- 1. 3D TRANSFORMATION 2. CONTENTS Transformation Types of transformation Why we use transformation 3D Transformation 3D Translation 3D Rotation 3D Scaling 3D Reflection 3D Shearing 3. TRANSFORMATION Transformations are a fundamental part of the computer graphics. Transformations are the movement of the object in Cartesian plane . 4
- 3D Transformation in Computer Graphics 1. Welcome To The Presentation World University Of Bangladesh 3D Transformation 2. INTRODUCTION Here we introduce to about 3D Transformation TRANSLATION ROTATION SCALINGREFLECTIONS SHEARING 3. OBJECTIVE To understand basic conventions for object transformations in 3D To understand basic transformations in.
- 1) 2D
**transformation**2)**3D****transformation**Types of 2D and**3D****transformation**1) Translation 2) Rotation 3) Scaling 4) Shearing 5) Mirror reflection 5. 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. - Computer Graphics topic:: Transformation in 3d Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website

- Tag: 2D and 3D Transformation in Computer Graphics PPT. 2D Transformations in Computer Graphics- We have discussed-Transformation is a process of modifying and re-positioning the existing graphics. 2D Transformations take place in a two dimensional plane. In computer graphics, various transformation techniques are
- g • Each transformation type can be expressed in a (4 x 4) matrix, called the Transformation Matrix NOTES: Ishan Parekh MBA(tech.) Manufacturing #315
- Computer Graphics 3D Transformations World Window to Viewport Transformation Week 2, Lecture 4 David Breen, William Regli and Maxim Peysakhov Department of Computer Science Drexel University. 2 Outline • World window to viewport transformation L-04_3DTransformations.ppt Author: David Bree
- A transformation that slants the shape of an object is called the shear transformation. Like in 2D shear, we can shear an object along the X-axis, Y-axis, or Z-axis in 3D. Like in 2D shear, we can shear an object along the X-axis, Y-axis, or Z-axis in 3D
- Computer Graphic - Transformations in 2D 1. 2 x 1 matrix: General Problem: [B] = [T] [A] [T] represents a generic operator to be applied to the points in A. T is the geometric transformation matrix. If A & T are known, the transformed points are obtained by calculating B. 2
- Advanced Computer Graphics: 2D/3D Transformations Kocaeli Universitesity Computer Engineering Department * * * * * Need to include coordinate transform and - A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 463644-MzUx

In Computer graphics, Transformation is a process of modifying and re-positioning the existing graphics. 3D Transformations take place in a three dimensional plane. 3D Transformations are important and a bit more complex than 2D Transformations Computer Graphics 3D Transformations Camera View Direction View Up View Right View Normal Camera View Up View Right What are the vectors? Graphics Pipeline So Far Object Object Coordinates Transformation Object -> World World World Coordinates Projection Xform World -> Projection Camera Projection Coordinates Screen Device Coordinates Normalize Xform & Clipping Projection -> Normalized. Computer Graphics • Algorithmically generating a 2D image from 3D data (models, textures, lighting) • Also called rendering • Raster graphics - Array of pixels - About 25x25 in the example ‐> • Algorithm tradeoffs: - Computation time - Memory cost - Image qualit Similar to 2D transformations, which used 3x3 matrices, 3D transformations use 4X4 matrices (X, Y, Z, W) 3D Translation: point (X,Y,Z) is to be translated by amount Dx, Dy and Dz to location (X',Y',Z' 3D Graphics Translation Translation Rotation Rotation Rotation Scaling The matrix expression for the scaling transformation of a position P = (xi, yi, zi) relative to coordinate origin can be written as: 3D Viewing Viewing in 3D involves the following considerations: - We can view an object from any spatial position, eg

Computer Graphics Introduction of Transformation with Computer Graphics Tutorial, Line Generation Algorithm, 2D Transformation, 3D Computer Graphics, Types of Curves, Surfaces, Computer Animation, Animation Techniques, Keyframing, Fractals etc University of Freiburg -Computer Science Department -Computer Graphics - 10 Rendering Pipeline Main Stages vertex processing / geometry stage / vertex shader processes all vertices independently in the same way performs transformations per vertex, computes lighting per vertex geometry shader generates, modifies, discards primitives primitive assembly and rasterization / rasterization stag 3D Scaling in Computer Graphics- In computer graphics, scaling is a process of modifying or altering the size of objects. Scaling may be used to increase or reduce the size of object. Scaling subjects the coordinate points of the original object to change - Computer Graphics by Zhigang Xiang, Schaum's Outlines. - Donald Hearn & M. Pauline Baker, Computer Graphics with OpenGL, 4th Edition, Boston : Addison Wesley, 2011. 3 Composite Transformations -3D Basic composite transformations : • R ,L = rotation about an axis L( V, P ) • S sx,sy,P = scaling w.r.t. point P

