Interactive Computer Graphics Book Summary 2013

8/12/2019 Interactive Computer Graphics Book Summary 2013

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Mark Pearl Summary

Oct 2013

Chapter 1 Graphic Systems and Models

Section 1.3 Images Physical and Synthetic

Two basic entities must be part of any image formation process

1. Object2. Viewer

The visible spectrum of light for humans is from 350 to 780 nm

A light source is characterized by its intensity and direction

A ray is a semi-infinite line that emanates from a point and travels to infinity

Ray tracing and photon mapping are examples of image formation techniques

Section 1.5 Synthetic Camera Model

Conceptual foundation for modern three dimensional computer graphics is the synthetic camera

model.

Few basic principles include:

Specification of object is independent of the specification of the viewer Compute the image using simple geometric calculationsCOPCenter of projection (center of the lens)

With synthetic cameras we move the clipping to the front by placing a clipping rectangle, or clipping

window in the projection plane. This acts as a window through which we view the world.

Section 1.7 - Graphic Architectures

2 main approaches

1. Object Oriented Pipelinevertices travel through the pipeline that determines the colorand pixel positions.

2. Image Oriented Pipelineloop over pixels. For each pixel work backwards to determinewhich geometric primitives can contribute to its color.

Object Orient Pipeline

History

Graphic architecture has progressed from single central processing to do graphics to a pipel ine

model. Pipeline architecture reduces the total processing time for a render (think of it as multiple


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specialized processors, each performing a function and then passing the result on to the next

processor).

Advantages

Each primitive can be processed independently which leads to fast performance Memory requirements reduced because not all objects are needed in memory at the same timeDisadvantages

Cannot handle most global effects such as shadows, reflections and blending in a physicallycorrect manner

4 major steps in pipeline

1. Vertex Processinga. Does coordinate transformationsb. Computes color for each vertex

2. Clipping and Primitive Assemblya. Clipping is performed on a primitive by primitive basis

3. Rasterizationa. Convert from vertices to fragmentsb. Output of rasterizer is a set of fragments

4. Fragment Processinga. Takes fragments generated by rasterizer and updates pixels

Fragmentsthink of them as a potential pixel that carries information including its color, location

and depth info.

6 major frames that occur in OpenGL

1. Object / Model Coordinates2. World Coordinates3. Eye or Camera Coordinates4. Clip Coordinates5. Normalized Device Coordinates6. Window or Screen Coordinates

Example Questions for Chapter 1

Textbook Question 1.1

What are the main advantages and disadvantages of the preferred method to form computer-

generated images discussed in this chapter?

Textbook Question 1.5

Each image has a set of objects and each object comprises a set of graphical primitives. What does

each primitive comprise? What are the major steps in the imaging process?


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Exam Jun 2011 1.a (6 marks)

Differentiate between the object oriented and image oriented pipeline implementation strategies

and discuss the advantages of each approach? What strategy does OpenGL use?


What is the main advantage and disadvantage of using the pipel ine approach to form computergenerated images?

Exam Jun 2012 1.b (4 marks)

Differentiate between the object oriented and image oriented pipeline implementation strategies

Exam Jun 2012 1.c (4 marks)

Name the frames in the usual order in which they occur in the OpenGL pipeline

Exam Jun 2013 1.3 (3 marks)

Can the standard OpenGL pipel ine easily handle light scattering from object to object? Explain?


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Chapter 2 Graphics ProgrammingKey concepts that need to be understood

Typical composition of Vertices / Primitive Objects

Size & ColourImmediate mode vs. retained mode graphics

Immediate mode

- Used to be the standard method for displaying graphics- There is no memory of the geometric data stored- Large overhead in time needed to transfer drawing instructions and model data for each

cycle to the GPU

Retained mode graphics

- Has the data stored in a data structure which allows it to redisplay the data with the optionof slight modifications (i.e. change color) by resending the array without regenerating the

points.

Retained mode is the opposite of immediate: most rendering data is pre-loaded onto the graphics

card and thus when a render cycle takes place, only render instructions, and not data, are sent.

Both immediate and retained mode can be used at the same time on all graphics cards, though the

moral of the story is that if possible, use retained mode to improve performance.

Coordinate SystemsDevice Dependent Graphics- Originally graphic systems required the user to specify all information

directly in units of the display device (i.e. pixels).

Device Independent Graphics- Allows users to work in any coordinate system that they desire.

World coordinate systemcoordinate system that the user decides to work in Vertex coordinatesthe units that an application program uses to specify vertex positions.

At some point with device independent graphics the values in the vertex coordinate system must be

mapped to window coordinates. The graphic system rather than the user is now responsible for this

task and mapping is performed automatically as part of the rendering process.

Color RGB vs. Indexed

With both the indexed and RGB color models the number of colors that can be displayed depends on

the depth of the frame (color) buffer.

Indexed Color Model

In the past, memory was expensive and small and displays had limited colors.

This meant that the indexed-color model was preferred because

- It had lower memory requirements


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- Displays had limited colors available.In an indexed color model a color lookup table is used to identify which color to display.

Color indexing presented 2 major problems

1) When working with dynamic images that needed shading we would typically need morecolors than were provided by the color index mode.

2) The interaction with the window system is more complex than with RGB color.RGB Color Model

As hardware has advanced, RGB has become the norm.

Think of RGB conceptually as three separate buffers, one for red, green and blue. It allows us to

specify the proportion of red, green and blue in a single pixel. In OpenGL this is often stored in a

three dimensional vector.

RGB color model can become unsuitable when the depth of the frame is small because shades

become too distinct/discreet.

Viewing Orthographic and Two Dimensional

The orthographic view is the simplest and OpenGLs default view. Mathematically, the orthographic

projection is what we would get if the camera in our synthetic camera model had an infinitely long

telephoto lens and we could then place the camera infinitely far from our objects.

In OpenGL, an orthographic projection with a right-parallelepiped viewing volume is the default. The

orthographic projection sees only those objects in the volume specified by the viewing volume.

Two dimensional viewingis a special case of three-dimensional graphics. Our viewing area is in the

plane z = 0, within a three dimensional viewing volume. The area of the world that we image is

known as the viewing rectangle, or clipping rectangle. Objects inside the rectangle are in the image;

objects outside are clipped out.

Aspect Ratio and Viewports

Aspect Ratio- The aspect ratio of a rectangle is the ratio of the rectangles width to its height. The

independence of the object, viewing, and workstation window specifications can cause undesirable

side effects if the aspect ratio of the viewing rectangle is not the same as the aspect ratio of thewindow specified.

