation aring ▪ Scaling ▪
  • 3. X-Shear • The transformation matrix for X-Shear can be represented as:- • Xsh = 1 Shx 0 0 1 0 0 0 1 • X' = X + ShX . Y • Y’ = Y
  • 4. Y-Shear • The Y-Shear can be represented in matrix from as − • Ysh = 1 0 0 Shy 1 0 0 0 1 • Y' = Y + Shy . X • X’ = X
  • 6.
  • 7. 2D SCALING • The scaling factor SX, SY scales the object in X and Y direction respectively. The above equations can also be represented in matrix form as below − • (X′Y′)= (XY) Sx 0 0 Sy [X' = X . SX and Y' = Y . SY ] OR P’ = P . S
  • 8.
  • 9. 2D ROTATION • Representing the above equation in matrix form, • [X′Y′]=[XY] cosθ sinθ -sinθ cosθ OR, P’ = P . R
  • 10. 2D ROTATION • The rotation angle can be positive and negative. • For positive rotation angle, we can use the above rotation matrix. However, for negative angle rotation, the matrix will change as shown below − • R= cos(−θ) sin(−θ) − sin(−θ) cos(−θ) cosθ −Sinθ (∵cos(−θ)=cosθand sin(−θ)=−sinθ) R= Sinθ cosθ
  • 11.
  • 12.