In Computer graphics, 3D Rotation is a process of rotating an object with respect to an angle in a three dimensional plane. Consider a point object O has to be rotated from one angle to another in a 3D plane 3D Projections: Parallel Projection, Perspective Projection * 3d Scaling Transformation In Computer Graphics In Hindi | 3d Scaling In Computer Graphics Hindi In the scaling process, you either expand or compress the dimensions of the object*. Scaling can be.. Three-dimensional transformations are performed by transforming each vertex of the object. If an object has five corners, then the translation will be accomplished by translating all five points to new locations. Following figure 1 shows the translation of point figure 2 shows the translation of the cube Computer Graphics Composite Transformation with Computer Graphics Tutorial, Line Generation Algorithm, 2D Transformation, 3D Computer Graphics, Types of Curves, Surfaces, Computer Animation, Animation Techniques, Keyframing, Fractals etc

2D Transformations: Translation, Rotation and Scalin Window to Viewport Transformation

Transformation is a process of modifying and re-positioning the existing graphics. 3D Transformations take place in a three dimensional plane. In computer graphics, various transformation techniques are- Translation; Rotation; Scaling; Reflection; Shear . In this article, we will discuss about 3D Reflection in Computer Graphics 2Dtransformation.ppt - Computer Graphics Subject code 2151603 Teaching Scheme 4 \u2013 0 \u2013 2 = credit 6 Prof Kruti J Dangarwala Associate Professor Dept. Unit 5:3D transformation and viewing [8 hours] 3D scaling, rotation and translation, composite transformation,. ** Computer Graphics Lecture 3 Transformations From the last lecture**... Transformations. Translation. P =T + P Scale P =S P Rotation P =R P We would like all transformations to be multiplications so we can concatenate them express points in homogenous coordinates 2D and **3D** **Transformations**, Homogeneous Coordinates Lecture 03 Patrick Karlsson patrick.karlsson@cb.uu.se Centre for Image Analysis Uppsala University **Computer** **Graphics** November 6 2006 Patrick Karlsson (Uppsala University) **Transformations** and Homogeneous Coords. **Computer** **Graphics** 1 / 23 Reading Instructions Chapters 4.1-4 .9. Edward Angel

Computer Graphics 3D Transformations World Window to Viewport Transformation Week 2, Lecture 4 David Breen, William Regli and Maxim Peysakhov Department of Computer Science Drexel University 2 Outline • World window to viewport transformation • 3D transformations • Coordinate system transformation 3 The Window-to-Viewport Transformation • In 3D, we use 4-vectors and 4 x 4 matrices •The extra coordinate is now an arbitrary value, w • You can think of it as scale, or weight • For all transformations except perspective, you can just set w=1 and not worry about it x' y' 1 a b d e 0 0 c f 1 = x y 1 5 the scene (viewing transformation). 2.Arrange the scene to be photographed into the desired composition (modeling transformation). 3.Choose a camera lens or adjust the zoom (projection transformation). 4.Determine how large you want the final photograph to be - for example, you might want it enlarged (viewport transformation) April 14, 2014 Computer Graphics 19 bit 1 Above bit 2 Below bit 3 Right bit 4 Left bit 5 Behind bit 6 Front April 14, 2014 Computer Graphics 20 3D Cohen-Sutherland Line Clipping April 14, 2014 Computer Graphics 21 3D Cohen-Sutherland Line Clipping Now we use a 6 bit out code to handle the near and far plane

* 2D Transformations • 2D object is represented by points and lines that join them*. • Transformations can be applied only to the the points defining the lines. • A point (x,y) is represented by a 2x1 column vector, and we can represent 2D transformations using 2x2 matrices: = x d x a b ' Presentation Graphics To produce illustrations which summarize various kinds of data. Except 2D, 3D graphics are good tools for reporting more complex data. Computer Art Painting packages are available. With cordless, pressure-sensitive stylus, artists can produce electronic paintings which simulate different brush strokes, brush widths, and.