In glut we use glutInitWindowSize to set this. Side effects can include distortion. Distortion is a

consequence of our default mode of operation, in which the entire clipping rectangle is mapped to

the display window.

Clipping Rectangle- The only way we can map the entire contents of the clipping rectangle to the

entire display window is to distort the contents of clipping rectangle to fit inside the display window.

This is avoided if the di splay window and clipping rectangle have the same aspect ratio.


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Viewport- Another more flexible approach is to use the concept of a viewport. A viewport is a

rectangular area of the display window. By default it is the entire window, but it can be set to any

smaller size in pixels.

OpenGL Programming Basics

Event Processing

Event processing allows us to program how we would like the system to react to certain events.

These could include mouse, keyboard or window events.

Callbacks (Display, Reshape, Idle, Keyboard, Mouse)

Each event has a callback that is specified. The callback is used to trigger actions when an event is

used.

The idle callback is invoked when there are no other events to trigger. A typical use of the idle

callback is to continue to generate graphical primitives through a display function while nothing else

is happening.

Hidden Surface Removal

Given the position of the viewer and the objects being rendered we should be able to draw the

objects in such a way that the correct image is obtained. Algorithms for ordering objects so that they

are drawn correctly are called visible-surface algorithms (or hidden-surface removal algorithms).

Z-buffer algorithm- A common hidden surface removal algorithm supported by OpenGL.

Double buffering

Why we need double buffering

Because an application program typically works asynchronously, changes can occur to the display

buffer at any time. Depending on when the display is updated, this can cause the display to show

partially updated results.

What is double buffering

A way to avoid partial updates. Instead of a single frame buffer, the hardware has two frame buffers.

Front bufferthe buffer that is displayed

Back bufferthe buffer that is being updated

Once updating the back buffer is complete, the front and back buffer are swapped. The new back

buffer is then cleared and the system starts updating it.

To trigger a refresh using double buffering in OpenGL we call glutSwapBuffers();

Menus

Glut provides pop-up menus that can be used.

An example of doing this in code would be

glutCreateMenu(demo_menu); //Create Callback for Menu

glutAddMenuEntry(quit,1);


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glutAddMenuEntry(start rotation, 2);

glutAttachMenu(GLUT_RIGHT_BUTTON);

void demo_menu(int id)

{

//react to menu}

Purpose of GLFlush statements

Similar to computer IO buffer, OpenGL commands are not executed immediately. All commands are

stored in buffers first, including network buffers and the graphics accelerator itself, and are awaiting

execution until buffers are full. For example, if an application runs over the network, it is much more

efficient to send a collection of commands in a single packet than to send each command over

network one at a time.

glFlush()- empties all commands in these buffers and forces all pending commands to be executedimmediately without waiting for buffers to get full. glFlush() guarantees that all OpenGL commands

made up to that point will complete executions in a finite amount time after calling glFlush().

glFlush() does not wait until previous executions are complete and may return immediately to your

program. So you are free to send more commands even though previously issued commands are not

finished.

Vertex Shaders and Fragment Shaders

OpenGL requires a minimum of a vertex and fragment shader.

Vertex Shader

A simple vertex shader determines the color and passes the vertex location to the fragment shader.

The absolute minimum a vertex shader must do is send a vertex location to the rasterizer.

In general a vertex shader will transform the representation of a vertex location from whatever

coordinate system in which is it specified to a representation in clip coordinates for the rasterizer.

Shaders are written using GLSL (which is very similar to a dumbed down c).

Example would be .

In vec4 vPosition

void main()

{

Gl_Position = vPosition;

}

Gl_Position is a special variable known by OpenGL and used to pass data to the rasterizer.

Fragment Shader

Each invocation of the vertex shader outputs a vertex that then goes through primitive assembly and

clipping before reaching the rasterizer. The rasterizer outputs fragments for each primitive inside theclipping volume. Each fragment invokes an execution of the fragment shader.


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At a minimum, each execution of the fragment shader must output a color for the fragment unless

the fragment is to be discarded.

void main(){

gl_FragColor = vec4(1.0, 0.0, 0.0, 1.0);}

Shaders need to be compiled and linked as a bare minimum for things to work.


Exam Nov 2011 1.1 (4 marks)

Explain what double buffering is and how it is used in computer graphics.


Discuss the difference between RGB color model and the indexed color model with respect to thedepth of the frame (color) buffer.


Discuss the difference between the RGB color model and the indexed color model with respect to

the depth of the frame (color) buffer.


A real-time graphics program can use a single frame buffer for rendering polygons, clearing the

buffer, and repeating the process. Why do we usually use two buffers instead?

Exam Jun 2013 8.2 (5 marks)GLUT uses a callback function event model. Describe how it works and state the purpose of the idle,

display and reshape callbacks.


What is the purpose of the OpenGL glFlush statement.


Is the following code a fragment or vertex shader

In vec4 vPosition;

void Main() {Gl_Position = vPosition;}


Explain the difference between immediate mode graphics and retained mode graphics.


Name two artifacts in computer graphics that may commonly be specified at the vertices of a

polygon and then interpolated across the polygon to give a value for each fragme nt within the

polygon.


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Chapter 3 Geometric Objects and TransformationsKey concepts you should know in this chapter are the following:

Surface Normals

Normals are vectors that are perpendicular to a surface. They can be used to describe the

orientation of direction of that surface.

Uses of surface normals include

Together with a point, a normal can be used to specify the equation of a plane The shading of objects depends on the orientation of their surfaces, a factor that is characterized

by the normal vector at each point.

Flat shading uses surface normals to determine if the normal is the same at all points on thesurface.

Calculating smooth (Gourand and Phong) shading. Ray tracing and light interactions can be calculated from the angle of incidence and the normal.Homogeneous Coordinates

Because there can be confusion between vectors and points we use homogenous coordinates.

For a point, the fourth coordinate is 1 and for a vector it is 0. For example

The point (4,5,6) is represented in homogenous coordinates by (4,5,6,1)

The vector (4,5,6) is represented in homogenous coordinates by (4,5,6,0)

Advantages of homogenous coordinates include

All affine (l ine preserving) transformations can be represented as matrix multiplications inhomogenous coordinates.

Less arithmetic work is involved. The uniform representation of all affine transformations makes carrying out successive

transformations far easier than in three dimensional space.

