Algorithmization in a Computer Graphics Environment

Zuzana Homanova

1,2

and Tatiana Havlaskova

1,2

University of Ostrava, Frani Sramka 3, Ostrava, Czech republic

Department of Information and Communication Technologies in Education, Czech republic

Keywords: Algorithmization, Vector Graphics, Learning, Vector Software, ICT in Education.

Abstract: Today’s digital age makes it possible for people to communicate via video or images. Therefore, computer

graphics is part of the elementary school curriculum. The paper is aimed at updating computer science

education at Czech elementary schools; it shows how pupils could develop their computational thinking when

creating vector graphics based on basic geometric shapes such as a circle, ellipse, square, rectangle and others.

The following methods were chosen to present the proposed processes: verbal expression for an algorithm,

visual projection and a flowchart.

1 INTRODUCTION

Schools and school facilities are currently trying to

respond to dynamic changes related to the

development of digital technologies. Pupils need to

develop their computational thinking as it is

considered one of the key competencies.

The paper shows why it is important that pupils

develop algorithmic thinking processes, defines

algorithmic thinking and stresses its importance in

education.

The Strategy for Education Policy of the Czech

Republic Until 2020 (MŠMT, 2017) states that pupils

should be able to not only use modern technology, but

also understand it and even create it. One of the

projects that supports this notion is PRIM (Supporting

the Development of Computational Thinking,

imysleni.cz).

The paper is aimed at the basic method of creating

vector graphics through objects and its algorithmic

expression via words, visual projection and a

flowchart.

1.1 General Issues of Algorithmization

There are many everyday activities where one needs to

follow instructions or the sequence of steps to achieve

the correct result – the output state. Consider, for

instance, cooking following the recipe, assembling

furniture following the instructions, or activities a

person performs from the moment they wake up until

they have to leave for work. There are elements of

algorithmization and algorithmic thinking in all these

situations.

1.2 Algorithm, Algorithmic Thinking

How can algorithmization be defined? The term itself

dates back to the turn of the 8

century A.D. when

Arabia mathematician Abū ʻAbd Allāh Muhammad

ibn Mūsā al-Chwārizmī published two books on

solving linear and quadratic equations. Today, the last

part of his name – al-Chwārizmī – is known as

Algorismi, i.e. algorithm (Online Etymology

Dictionary, 2018).

Educational institutions should help pupils develop

algorithmic thinking as it is one of the key

competencies though which they can learn how to use

information and communication technology and

incorporate it into their everyday lives. The following

are the basic components of algorithmic thinking:

 Functional decomposition (into smaller parts);

 Use of data;

 Term generalization;

 Proceeding step by step;

 …

Many authors are of the opinion that algorithmic

thinking is a cognitive process concept with a clearly

defined sequence of mental operations (with every

important one being described in detail or optimized)

and end result (Pervin, 2007).

However, there is another definition, which

describes algorithmic thinking as a set of mental

operations, actions, methods and strategies aimed at

466

Homanova, Z. and Havlaskova, T.

Algorithmization in a Computer Graphics Environment.

DOI: 10.5220/0007752704660473

In Proceedings of the 11th International Conference on Computer Supported Education (CSEDU 2019), pages 466-473

ISBN: 978-989-758-367-4

completing a theoretical and practical task, with

algorithms being the result (Kopayev, 2018).

Different literatures define the terms algorithm and

algorithmic thinking in different ways. However, for

the purposes of this paper, the following definition is

accurate enough. It describes an algorithm as a specific

way of solving a problem with clearly defined

guidelines.

In the last two decades, many scholars have tried

to define the term algorithmic thinking, arguing that it

is the most important competence which pupils can

learn in school (Snyder, 2000).

In the broader context, algorithmic thinking is a set

of skills aimed at constructing and understanding an

algorithm:

 Ability to analyze problems;

 Ability to specify a problem;

 Ability to find operations required to solve a

problem;

 Ability to use basic operations to construct a

correct algorithm for a particular problem;

 Ability to consider all problem variations (both

normal and specific);

 Ability to make an algorithm more effective.

