Transformation:
Transformations are a fundamental part of the computer graphics. Transformations are the movement of the object in Cartesian plane.
Types of transformation
Why we use transformation
3D Transformation
3D Translation
3D Rotation
3D Scaling
3D Reflection
3D Shearing
Transformation:
Transformations are a fundamental part of the computer graphics. Transformations are the movement of the object in Cartesian plane.
Types of transformation
Why we use transformation
3D Transformation
3D Translation
3D Rotation
3D Scaling
3D Reflection
3D Shearing
with today's advanced technology like photoshop, paint etc. we need to understand some basic concepts like how they are cropping the image , tilt the image etc.
In our presentation you will find basic introduction of 2D transformation.
a spline is a flexible strip used to produce a smooth curve through a designated set of points.
Polynomial sections are fitted so that the curve passes through each control point, Resulting curve is said to interpolate the set of control points.
it is related to Computer Graphics Subject.in this ppt we describe what is 2D Transformation, Translation, Rotation, Scaling : Uniform Scaling,Non-uniform Scaling ;Reflection,Shear,Composite Transformations
Comprehensive coverage of fundamentals of computer graphics.
3D Transformations
Reflections
3D Display methods
3D Object Representation
Polygon surfaces
Quadratic Surfaces
with today's advanced technology like photoshop, paint etc. we need to understand some basic concepts like how they are cropping the image , tilt the image etc.
In our presentation you will find basic introduction of 2D transformation.
a spline is a flexible strip used to produce a smooth curve through a designated set of points.
Polynomial sections are fitted so that the curve passes through each control point, Resulting curve is said to interpolate the set of control points.
it is related to Computer Graphics Subject.in this ppt we describe what is 2D Transformation, Translation, Rotation, Scaling : Uniform Scaling,Non-uniform Scaling ;Reflection,Shear,Composite Transformations
Comprehensive coverage of fundamentals of computer graphics.
3D Transformations
Reflections
3D Display methods
3D Object Representation
Polygon surfaces
Quadratic Surfaces
Digital signatures are often used to implement electronic signatures, a broader term that refers to any electronic data that carries the intent of a signature, but not all electronic signatures use digital signatures. In some countries, including the United States, India, and members of the European Union, electronic signatures have legal significance.
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In this section, we focus on a subgoals of realistic picture. This co-ordinate reference defines the position and orientation for the planeof the camera, as shown in next slide.This plane must be used to display a view of the object; its description has to transferred to thecamera reference co-ordinates and projected onto the selected display plane. Then we can displayobject in wire frame form or we can apply lighting and surface rendering techniques to shade thevisible surfaces
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This will be used as part of your Personal Professional Portfolio once graded.
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Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
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This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
3. CONTENTS
Transformation
Types of transformation
Why we use transformation
3D Transformation
3D Translation
3D Rotation
3D Scaling
3D Reflection
3D Shearing
4. TRANSFORMATION
Transformations are a fundamental part of the computer
graphics. Transformations are the movement of the object in
Cartesian plane .
5. TYPES OF
TRANSFORMATION
There are two types of transformation in computer graphics.
1) 2D transformation
2) 3D transformation
Types of 2D and 3D transformation
1) Translation
2) Rotation
3) Scaling
4) Shearing
5) Mirror reflection
6. WHY WE USE
TRANSFORMATION
Transformation are used to position objects , to shape object , to
change viewing positions , and even how something is viewed.
In simple words transformation is used for
1) Modeling
2) viewing
7. 3D TRANSFORMATION
When the transformation takes place on a 3D plane .it is called
3D transformation.
Generalize from 2D by including z coordinate
Straight forward for translation and scale, rotation more difficult
Homogeneous coordinates: 4 components
Transformation matrices: 4×4 elements
1000
z
y
x
tihg
tfed
tcba
8. 3D TRANSLATION
Moving of object is called translation.
In 3 dimensional homogeneous coordinate representation , a
point is transformed from position P = ( x, y , z) to P’=( x’, y’,
z’)
This can be written as:-
Using P’ = T . P
11000
100
010
001
1
z
y
x
t
t
t
z
y
x
z
y
x
9. 3D TRANSLATION
The matrix representation is equivalent to the three equation.
x’=x+ tx , y’=y+ ty , z’=z+ tz
Where parameter tx , ty , tz are specifying translation distance for the
coordinate direction x , y , z are assigned any real value.
10. 3D ROTATION
Where an object is to be rotated about an axis that is parallel to one
of the coordinate axis, we can obtain the desired rotation with
the following transformation sequence.
Coordinate axis rotation
Z- axis Rotation(Roll)
Y-axis Rotation(Yaw)
X-axis Rotation(Pitch)
12. X-AXIS ROTATION
The equation for X-axis rotation
x’ = x
y’ = y cosθ – z sinθ
z’ = y sinθ + z cosθ
11000
0cossin0
0sincos0
0001
1
'
'
'
z
y
x
z
y
x
13. Y-AXIS ROTATION
The equation for Y-axis rotaion
x’ = x cosθ + z sinθ
y’ = y
z’ = z cosθ - x sinθ
11000
0cos0sin
0010
0sin0cos
1
'
'
'
z
y
x
z
y
x
14. The equation for Y-axis rotaion
x’ = x cosθ – y sinθ
y’ = x sinθ + y cosθ
z’ = z
*Z-AXIS ROTATION
11000
0100
00cossin
00sincos
1
'
'
'
z
y
x
z
y
x
15. 3D SCALING
Changes the size of the object and repositions the object relative
to the coordinate origin.
11000
000
000
000
1
z
y
x
s
s
s
z
y
x
z
y
x
16. 3D SCALING
The equations for scaling
x’ = x . sx
Ssx,sy,sz y’ = y . sy
z’ = z . sz
17. 3D REFLECTION
Reflection in computer graphics is used to emulate reflective
objects like mirrors and shiny surfaces
Reflection may be an x-axis
y-axis , z-axis. and also in
the planes xy-plane,yz-plane , and
zx-plane.
Reflection relative to a given
Axis are equivalent to 180
Degree rotations
19. 3D REFLECTION
The matrix for reflection about y-axis:-
-1 0 0 0
0 1 0 0
0 0 -1 0
0 0 0 1
Reflection about z-axis:-
x’=-x y’=-y z’=z
-1 0 0 0
0 -1 0 0
0 0 1 0
0 0 0 1
20. 3D SHEARING
Modify object shapes
Useful for perspective projections
When an object is viewed from different directions and at
different distances, the appearance of the object will be
different. Such view is called perspective view. Perspective
projections mimic what the human eyes see.
21. 3D SHEARING
E.g. draw a cube (3D) on a screen (2D) Alter the values for x and y
by an amount proportional to the distance from zref
22. 3D SHEARING
Matrix for 3d shearing
Where a and b can
Be assigned any real
Value.