Modern hardware implements homogenous coordinate operations directly, using parallelism toachieve high speed calculations.

Instance Transformations

An instance transformation is the product of a translation, a rotation and a scaling.

The order of the transformations that comprise an instance transformation will effect the outcome.

For instance, if we rotate a square before we apply a non-uniform scale, we will shear the square,

something we cannot do if we scale then rotate.

Frames in OpenGL

The following is the usual order in which the frames occur in the pipeline.


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1) Object (or model) coordinates2) World coordinate3) Eye (or camera) coordinates4) Clip coordinates5) Normalized device coordinates6) Window (or screen) coordinates

Model Frame (Represents an object we want to render in our world).

A scene may comprise of many modelseach is oriented, sized and positioned in the World

coordinate system.

World Frame - also referred to as the application frame - represents values in world coordinates.

If we do not apply transformations to our object frames the world and model coordinates are the

same.

The camera frame (or eye frame) is a frame whose origin is the center of the camera lens and whose

axes are aligned with the sides of the camera.

Because there is an affine transformation that corresponds to each change of frame, there are 4x4

matrices that represent the transformation from model coordinates to world coordinates and from

world coordinates to eye coordinates. These transformations are usually concatenated together into

the model-view transformation, which is specified by the model-view matrix.

After transformation, vertices are stil l represented in homogenous coordinates. The division by the

w component called perspective division, yields three dimensional representations in normalizeddevice coordinates.

The final translation takes a position in normalized device coordinates and, taking into account the

viewport, creates a three dimensional representation in window coordinates.

Translation, Rotation, Scaling and Shearing

Know how to perform Translation, Rotation, Scaling and Shearing (You do not have to learn off the

matrices, they will be given to you if necessary).

Affine transformation- An affine transformation is any transformation that preserves collinearity

(i.e., all points lying on a line initially still lie on a li ne after transformation) and ratios of distances

(e.g., the midpoint of a line segment remains the midpoint after transformation).

Rigid-body Transformations- Rotation and translation are known as rigid-body transformations. No

combination of rotations and translations can alter the shape or volume of an object, they can alter

only the objects location and orientation.

Within a frame, each affine transformation is represented by a 4x4 matric of the form


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Translation

Translation displaces points by a fixed distance in a given direction.

P=P+d

We can also get the same result using the matrix multiplication

P = Tp

where

T is called the translation matrix

Rotation

Two dimensional rotations

Three dimensional rotations.

Rotation about the x-axis by an angle followed by rotation about the y-axis by an angle does not

give us the same result as the one that we obtain if we reverse the order of rotations.


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ScalingP = sP, where

Sheer

Sections that are not examinable include 3.13 & 3.14

Examples of different types of matrices are below


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Exam Jun 2011 2 (6 marks)

Consider the diagram below and answer the question that follows

a) Determine the transformation matrix which will transform the square ABCD to the squareABCD. Show all workings.

Hint Below is the transformation matrices for clockwise and anticlockwise rotation about the z -axis.

b) Using the transformation matrix in a, calculate the new position of A if the transformationwas performed on ABCD

Exam Nov 2011 2.1 & 2.2 (6 marks)

Consider a triangular prism with vertices a,b,c,d,e and f at (0,0,0),(1,0,0),(0,0,1),(0,2,0),(1,2,0) and

(0,2,1), respectively.

Perform scaling by a factor of 15 along the x-axes. (2 marks)

Then perform a clockwise rotation by 45 about the y-axis (4 marks)

Hint: The transformation matrix for rotation about the y-axis is given alongside (where theta is the

angle of rotation)


Consider the following 4x4 matrices


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Which of the matrices reflect the following (give the correct letter only)

2.2.1 Identity Matric (no effect)2.2.2 Uniform Scaling2.2.3 Non-uniform scaling2.2.4 Reflection2.2.5 Rotation about z2.2.6 Rotation

Exam June 2012 2.a (1 marks)What is an instance transformation?

Exam June 2012 2.b (3 marks)

Will you get the same effect if the order of transformations that comprise an instance

transformation were changed? Explain using an example.

Exam June 2012 2.c (4 marks)

Provide a mathematical proof to show that rotation and uniform scaling commute.

Exam June 2013 2.1 (3 marks)

Do the following transformation sequences commute? If they do commute under certain conditionsonly, state those conditions.

2.1.1 Rotation

2.1.2 Rotation and Scaling

2.1.3 Two Rotations


Consider a line segment (in 3 dimensions) with endpoints a and b at (0,1,0) and (1,2,3) respectively.

Compute the coordinates of vertices that result after each application of the following sequence of

transformations of the line segment.

2.2.1 Perform scaling by a factory of 3 along the x-axis

2.2.2 Then perform a translation of 2 units along the y-axis

2.2.3 Finally perform an anti-clockwise rotation by 60 about the z-axis

Hintthe transformation matric for rotation about the z-axis is given below (where omega is the

angle of anti-clockwise rotation)


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Chapter 4 - ViewingImportant concepts for Chapter 4 include

Planar Geometric Projectionsare the class of projections produced by parallel and perspective

views. A planar geometric projection is a projection where the surface is a plane and the projectors

are lines.

4.1 Classical and Computer Viewing

Two types of views

1. Perspective ViewsViews with finite COP2. Parallel ViewsViews with infinite COP

Classical and computer viewing COP / DOP

COPCenter of Projections. For computers is the origin of the camera frame for perspective views.DOPDirection of projections

PRPProjection Reference Point

In classical viewing there is an underlying notion of a principle face.

Different types of classical views include

Parallel Viewing

Orthographic Projectionsparallel viewshows a single plane Axonometric Projectionsparallel view - projection are still orthogonal to the projection plane

but the projection plane can have any orientation with respect to the object (isometric,

diametric and trimetric views)

Oblique Projectionsmost general parallel viewmost diffi cult views to construct by hand.


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Perspective Viewing

Characterized by diminution of size Classical perspective views are known as one, two and three point perspective Parallel l ines in each of the three principal directions converges to a finite vanishing pointPerspective foreshortening- The farther an object is from the center of projection ,the smaller it

appears. Perspective drawings are characterized by perspective foreshortening and vanishing points.

Perspective foreshorteningis the il lusion that object and lengths appear smaller as there distance

from the center of projection increases. These points are called vanishing point. Principal vanishing

points are formed by the apparent intersection of lines parallel to one of the three x,y or z axis. The

number of principal vanishing points is determined by the number of principal axes interested by the

view plane.