(Futschek, 2006).

Without algorithmic thinking, one cannot possibly

construct algorithms and processes for solving difficult

problems. Futschek (2018, p. 160) agrees with this

statement, arguing that algorithmic thinking is a highly

creative process. If one is to construct an algorithm,

they need to have mastered algorithmic thinking.

2 ALGORITHM PROPERTIES

An algorithm must have the following properties:

 Determination – each step needs to be clearly

defined. There cannot be a situation where it is not

clear which steps will follow.

 Generality – the created algorithm is applicable to

all problems of a similar nature, not only one type.

 Resultativity – realization of a particular number of

steps leads to the correct result.

 Finality – following the realization of individual

steps, each algorithm must end.

There are situations when one can reach the correct

result through various algorithms with different

numbers of steps, with the aforementioned number of

steps (i.e. the effectiveness of an algorithm) playing the

key role. The less steps an algorithm has, the shorter

the realization time will be (and the more effective the

algorithm will be) (Krček, Kreml, 1993; Pšenčíková,

2009). There are many ways to write an algorithm –

verbal description, graphic representation using a

flowchart and instruction sequence using images.

2.1 Verbal Description of an Algorithm

Verbal description of an algorithm helps us express

any activity realized in everyday situations.

Crossing a street with traffic lights:

1. Go right up to the traffic lights.

2. Is a red light on?

Yes – wait, go back to Point 2.

No – continue to Point 3.

3. Cross the street.

Even though it is evident that a number of (not

only) everyday activities could be expressed through a

verbal description of an algorithm, it could also lead to

inaccuracies caused by different formulations and/or

figures of speech. A natural language should be

replaced with a structured language, i.e. a natural

language bound by certain rules.

2.2 Algorithm Flowchart

Graphic representation of an algorithm through a

flowchart is often used. It uses pre-defined structures

and symbols which make the algorithm easier to

understand.

The following are the main flowchart symbols:

Figure 1: Symbol for the beginning and the end.

Figure 2: Symbol for an operation, instruction.

Figure 3: Symbol for a Condition, Decision.

A flowchart representing a verbal description of

crossing a street with traffic lights may have the

following form:

Algorithmization in a Computer Graphics Environment

467

Figure 4: Crossing a street with traffic lights.

The following figure presents an interesting view

of how a flowchart could be used in the music

industry (Lessner, 2014):

Figure 5: The song “Hey Jude”.

Why is it better to use a graphic representation than a

verbal description of an algorithm?

 We can see the entire structure of an algorithm, not

only its parts.

 It enables us explore and understand the entire

process, helping us to see how it could be changed

or improved.

 It allows us to discover redundant steps in the

creation process.

 It makes communication easier when working in

a team. (Umenie kreativity, 2018).

2.3 Picture Instructions

The sequence of instructions can also be expressed

through various pictures, symbols or even

pictograms, helping to bring algorithmization to the

attention of a wider public (today, it is used almost

exclusively by experts, teachers and pupils of

computer science and other related fields).

Figure 6: Picture instructions (source: Keliwood.cz).

3 COMPUTER GRAPHICS

Computer graphics is dynamically developing.

Thanks to the widespread use of mobile technology

and graphic applications and software, graphics has

become ubiquitous in the lives of people of different

age groups. Not only cameras built into mobile

devices, but also mobile applications, web

applications, commercial and open source software,

creative filters, GIF images, graphic file databases,

shared galleries and other online tools help us

develop our creativity.

Computer graphics can be divided into:

 Raster graphics,

 Vector graphics.