Computer Graphics CSE 167 Lecture 3. CSE 167: Computer Graphics 3D affine transformation • Linear transformation followed by translation CSE 167, Winter 2018 14 Using Microsoft PowerPoint - lec3.pptx Author: bochoa Created Date: 1/17/2018 1:44:06 PM. In the 2D system, we use only two coordinates X and Y but in 3D, an extra coordinate Z is added. 3D graphics techniques and their application are fundamental to the entertainment, games, and computer-aided design industries

3D Viewing & Clipping Where do geometries come from? Pin-hole camera Perspective projection Viewing transformation Clipping lines & polygons Where do geometries come from? Pin-hole camera Perspective projection Viewing transformation Clipping lines & polygons Angel Chapter 5 Getting Geometry on the Screen • Transform to camera coordinate syste 3D Geometry Representation for Computer Graphics November 3, 2016. Outline • Implicit vs . parametric equations for surfaces • Use 3D (non-homogeneous form), for instance sphere: Microsoft PowerPoint - Oct_29 (2) Author: sbarga ** 3D Rotation in Computer Graphics is a process of rotating an object with respect to an angle in 3D plane**. Rotation in Computer Graphics Definition, Solved Examples and Problems 2D/3D Geometric Transformations. CS485/685 Computer Vision Dr. George Bebis 2D Translation. Moves a point to a new location by adding translation amounts to the coordinates of the point. or. or 2D Translation (contd) To translate an object, translate every point of the object by the same amount Three-Dimensional Graphics A 3D point (x,y,z) - x,y, and Z coordinates We will still use column vectors to represent points Homogeneous coordinates of a 3D point (x,y,z,1) Transformation will be performed using 4x4 matrix T x y

- ations like NTA UGC NET Computer Science and Applications, GATE Computer Science, ISRO, DRDO, Placements, etc. If you want.
- 2D Transformations take place in a two dimensional plane. Transformations are helpful in changing the position, size, orientation, shape etc of the object. Transformation Techniques- In computer graphics, various transformation techniques are
- g, Fractals etc
- w Mathematical properties of affine vs. projective transformations. w The classification of different types of projections. w The concepts of vanishing points and one-, two-, and three-point perspective. w An appreciation for the various coordinate systems used in computer graphics. w How the perspective transformation works
- CS 543: Computer Graphics Lecture 4 (Part I): 3D Affine transforms Emmanuel Agu. Introduction to Transformations n Introduce 3D affine transformation: n Position (translation) n Size (scaling) n Orientation (rotation) n Shapes (shear) n Previously developed 2D (x,y) n Now, extend to 3D or (x,y,z) cas

Computer Graphics 3D Rotation with Computer Graphics Tutorial, Line Generation Algorithm, 2D Transformation, 3D Computer Graphics, Types of Curves, Surfaces, Computer Animation, Animation Techniques, Keyframing, Fractals etc Transformations in 2D: PDF unavailable: 7: Transformations in 2D (Contd) PDF unavailable: 8: Three Dimensional Graphics: PDF unavailable: 9: Three Dimensional Graphics (Contd) PDF unavailable: 10: Three Dimensional Graphics (Contd) PDF unavailable: 11: Projection Transformations And Viewing Pipeline: PDF unavailable: 12: 3D Viewing - Projection. Three Dimensional Graphics The three-dimensional transformations are extensions of two-dimensional transformation. In 2D two coordinates are used, i.e., x and y whereas in 3D three co-ordinates x, y, and z are used. For three dimensional images and objects, three-dimensional transformations are needed The primary use of clipping in computer graphics is to remove objects, lines, or line segments that are outside the viewing pane. The viewing transformation is insensitive to the position of points relative to the viewing volume − especially those points behind the viewer − and it is necessary to remove these points before generating the view

** Text Book: Computer Graphics, by Donald Hearn, M**. Pauline Baker Lecture 19: 3D Transformation Presentation Submission Lab Manual Task 6: Animation of 2D object Click 2D Transformation.ppt link to view the file. Previous Activity Window to Viewport Transformation is the process of transforming a 2D world-coordinate objects to device coordinates.Objects inside the world or clipping window are mapped to the viewport which is the area on the screen where world coordinates are mapped to be displayed 3D Cafe's Free 3d models Rich's Transformation Slides, Lec 6 (10.8.03) Project Slides Project Read Ch 1 - 3 Fundamentals of Computer Graphics Project #1: Rasterization and Linear Interpolation Oct. 2 Before class: Read Ch 4 Fundamentals of Computer Graphics