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4.2 Viewing with a computer read only

4.3.1 Positioning of camera frame read only

4.3.2 Normalization

Normalization transformation- specification of the projection matrix

VRPView Reference Point

VRCView Reference Coordinate

VUPView Up Vector - the up direction of the camera

VPNView Plane Normalthe orientation of the projection plane or back of the camera

Camera is positioned at the origin, pointing in the negative z direction. Camera is centered at a point

called the View Reference Point (VRP). Orientation of the camera is specified by View Plane Normal

(VPN) and View Up Vector (VUP). The View Plane Normal is the orientation of the projection plane

or back of camera. The orientation of the plane does not specify the up direction of the camera

hence we have View Up Vector (VUP) which is the up direction of the camera. VUP fixes the camera.


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Viewing Coordinate SystemThe orthogonal coordinate system (see pg 240)

View Orientation Matrixthe matrix that does the change of frames. It is equivalent to the viewing

component of the model-view matrix. (Not necessary to know formulae or derivations)

4.3.3 Look-at function

The use of VRP, VPN and VUP is but one way to provide an API for specifying the position of a

camera.

The LookAt function creates a viewing matrix derived from an eye point, a reference point indicating

the center of the scene, and an up vector. The matrix maps the reference point to the negative z-axis

and the eye point to the origin, so that when you use a typical projection matrix, the center of the

scene maps to the center of the viewport. Similarly, the direction described by the up vector

projected onto the viewing plane is mapped to the positive y-axis so that it points upward in theviewport. The up vector must not be parallel to the line of sight from the eye to the reference point.


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Eye and pointsVPN = a-e (Not necessary to know other formulae or derivations)

4.3.4 Other Viewing APIs - read only

4.4 Parallel Projections

A parallel projectionis the limit of a perspective projection in that the center of projection (COP) is

infinitely far from the object being viewed.

Orthogonal projections- a special kind of parallel projection in which the projector are parallel to

the view plane. A single orthogonal view is restricted to one principal face of an object.

Axonometric viewprojectors are perpendicular to the projection plane but projection plane can

have any orientation with respect to object.

Oblique projectionsprojectors are parallel but can make an arbitrary angle to the projection plane

and projection plane can have any orientation with respect to object.

Projection Normalizationa process using translation and scaling that will transform vertices in

camera coordinates to fit inside the default view volume. (see page 247/248 for detailed

explanation).

4.4.5 Oblique Projections - Leave out

4.5 Perspective projections

Perspective projections are what we get with a camera whose lens has a finitelength, or in terms of

our synthetic camera model, the center of the projection is finite.

4.5.1 Simple Perspective Projections - Not necessary to know formulae and derivations

Read pg. 257


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4.6 View volume, Frustum, Perspective Functions

Two perspective functions you need to know

1. Mat4 Frustrum(left, right, bottom, top, near, far)2. Mat4 Perspective(fovy, aspect, near, far)

(All variables are of type GlFloat)

View Volume (Canonical)

The view volume can be thought of as the volume that a real camera would see through its lens

(Except that it is also l imited in distance from the front and back). It is a section of 3D space that is

visible from the camera or viewer between two distances.

When using orthogonal (or parallel) projections, the view volume is rectangular. In OpenGL, an

orthographic projection is defined with the function call glOrtho(left, right, bottom, top, near, far).


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When using perspective projections, the view volume is a frustrum and has a truncated pyramid

shape. In OpenGL, a perspective projection is defined with the function all glFrustum(xmin, xmax,

ymin, ymax, nbear, far)or gluPerspective(fovy, aspect, near, far).

NB: Not necessary to know formulae or derivations.

4.7 Perspective-Projection Matrices read only

4.8 Hidden surface removal

Conceptually we seek algorithms that either remove those surfaces that should not be visible to the

viewer, called hidden-surface-removal algorithms, or find which surfaces are visible, called visible-

surface-algorithms.

OpengGL has a particular algorithm associated with it, the z-buffer algorithm, to which we can

interface through three function calls.

Hidden-surface-removal algorithms can be divided into two broad classes

1. Object-space algorithms2. Image-space algorithms

Object-space algorithms

Object space algorithms attempt to order the surfaces of the objects in the scene such that

rendering surfaces in a particular order provides the correct image. i.e. render objects furthest back

first.

This class of algorithms does not work well with pipeline architectures in which objects are passed

down the pipeline in an arbitrary order. In order to decide on a proper order in which to render the

objects, the graphics system must have all the objects available so it can sort them into the desi red

back-to-front order.

Depth Sort Algorithm

All polygons are rendered with hidden surface removal as a consequence of back to front rendering

of polygons. Depth sort orders the polygons by how far away from the viewer their maximum z-

value is. If the minimum depth (z-value) of a given polygon is greater than the maximum depth of

the polygon behind the one of interest, we can render the polygons back to front.


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Image-space algorithms

Image-space algorithms work as part of the projection process and seek to determine the

relationship among object points on each projector. The z-buffer algorithm is an example of this.

Z-Buffer Algorithm

The basic idea of the z-buffer algorithm is that for each fragment on the polygon corresponding tothe intersection of the polygon with a ray (from the COP) through a pixel we compute the depth

from the center of projection. If the depth is greater than the depth currently stored in the z -buffer,

it is ignored else z-buffer is updated and color buffer is updated with the new color fragment.

Ultimately we display only the closest point on each projector. The algorithm requires a depth

buffer, or z-buffer, to store the necessary depth information as polygons are rasterized.

Because we must keep depth information for each pixel in the color buffer, the z-buffer has the

same spatial resolution as the color buffers. The depth buffer is initialized to a value that

corresponds to the farthest distance from the viewer.

For instance with the diagram below, a projector from the COP passes through two surfaces.

Because the circle is closer to the viewer than to the triangle, it is the circles color that determines

the color placed in the color buffer at the location corresponding to where the projector pierces the

projection plane.

2 Major Advantages of Z-Buffer Algorithm

- Its complexity is proportional to the number of fragments generated by the rasterizer- It can be implemented with a small number of additional calculations over what we have to

do to project and display polygons without hidden-surface removal

Handling Translucent Objects using the Z-Buffer Algorithm

Any object behind an opaque object (solid object) should not be rendered. Any object behind a

translucent object (see through objects) should be composited.

Basic approach in the z-buffer algorithm would be


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- If the depth information allows a pixel to be rendered, it is blended (composited) with the pixelalready stored there.

