The document discusses three types of transformations of parent functions: shifts, reflections, and stretches/compressions. Shifts move the graph up, down, left or right along an axis. Reflections flip the graph across an axis. Stretches/compressions change the scale of the graph by multiplying the function by a constant, either horizontally or vertically. Examples are given of transforming the quadratic function by shifting, reflecting, and stretching.
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
Comprehensive coverage of fundamentals of computer graphics.
3D Transformations
Reflections
3D Display methods
3D Object Representation
Polygon surfaces
Quadratic Surfaces
Slides from when I was teaching CS4052 Computer Graphics at Trinity College Dublin in Ireland.
These slides aren't used any more so they may as well be available to the public!
There are some mistakes in the slides, I'll try to comment below these.
This is the third lecture - on using linear algebra for transformations.
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
Comprehensive coverage of fundamentals of computer graphics.
3D Transformations
Reflections
3D Display methods
3D Object Representation
Polygon surfaces
Quadratic Surfaces
Slides from when I was teaching CS4052 Computer Graphics at Trinity College Dublin in Ireland.
These slides aren't used any more so they may as well be available to the public!
There are some mistakes in the slides, I'll try to comment below these.
This is the third lecture - on using linear algebra for transformations.
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Determine whether a function is even, odd, or neither from its graph.
* Graph functions using compressions and stretches.
* Combine transformations.
* Recognize graphs of common functions.
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Graph functions using compressions and stretches.
* Combine transformations.
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The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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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.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
2. Take a moment and quietly discuss with a
neighbor, what are some parent functions
that you remember from earlier in this unit?
Do you recall the nameAND the equation?
3.
4. Now that we remember some of our parent
functions, we can start to manipulate, or
transform them!
Definition:
The graph of a function is transformed when its
parent function is changed.
There are three (3) types of transformations:
1. Shifts
2. Reflections
3. Stretches and Compressions
5. Definition:
When a graph is shifted it moves either up, down,
left, or right.
Think about the x-y coordinate plane.Which
axis goes from left to right?What about up
and down?
6. When an image is reflected, it is flipped like a
mirror
There are 2 main reflections:
About (across) the x-axis
About the y-axis
7. The coefficients of a function determine how
much it is stretched or compressed
Given y = f(x),
Horizontal stretching/compression will give you
y = f(ax), where “a” is a constant
Vertical stretching/compression will give you
y = a f(x), again “a” is a constant
8. A horizontal stretching
moves the graph away from
the y-axis
A horizontal compression
squeezes the graph toward
the y-axis
In changing a function from
f(x) to f(ax),
▪ If 0<a<1, its is stretched
horizontally by “a” units
▪ If a>1, the graph is compressed
horizontally by “a” units
9. A vertical stretching
moves the graph away
from the x-axis
A vertical compression
squeezes the graph
toward the x-axis
In changing a function from
f(x) to f(ax),
▪ If 0<a<1, its is compressed
vertically by “a” units
▪ If a>1, the graph is stretched
vertically by “a” units
10. Here’s a short video to go over what we just learned…
https://www.youtube.com/watch?v=7S5HF38DnUY
11. Using the quadratic as your parent function,
write the equations of the given
transformations:
Shifted 5 units up
Shifted 3 units left, and stretched horizontally by
2
Reflected across the y-axis, and shifted up 4