University of Freiburg -Computer Science Department -2 Homogeneous Coordinates -Summary − with are the homogeneous coordinates of the 3D position − is a point at infinity in the direction of − is a vector in the direction of − is a transformation that represents rotation, scale, shear, translation, projectio Computer Graphics MCQ 05 1. A three dimensional graphics has . a. Two axes. b. Three axes. c. Both a & b The transformation in which an object can be shifted to any coordinate position in three dimensional plane are called. The object refers to the 3D representation through linear, circular or some other representation are called Matrices in Computer Graphics In OpenGL, we have multiple frames: model, world, camera frame To change frames or representation, we use transformation matrices All standard transformations (rotation, translation, scaling) can be implemented as matrix multiplications using 4x4 matrices (concatenation

** Computer Graphics | Clipping with Computer Graphics Tutorial, Line Generation Algorithm, 2D Transformation, 3D Computer Graphics, Types of Curves, Surfaces, Computer**. Introduction: In two-dimensional graphics applications, viewing operations transfer positions from the world-coordinate plane to pixel positions in the plane of the output device. Using the rectangular boundaries for the world-coordinate window and the device viewport, a two-dimensional package maps the world scene to device coordinates and clips the scene against the four boundaries of the. Courses | Computer Science | Virginia Tec A term that you may not have heard yet is composite transformations, which is to say that graphics processes will use multiple transformations in order to change an image to what a program orders. An example of this would be if we wanted to scale an image to make it larger while also rotating at a certain angle

Computer Graphics 15-4621 Announcements Movie from Assignment 1 Grades out soon 3D Viewing & Clipping Where do geometries come from? Pin-hole camera Perspective projection Viewing transformation Clipping lines & polygons COMPUTER GRAPHICS 15-462 12 Sept 2001 Watt 5.2 and 6.1 University of Texas at Austin CS384G - Computer Graphics Fall 2010 Don Fussell 14 Linear transformations The unit square observations also tell us the 2x2 matrix transformation implies that we are representing a point in a new coordinate system: where u=[a c]T and v=[b d]T are vectors that define a new basis for a linear space Eye Coordinate Frame New Origin:eye position (that was easy) 3 basis vectors: one is the normal vector (n) of the viewing plane, other two (u and v) span the viewing plane eye Lookat Point n u v world origin Remember u,v,n should be all unit vectors n is pointing away from the world because we use left hand coordinate syste Transformations in 3D Understanding basic spatial transformations, and the relation between mathematics and geometry. This module mainly discusses the same subject as: 2D transformations , but has a coordinate system with three axes as a basis etc. When a transformation takes place on a 2D plane, it is called 2D transformation. Transformations play an important role in computer graphics to reposition the graphics on the screen and change their size or orientation. Homogenous Coordinates To perform a sequence of transformation such as translation followed by rotation and scaling, w

Computer Graphics WS07/08 - Camera Transformations Coordinate Transformations • Local (object) coordinate system (3D) - Object vertex positions • World (global) coordinate system (3D) - Scene composition and object placement • Rigid objects: constant translation, rotation per objec 3D transformations can be specified in 3D tools such as Maya, Blender, or 3DS Max, and then loaded into the host program. It can also be created by users at runtime via input devices (e.g. pushing a mouse). A program can generate transformations based on internal algorithms (e.g. particles, physics, etc. C.5 3D form of the affine transformations ::::: 340 C.1 THE NEED FOR GEOMETRIC TRANSFORMATIONS One could imagine a computer graphics system that requires the user to construct ev-erything directly into a single scene. But, one can also immediately see that this would be an extremely limiting approach.. Composite transformation in hindi तब होता है जब दो या दो से अधिक transformations को एक single picture पर perform किया जाता हनया shape प्राप्त होता है

- They are invariant under an affine transformation. Bezier curves exhibit global control means moving a control point alters the shape of the whole curve. A given Bezier curve can be subdivided at a point t=t0 into two Bezier segments which join together at the point corresponding to the parameter value t=t0
- g. It involves computations, creation, and manipulation of data. In other words, we can say that computer graphics is a rendering tool for the generation and manipulation of images. Cathode Ray Tub
- es a line, the line deter
- Computer Graphics Curves - Learn about Computer Graphics in simple and easy terms starting from trends in Computer Graphics, Basics, Line Generation Algorithm, Circle Generation Algorithm, Polygon Filling Algorithm, viewing and Clipping, 2D Transformation, 3D Computer Graphics, 3D Transformation, Computer Graphics Curves, Computer Graphics Surfaces, Visible Surface Detection, Fractals.
- 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 reflectio