- If the pixel is part of an opaque polygon, the depth data is updated.4.9 Displaying Meshes read only

4.10 Projections and Shadows - Know

The creation of simple shadows is an interesting application of projection matrices.

To add physically correct shadows we would typically have to do global calculations that are difficult.

This normally cannot be done in real time.

There is the concept of a shadow polygonwhich is a flat polygon which is the projection of the

original polygon onto the surface with the center of projection at the light source.

Shadows are easier to calculate if the light source is not moving, if i t is moving, the shadows wouldpossibly need to be calculated in the idle callback function.

For a simple environment such as a plane flying over a flat terrain casting a single shadow, this is an

appropriate approach. When objects can cast shadows on other objects, this method becomes

impractical



Differentiate between orthographic and perspective projections in terms of projectors and theprojection plane.


Define the term View Volume with respect to computer graphics and with reference to both

perspective and orthogonal views.


Define the term View Volume with respect to computer graphics and with reference to both

perspective and orthogonal views.

Exam Nov 2012 1.3 (6 marks)Define the term View Volume with reference two both perspective and orthogonal views. Provide

the OpenGL functions that used to define the respective view volumes.


Orthogonal, oblique and axonometric view scenes are all parallel view scenes. Explain the

differences between orthogonal, axonometric, and oblique view scenes.


Explain what is meant by non-uniform foreshortening of objects under perspective camera.


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What is the purpose of projection normalization in the computer graphics pipeline? Name one

advantage of using this technique.


Draw a view Frustum. Position and name the three important rectangular planes at their correctpositions. Make sure that the position of the origin and the orientation of the z -axis are clearly

distinguishable. State the name of the coordinate system (or frame) in which the view frustum is

defined.


Draw a picture of a set of simple polygons that the Depth sort algorithm cannot render without

splitting the polygons


Why cant the standard z-buffer algorithm handle scenes with both opaque and translucent objects?

What modifications can be made to the algorithm for it to handle this?

Exam June 2012 3.a (4 marks)

Hidden surface removal can be divided into two broad classes. State and explain each of these

classes.


Explain the problem of rendering translucent objects using the z-buffer algorithm, and describe how

the algorithm can be adapted to deal with this problem (without sorting the polygons).

Exam June 2012 4.a (4 marks)What is parallel projection? What specialty do orthogonal projections provide? What is the

advantage of the normalization transformation process?


Why are projections produced by parallel and perspective viewing known as planar geometric

projections?


The specification of the orientation of a synthetic camera can be divided into the specification of the

view reference point (VRP), view-plane normal (VPN) and the view-up-vector (VUP). Explain each of

these?


Differentiate between Depth sort and z-buffer algorithms for hidden surface removal.


Briefly describe, with any appropriate equations, the algorithm for removing (or culling) back facing

polygons. Assume that the normal points out from the visible side of the polygon


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Chapter 5 Lighting and ShadingA surface can either emit light by self -emission, or reflect light from other surfaces that illuminate it.

Some surfaces can do both.

Rendering equation- to represent lighting correctly we would need a recursive call that would blend

light between sourcesthis can mathematically be described using the rendering equation. There

are various approximations of this e quation using ray tracing unfortunately these methods cannot

render scenes at the rateat which we can pass polygons through the modeling-projection pipeline.

For render pipeline architectures we focus on a simpler rendering model, based on the Phong

reflection model that provides a compromise between physical correctness and efficient calculation.

Rather than looking at a global energy balance, we fol low rays of light from light -emitting (or self-

luminous) surfaces that we call light sources. We then model what happens to these rays as they

interact with reflecting surfaces in the scene. This approach is similar to ray tracing, but we consider

only single interactions between light sources and surfaces.

2 independent parts of the problem

1. Model the l ight sources in the scene2. Build a reflection model that deals with the interactions between materials and light.

We need to consider only those rays that leave the source and reach the viewers eye (either directly

or through interactions with objects). These are the rays that reach the center of projection (COP)

after passing through the clipping rectangle.


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Interactions between light and materials can be classified into three groups depicted.

1. Specular Surfacesappear shinny because most of the light that is reflected or scattered isin a narrow range of angles close to the angle of reflection. Mirrors are perfectly specular

surfaces.

2. Diffuse surfacescharacterized by reflected light being scattered in all directions. Wallspainted with matt paint are diffuse ref lectors.

3. Translucent Surfacesallow some light to penetrate the surface and to emerge fromanother location on the object. The process of refraction characterizes glass and water.

5.1 Light and Matter

There are 4 basic types of l ight sources

1. Ambient Lighting2. Point Sources3. Spotlights4. Distant Lights

These four lighting types are sufficient for rendering most simple scenes.

5-2 Light Sources

Ambient Light

Ambient l ight produces light of constant intensity throughout the scene. All objects are illuminated

from all sides.

Point SourcesPoint sources emit light equally in all direction, but the intensity of the light diminishes with the

distance between the light and the objects it illuminates. Surfaces facing away from the light source

are not illuminated.

Umbrathe area that is fully in the shadow

Penumbrathe area that is partially in the shadow

Spotlights

A spot light source is similar to a point light source except that its illumination is restricted to a cone

in a particular direction.


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Spotlights are characterized by a narrow range of angles through which light is emitted. More

realistic spotlights are characterized by the distribution of light within the coneusually with most

of the light concentrated in the center of the cone.

Distant Light Sources

A distant light source is like a point light source except that the rays of light are all parallel.

Most shading calculations require the direction from the point on the surface to the l ight source

position. As we move across a surface, calculating the intensity at each point, we should re-compute

this vector repeatedlya computation that is a significant part of the shading calculation. Distant

light sources can be calculated faster than near light sources (see pg. 294 for parallel light).

5.3 - Phong Reflection Model

The Phong model uses 4 vectors to calculate a color for an arbitrary point P on a surface.

1. lfrom p to light source2. nthe normal at point p3. vfrom p to viewer4. rreflection of ray from l

The Phong model supports the three types of material-light interactions

1. Ambient Light, I = kL where k is the reflection coefficient, L is ambient term2. Diffuse Light, I = k(I.n)L3. Specular Light, I=k.L Max((rv),0) is the shininess coefficient

There are 3 types of reflection

1. Ambient Reflection2. Diffuse Reflection3. Specular Reflection

What is referred to as the Phong model, including the distance term is written


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Lambertian Surfaces (Applies to Diffuse Reflection)

An example of a lambertian surface is a rough surface. This can also be referred to as diffuse

reflection.

Lamberts Lawthe surface is brightest at noon and dimmest at dawn and dusk because we see only

the vertical component of the incoming light.

More technical, the amount of di ffuse light reflected is directly proportional to Cos where is the

angle between the normal at the point of interest and the direction of the light source.

If both l and n are unit-length vectors, then

Cos = l n

Using Lamberts Law, derive the equation for calculating approximations to diffuse reflection on

a computer.

If we consider the direction of light source (l) and the normal at the point of interest (n) to beunit length vectors, then cos = l dot n;

If we add a reflection component kdrepresenting the fraction of incoming diffuse light that isreflected, we have the diffuse reflection term:

Id= kd(l n)Ld, where L is the light sourceDifference between the Phong Model and the Blinn-Phong Model

The Blinn-Phong model attempts to provide a performance optimization by using the unit vector

halfway between the viewer vector and the light-source vector which avoids the recalculation of r.

When we use the halfway vector in the calculation of the specular term we are using the Blinn -

Phong model. This model is the default in systems with a fixed-function pipeline.

5.4 Computation of Vectors Read Only

5.5 Polygonal Shading

Flat Shadinga polygon is fil led with a single color or shade across its surface. A single normal is

calculated for the whole surface, and this determines the color. It works on the basis that if three

vectors are constant, then the shading calculation needs to be carried out only once for each

polygon, and each point on the polygon is assigned the same shade.

Smooth Shading- the color per vertex is calculated using vertex normal and then this color isinterpolated across the polygon.


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Gouraud Shadingan estimate to the surface normal of each vertex in is found. Using this value,

lighting computations based on the Phong reflection model are performed to produce color

intensities at the vertices.

Phong Shading- the normals at the vertices are interpolated across the surface of the polygon. The

lighting model is then applied at every point within the polygon. Because normals give the localsurface orientation, by interpolating the normals across the surface of a polygon, the surface

appears to be curved rather than flat hence the smoother appearance of Phong shaded images.

5.6 Approximation of a sphere by recursive subdivision - Read Only

5.7 Specifying Lighting Parameters

Read pg. 314-315

5.8 - Implementing a Lighting Model

Read pg. 314-315

5.9 - Shading of the sphere model

5.10 Per fragment Lighting

5.11 Global Illumination



The Phong reflection model is an approximation of the physical reality to produce good renderingsunder a variety of lighting conditions and material properties. In this model there are three terms, an

ambient term, a diffuse term, and a specular term. The Phong shading model for a single light source

is

Exam Nov 2013 4.1.1 (4 marks)

Describe the four vectors the model uses to calculate a color for an arbitrary point p. Il lustrate with a

figure.


In the specular term, there is a factor of (rv)P. What does p refer to? What effect does varying the

power p have?


What is the term kaLa? What does karefer to? How will decreasing kaeffect the rendering of the

surface?


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Exam June 2012 5.a (4 marks)

Interactions between light and materials can be classified into three categories. State and describe

these categories.


State and explain Lamberts Law using a diagram.

Exam Nov 2011 4.b (3 marks)

State and explain Lamberts Law using a diagram

Exam Nov 2011 4.c (3 marks)

Using Lamberts Law, derive the equation for calculating approximations to the diffuse reflection

term used in the Phong lighting model.


Using Lamberts Law derive the equation for calculating approximations to diffuse reflection on a

computer.


The shading intensity at any given point p on a surface is in general comprised of three

contributions, each of which corresponds to a distinct physical phenomenon. List and describe all

three, stating how they are computed in terms of the following vectors.

nthe normal at point

vfrom p to viewer

Ifrom p to light source

rreflection of ray from light source to p


Consider Gouraud and Phong shading. Which one is more realistic, especially for highly curved

surfaces? Why?

Exam Jun 2011 4.e (3 marks)

Why does Phong shaded images appear smoother than Gouraud or Flat shaded images?


Explain what characterizes a diffuse ref lecting surface.

Exam Jun 2011 4.d (6 marks)

Describe distinguishing features of ambient, point, spot and distant light sources.


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Chapter 6 From Vertices to Fragments

6.1 Basic Implementation Strategies

There are two basic implementation strategies

1. Image Oriented Strategy2. Object Oriented Strategy

Image Oriented Strategy

Loop through each pixel (called scanlines) and work our way back to determine what determines the

pixels color.

Main disadvantageunless we first build a data structure from the geometric data, we do not know

which primitives affect which pixels (These types of data structures can be complex).

Main AdvantageThey are well suited to handle global effects such as shadows and reflections (e.g.

Ray Tracing).

Object Oriented Strategy

Loop through each object and determine each objects colors and whether it is visible.

In past main disadvantage was memory required doing this, however this has been overcome as

memory has reduced in price and become denser.

Main disadvantage- each geometric primitive is processed independentlycomplex shading effects

that involve multiple geometric objects such as reflections cannot be handled except by approximate

methods.

Main advantagereal-time processing and generation of 3d views.

One major exceptionto this is hidden-surface removal, where the z buffer is used to store global

information.

6.2 Four Major Tasks

There are four major tasks that any graphics system must perform to render a geometric entity, such

as a 3d polygon. They are

1. Modeling2. Geometry Processing3. Rasterization4. Fragment Processing

Modeling

Think of the modeler as a black box that produces geometric objects and is usually a user program.

One function a modeler can perform is to perform clipping or intel ligently el iminate objects that

do not need to be rendered or that can be simplified.

Geometry Processing

The first step in geometry processing is to change representations from object coordinates to

camera or eye coordinates using the model-view transformation.


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The second step is to transform vertices using the projection transformation to a normalized view

volume in which objects that might be visible are contained in a cube centered at the origin.

Geometric objects are transformed by a sequence of transformations that may reshape and move

them or may change their representations.

Eventually only those primitives that fit within a specified volume (the view volume) can appear on

the display after rasterization.

2 reasons why we cannot allow all objects to be rasterized are

1. Rasterizing objects that lie outside the view volume is inefficient because such objectscannot be visible.

2. When vertices reach the rasterizer, they can no longer be processed individually and firstmust be assembled into primitives.

RasterizationTo generate a set of fragments that give the locations of the pixels in the frame buffer corresponding

to these vertices, we only need their x, y components or, equivalently, the results of the orthogonal

projection of these vertices. We determine these fragments through a process called rasterization.

Rasterization determines which fragments should be used to approximate a line segment between

the projected vertices.