* Utah School of Computing Fall 2015 Computer Graphics CS4600 3 5 ThenRotate about x by + :Rx( ) x z y Rotate in the (y-z)-planea 6 Now*,+ Rotation about z-axis:Rz(+ ) x z y a Now aligned with z-axis 3D Coordinates & Transformations Prof. Aaron Lanterman (Based on slides by Prof. Hsien-Hsin Sean Lee) School of Electrical and Computer Engineering Georgia Institute of Technology . 2 3D graphics rendering pipeline (1) 3D graphics rendering pipeline (3) • Geometry Pipelin Transformation and Viewing Sphere, cylinder, and cone Earth Computer Graphics Author: Jim X. Chen Last modified by: user Created Date: Times New Roman Arial SimSun Blank Presentation Microsoft Equation 3.0 PowerPoint Presentation PowerPoint Presentation PowerPoint Presentation glMatrixMode(GLenum mode); PushMatrix and PopMatrix.

OpenGL Geometric Transformation Functions Basic OpenGL geometric transformations on the matrix: glTranslate* (tx, ty, tz); [ glTranslatef (25.0, -10.0, 10.0);-Post-multiplies the current matrix by a matrix that moves the object by the given x-, y-, and z-values glScale* (sx, sy, sz); [ glScalef (2.0, -3.0, 1.0); ] - Post-multiplies the current matrix by a matrix that scales an object about the. Computer Graphics Lecture 2 1 Lecture 2 Transformations 2 Transformations. What is a transformation? For 3D rotations , need to be more careful is the same • Always need to think the transformation in the world coordinate syste What is 3D Graphics? Why 3D? Draw one frame at a time X 24 frames per second 150,000 frames for a feature film Realistic rendering is hard Camera movement is hard Interactive animation is hard Model only once Color / texture only once Realism / hyper realism A lot of reuse Computer time instead of artists time Can be interactive (games View Transformation. A 3D scene can be viewed from any posistion in 3D space. A synthetic camera positioned and oriented in 3D space can be used to describe the viewing, and the part of the image or scene to be viewed . It has the following three principal ingredients. View plane: The window is defined in this plane

References: Interactive Computer Graphics with OpenGL 3 rd Edition (Edward Angel, Addison Wesley, 2002): Introduction to Computer Graphics (James D. Foley, Andries van Dam, Steven K. Feiner, and John F. Hughes, Addison Wesley, 1994 Clipping, in the context of computer graphics, is a method to selectively enable or disable rendering operations within a defined region of interest.Mathematically, clipping can be described using the terminology of constructive geometry.A rendering algorithm only draws pixels in the intersection between the clip region and the scene model. Lines and surfaces outside the view volume (aka.

- R.W. Lindeman - WPI Dept. of Computer Science 2 Overview of 3D Modeling Modeling Create 3D model of scene/objects OpenGL commands Coordinate systems (left hand, right hand) Basic shapes (cone, cylinder, etc.) Transformations/Matrices Lighting/Materials Synthetic camera basics View volume Projection GLUT models (wireframe/solid
- Three dimensional transformation . The world composed of three-dimensional images . Objects have height ,width ,and depth . The computer uses mathematical model to create the image . Coordinate.
- Title: lecture8.PDF Author: emmanuel Created Date: 10/31/2006 4:21:46 P
- Approach 1: 3D Rotation using Euler Theorem Classic: use Euler's theorem Euler's theorem: any sequence of rotations = one rotation about some axis Want to rotate about arbitrary axis u through origin Our approach: 1. Use two rotations to align u and x‐axis 2. Do x‐rollthrough angle 3. Negate two previous rotations to de‐align u and x‐axi