The rasterizer starts with vertices in normalized device coordinates but outputs frames whose

locations are in units of the display (window coordinates)

Fragment Processing

The process of taking fragments generated by rasterizer and updating pixels in the frame buffer.

Depth information together with transparency of fragments in frontas well as texture and bump

mapping are used to update the fragments in the frame buffer to form pixels that can be displayed

on the screen.

Hidden-surface removal is typically carried out on a fragment by fragment basis. In the simplest

situation, each fragment is assigned a color by the rasterizer and this color is placed in the frame

buffer at the location corresponding to the fragment location.

6.3 ClippingClipping is performed before perspective division.

The most common primitives to pass down the pipeline are line segments and polygons and there

are techniques for clipping on both types of primitives.

6.4 Line-segment Clipping

A clipper decides which primitives are accepted (displayed) or rejected. There are two wel l know

clipping algorithms for line segments, they are

1. Cohen-Sutherland Clipping2. Liang-Barsky Clipping


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Liang-Barksy Clipping is more efficient than Cohen-Sutherland Clipping.

Cohen-Sutherland Clipping

The Cohen-Sutherland algorithm was the first to seek to replace most of the expensive floating-point

multipl ications and divisions with a combination of floating-point subtractions and bit operations.

The center region is the screen, and the other 8 regions are on different sides outside the screen.

Each region is given a 4 bit binary number, called an "outcode". The codes are chosen as follows:

If the region is above the screen, the first bit is 1

If the region is below the screen, the second bit is 1

If the region is to the right of the screen, the third bit is 1

If the region is to the left of the screen, the fourth bit is 1

Obviously an area can't be to the left and the right at the same time, or above and below it at the

same time, so the third and fourth bit can't be 1 together, and the first and second bit can't be 1

together. The screen itself has all 4 bits set to 0.

Both endpoints of the line can lie in any of these 9 regions, and there are a few trivial cases:

If both endpoints are inside or on the edges of the screen, the line is inside the screen or clipped,and can be drawn. This case is the trivial accept.

If both endpoints are on the same side of the screen (e.g., both endpoints are above the screen),certainly no part of the line can be visible on the screen. This case is the trivial reject, and the

line doesn't have to be drawn.

Advantages

1. This algorithm works best when there are many line segments but few are actuallydisplayed.

2. The algorithm can be extended to three dimensions


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Disadvantage

1. It must be used recursivelyLiang-Barsky Clipping

The LiangBarsky algorithm uses the parametric equation of a line and inequalities describing therange of the clipping window to determine the intersections between the line and the clippingwindow. With these intersections it knows which portion of the l ine should be drawn.

How it works

Suppose we have a line segment defined by two endpoints p(x1,y1) q(x1,y1). The parametric

equation of the line segment gives x-values and y-values for every point in terms of a parameter

that ranges from 0 to 1.

x() = (1- ) x1 + x2

y() = (1- ) y1 + y2

There are four points where line intersects side of windowstB, tL, tT, tR

We can order these points and then determine where clipping needs to take place. If for example tL

> tR, this implies that the line must be rejected as it falls outside the window.

To use this strategy effectively we need to avoid computing intersections until they are needed.

Many l ines can be rejected before all four intersections are known.

Efficiency

Efficient implementation of this strategy requires that we avoid computing intersections until they

are needed.

The Liang-Barsky algorithm is significantly more efficient than CohenSutherland.

The efficiency of this approach, compared to that of Cohen-Sutherland algorithm is that we avoid

multiple shortening of line segments and the related re-executions of the clipping algorithm.


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6.5 Polygon Clipping do not learn

6.6 - Clipping of other primitives do not learn

6.7 - Clipping in three dimensions do not learn

6.8 Rasterization

Rasterization is the task of taking an image described in a vector graphics format (shapes) and

converting it into a raster image (pixels or dots) for output on a video display or printer, or for

storage in a bitmap file format.

In normal usage, the term refers to the popular rendering algorithm for displaying three -dimensional

shapes on a computer. Rasterization is currently the most popular technique for producing real -time

3D computer graphics. Real-time applications need to respond immediately to user input, and

generally need to produce frame rates of at least 24 frames per second to achieve smooth

animation.

Compared with other rendering techniques such as ray tracing, rasterization is extremely fast.

However, rasterization is simply the process of computing the mapping from scene geometry to

pixels and does not prescribe a particular way to compute the color of those pixels. Shading,

including programmable shading, may be based on physical light transport, or artistic intent.

6.9 Bresenhams Algorithm

Bresenham derived a line-rasterization algorithm that avoids all floating point calculations and has

become the standard algorithm used in hardware and software rasterizers.

It is preferred over the DDA algorithm because although the DDA algorithm is eff icient and can be

coded easily, it requires a floating-point addition for each pixel generated which Bresenhams

algorithm doesnt require.

6.10 Polygon Rasterization

There are several different types of polygon rasterization. Some of the ones that work with the

OpenGL pipeline include.

Inside-Outside Testing Concave Polygons Fill and Sort Flood Fill Singularities

Crossing or Odd-Even Test

The most widely used test for making inside-outside decisions. Suppose P is a point inside a polygon,

and then pretend there is a ray emanating from p, going off into infinity. Now follow that 'ray' from

outside (somewhere) to P. If it crosses an even amount of edges, then P is inside the polygon, else

its outside

Winding Testp.g. 358


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6.11 Hidden Surface Removal

2 main approaches

1)

Object space approaches2) Image space approaches (Image space approaches are more popular)

Scanline Algorithms

-

Back-Face Removal (Object Space Approach)

A simple object space algorithm is Back-Face removal (or back face cull) where no faces on the back

of the object are displayed.

Limitations on Back-face removal algorithm

It can only be used on solid objects modeled as a polygon mesh. It works fine for convex polyhedra but not necessarily for concave polyhedra.

Z-Buffer Algorithm (Image Space Approach)

The easiest way to achieve hidden-surface removal is to use the depth buffer (sometimes called a z-

buffer). A depth buffer works by associating a depth, or distance from the viewpoint, with each pixel

on the window. Initially, the depth values for all pixels are set to the largest possible distance, and

then the objects in the scene are drawn in any order.

Graphical calculations in hardware or software convert each surface that's drawn to a set of pixels

on the window where the surface will appear if it isn't obscured by something else. In addition, the

distance from the eye is computed. With depth buffering enabled, before each pixel is d rawn, a

comparison is done with the depth value already stored at the pixel.

If the new pixel is closer to the eye than what is there, the new pixel's color and depth values replace

those that are currently written into the pixel. If the new pixel's depth is greater than what is

currently there, the new pixel would be obscured, and the color and depth information for the

incoming pixel is discarded.

Since information is discarded rather than used for drawing, hidden-surface removal can increase

your performance.

Shading is performed before hidden surface removal. In the z-buffer algorithm polygons are fisrt

rasterized and then for each fragment of the polygon depth values are determined and compared to

the z-buffer.

Scan Conversion with the z-Buzzer

-

Depth Sort and the Painters Algorithm (Object Space Approach)


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The idea behind the Painter's algorithm is to draw polygons far away from the eye first, followed by

drawing those that are close to the eye. Hidden surfaces will be written over in the image as the

surfaces that obscure them are drawn.

Situations where depth sort algorithm is troublesome include.

If three or more polygons operate cyclically If a polygon pierces another polygon6.12 Antialiasing

An error arises whenever we attempt to go from the continuous representation of an object (which

has infinite resolution) to a sampled approximation, which has limited resolutionthis is called

aliasing.

Aliasing errors are caused by 3 related problems with the discrete nature of the frame buffer.

1. The number of pixels of the frame buffer is fixed. Many different line segments may beapproximated by the same pattern of pixels. We can say that all these segments are aliased

as the same sequence of pixels.2. Pixel locations are fixed on a uniform grid; regardless of where we would like to place pixels,

we cannot place them at other than evenly spaced locations.

3. Pixels have a fixed size and shape.In computer graphics, antialiasing is a software technique for diminishing jaggies - stairstep-like

lines that should be smooth.

Jaggies occur because the output device, the monitor or printer, doesn't have a high enough

resolution to represent a smooth line. Antialiasing reduces the prominence of jaggies by surrounding

the stairsteps with intermediate shades of gray (for gray-scaling devices) or color (for color devices).

Although this reduces the jagged appearance of the lines, it also makes them fuzzier.

Another method for reducing jaggies is called smoothing, in which the printer changes the size and

horizontal alignment of dots to make curves smoother.

Antialiasing is sometimes called oversampling.

Interpolation

Interpolation is a way of determining value (of some parameter) for any point between two

endpoints of which the parameter values are known (e.g. the color of any points between two point,

or the normal of any point between two points).


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Accumulation Buffer

The accumulation buffer can be used for a variety of operations that involve combining multiple

images. One of the most important uses of the accumulation buffer is for antialiasing. Rather than

antialiasing individual lines and polygons, we can anti-alias an entire scene using the accumulation

buffer.

6.13 Display Considerations do not learn



Briefly explain what the accumulation buffer is and how it is used with respect to anti -aliasing.

Exam Nov 2012 6 (6 marks)

Using diagrams describe brief ly the Liang-Barsky clipping algorithm

Exam Jun 2012 7.a (8 marks)Describe, with the use of diagrams, the Cohen-Sutherland line clipping algorithm


What are the advantages and disadvantages of the Cohen-Sutherland line clipping algorithm?


Give one advantage and one disadvantage of the Cohen -Sutherland line clipping algorithm.


What is the crossing or odd even test? Explain i t with respect to a point p inside a polygon


In the case of the z-buffer algorithm for hidden surface removal, is shading performed before or

after hidden surfaces are eliminated? Explain.

Exam Jun 2011 5.c (2 marks)

Bresenham derived a line-rasterization algorithm that has become the standard approach used in

hardware and software rasterizers as opposed to the more simpler DDA algorithm. Why is this so?


Give brief definitions of the following terms in the context of computer graphics

i) Anti-aliasingii) Normal Interpolation


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Chapter 7 Discrete Techniques

7.1 Buffers Do not learn

7.2 Digital Images Do not learn

7.3 - Writing into Buffers Do not learn

7.4 - Mapping Methods

Mimapping

A way to deal with the minification problem i.e. the distortion of a mapped texture due to the texel

being smaller than one pixel. Mimapping enables us to use a sequence of texture images at different

resolutions to give a texture values that are the average of texel values over various are

7.5 Texture Mapping

Texture mapping maps a pattern (of colors) to a surface.

All approaches of texture mapping require a sequence of steps that involve mappings among three

or four different coordinate systems. They are

Screen Coordinateswhere the final image is produced World Coordinatewhere the objects up which the textures will be mapped are described Texture coordinatesare used to describe the texture Parametric coordinateused to define curved surfaces7.6 Texture Mapping in OpengGL

7.7 - Texture Generation Do not learn

7.8 - Environment Maps

7.9 Reflection Map Example Do not learn

7.10 Bump Mapping

Whereas texture maps give detail by mapping patterns onto surfaces, bump maps distort the normal

vectors during the shading process to make the surface appear to have small variations in shape, l ike

bumps or depressions.

7.11 Compositing Techniques

7.12 - Sampling and Aliasing Do not learn



Explain what is meant by bump mapping. What does the value at each pixel in a bump map

correspond to? How is this data used in rendering?

Exam Jun 2013 5.2 (1 marks)What technique computes the surroundings visible as a reflected image in a shinny object?


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Describe what is meant by point sampling and linear filtering? Why is linear filtering a better choice

than point sampling in the context of aliasing of textures?


The 4 major stages of the modern graphics pipeline are.

a. Vertex Processingb. Clipping and primitive assemblyc. Rasterizationd. Fragment processing

In which of these 4 stages would the fol lowing normally occur.

1.4.1 Texture Mapping1.4.2 Perspective Division

!.4.3 Inside-outside testing1.4.4 Vertices are assembled into objects

1.4.5 Z-buffer algorithm


Explain the term texture mapping


Consider the texture map with U,V coordinates in the diagram on the left below. Draw the

approximate mapping if the square on right were textured using the above image.

Exam May 2012 6.a (3 marks)

Texture mapping requires interaction between the application program, the vertex shader and thefragment shade. What are the three basic steps of texture mapping.

Exam May 2012 6.b (4 marks)

Explain how the alpha channel and the accumulation buffer can be used to achieve antialiasing with

line segments and edges of polygons.

Exam May 2012 6.c (3 marks)

Explain what is meant by texture aliasing. Explain how point sampling and linear filtering help to

solve this problem.


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Define the following terms and briefly explain their use in computer graphics

i) Bitmapii) Bump Mappingiii) Mimapping

Interactive Computer Graphics Book Summary 2013

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