A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane. This concept of extending 2D geometry to 3D was mastered by Heron of Alexandria in the first century Principles of Traditional Animation Applied to **3D** **Computer** **Graphics**, SIGGRAPH'87, pp. 35-44. • See also The Illusion of Life: Disney Animation, by Frank Thomas and Ollie Johnston. Traditional Animation Principles . 3 This 3D coordinate system is not, however, rich enough for use in computer graphics. Though the matrix M could be used to rotate and scale vectors, it cannot deal with points, and we want to be able to translate points (and objects). In fact an arbitary a ne transformation can be achieved by multiplication by a 3 3 matrix and shift by a vector Modeling or 3D Design, is a collection of rules and techniques for mathematical and computer modeling of solids. It is distinguished from related areas such as computer graphics by its emphasis on physical ﬁdelity. In other words, accuracy of models that are used in 3D computer games is very different from the accuracy that is required i

2IV60 Computer Graphics 2D transformations Jack van Wijk TU/e Order of transformations 3 OpenGL: glRotate, glScale, etc.: Post-multiplication of current transformation matrix Always transformation in local coordinates Global coordinate version: read in reverse order H&B 7-4:232 Order of transformations 4 glTranslate(); glRotate(); x y x'' y'' x' y' Local trafo interpretation. Visible Surface Detection - When we view a picture containing non-transparent objects and surfaces, then we cannot see those objects from view which are behind from objects closer to eye Composite transformation in Computer Graphics. It is possible to integrate a range of transformations or series of transformations into some kind of a single one which is known as composition. The combined matrix is known as the resultant matrix. The merger procedure is termed as concatenation A scaling transformation requires two inputs: an input vector and a scaling 3-tuple, which defines how the input vector should be scaled in regards to each of the space's basis axes. For example, in the scaling tuple (s 0, s 1, s 2), s 0 represents the scaling along the X axis, s 1 along the Y axis, and s 2 along the Z axis

The Graphics Pipeline • monolithic graphics workstations of the 80s have been replaced by modular GPUs (graphics processing units); major companies: NVIDIA, AMD, Intel • early versions of these GPUs implemented fixed-functionrendering pipeline in hardware • GPUs have become programmable starting in the late 90 3D Transformations - Part 1 Matrices. website creator Transformations are fundamental to working with 3D scenes and something that can be frequently confusing to those that haven't worked in 3D before.In this, the first of two articles I will show you how to encode 3D transformations as a single 4×4 matrix which you can then pass into the appropriate RealityServer command to position.

3D object. Due to the barrier, only one (or a few) of these rays of light passes through the aperture and hits the lm. Therefore, we can establish a one-to-one mapping between points on the 3D object and the lm. The result is that the lm gets exposed by an \image of the 3D object by means of this mapping Computer Graphics •Homogeneous coordinates are key to all computer graphics systems -All standard transformations (rotation, translation, scaling) can be implemented with matrix multiplications using 4 x 4 matrices -Hardware pipeline works with 4 dimensional representations -For orthographic viewing, we can maintain w = -For 3-D graphics, the 4D projective space point (x,y,z,w) maps to the 3D point (x,y,z) in the same way. Homogeneous 2D Transformations The basic 2D transformations become Translate: Scale: Rotate: Any affine transformation can be expressed as a combination of these. We can combine homogeneous transforms by multiplication

- 3D Computer Graphics (Watt) - 3D Computer Graphics: A Mathematical Introduction with OpenGL (Buss) • There is a free online version. available from Books24x7 - Real-Time Rendering, 3rd ed. (Akenine-Möller, Haines, Hoffman) - Fundamentals of Computer Graphics, 3rd ed. (Shirley, Marschner) 34 . Textbook Definition of Computer Graphics-Computer graphics can be a series of images which is most often called a video or single image.Computer graphics is the technology that concerns with designs and pictures on computers. That's why, computer graphics are visual representations of data shown on a monitor made on a computer transformations. w The classification of different types of projections. w The concepts of vanishing points and one-, two-, and three-point perspective. w An appreciation for the various coordinate systems used in computer graphics. w How the perspective transformation works graphics pipeline involves a change of coordinate system. Transformations are central to understanding 3D computer graphics. Modeling Transformations Illumination (Shading) Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Scan Conversion (Rasterization) Visibility / Display Questions? Toda Steps for Window to Viewport Transformation: We can follow the following steps for transform window to viewport: Step 1: Translation of the window towards the Origin- If we shift the window towards the origin, the upper left, and the lower-left corner of the window will be negative (-).The translation factor also should be negative (-) What is transformation? In many cases a complex picture can always be treated as a combination of straight line, circles, ellipse etc., and if we are able to generate these basic figures, we can also generate combinations of them. Once we have drawn these pictures, the need arises to transform these pictures