Both vector and raster graphics have their unique

features such as the properties of graphic files and the

way they are used. One of the main differences is the

way in which a particular object is described

(Procházková et al., 2007). While raster graphics uses

pixels, vector graphics is based on Bézier curves and

mathematical shapes (circles, ellipses, polygons, etc.)

defined by mathematical equations. Both raster and

vector graphics can also be used at another graphic

level. Vector graphics is used for creating

illustrations, diagrams, promotional materials

(leaflets, business cards, and logotypes), etc. Vector

graphics is taught in elementary school (as part of the

subject "Informatics").

However, this division is not the only one. There

are approaches that define computer graphics as an

instrument for (Dannhoferová, 2012; Španěl, 2013):

 Infographic image modeling,

 Creating and modifying an infographic image,

 Displaying an infographic image,

 Interpreting an infographic image,

or according to the space dimension (2D graphics, 3D

graphics).

Come to the

traffic light

Is the red light on

the traffic light?

Wait

Yes

Go through the

transition

CSEDU 2019 - 11th International Conference on Computer Supported Education

468

3.1 Vector Graphics in Elementary

School Instruction

In schools, teachers can use a number of different (both

printed and electronic) sources when teaching

computer graphics – e.g. professional channels on

social networks, MOOC courses, shared forums,

clouds, portals aimed at experience exchange (e.g.

Adobe Education Exchange).

Vector graphics instruction helps pupils develop

imagination and creativity. The national curriculum

document – The Framework Educational Program for

Basic Education (MSMT, 2017) – places it under the

area of information processing and management.

Upper primary school pupils should be able to:

 Work with text, graphic and table editors and use

appropriate applications,

 Apply the basic esthetic and typographic rules for

working with text and image,

 Work with information in accordance with

Intellectual Property Law,

 Use information from different sources and

evaluate relations between facts,

 Process and present information at the user level in

text, graphic and multimedia form.

Pupils are usually first introduced to vector software in

computer science class. Zoner Callisto and Inkscape

are the most popular free software used in Czech

elementary schools. The current version of Zoner

Callisto 5 Free is free of charge. The advantage of this

program is Czech location and technical support.

Inkscape is an open-source vector graphics editor, with

capabilities similar to Adobe Illustrator, CorelDraw,

etc. using the W3C standard Scalable Vector Graphics

file format.

3.2 Basic Terms: Vector Graphic File,

Curve, Path

A vector graphic file (or a graphic object) is a set of

individual graphic elements which create a graphic

image. A vector graphic file can be described as a set

of curves containing information about an object’s

shape (if it is a circle, square, rectangle, curve, etc.),

coordinates, color fill or contour thickness

(Procházková et al., 2007).

Curves are the basic building block of vector

graphics. They are defined by node points – there are

node control points (which indicate the shape of the

curve) and node anchor points (which provide

information about the beginning and the end of the

curve). Glitschka (2013, p. 22) defines a Bézier curve

as “a path which can be bent at either end using handles

sticking out of the node points at the path’s ends”.

Vector graphic images can be:

 taken from other authors,

 newly created.

Each graphic design is preceded by an idea. Lieng

(2017) argues that graphic designers often draw

inspiration from online sources, using selected parts of

such designs in their work. There are various online

databases that contain both free and paid computer

graphic images (e.g. freepik.com, deviantart.com,

stock.adobe.com, vecteezy.com, etc.), which can be

used in projects or in instruction. Since a vector image

can be downloaded from the Internet and then edited

in one of the many vector softwares (both commercial

and open source), pupils can learn how graphic objects

are created – learn about the layout of node control and

anchor points which determine path trajectory, of how

many points individual curves consist, etc.

In vector graphics, images can be created in a

variety of ways, i.e. there is no one correct solution.

3.3 Basic Tools in Vector Graphics

Instruction

In vector graphics instruction, pupils/pupils learn to

use graphic software. They learn the following:

 Become familiar with the working environment,

 Create and modify basic shapes and curves,

 Set basic properties of graphic objects (contour,

filling),

 Alignment and arrangement of graphic objects,

 Transform objects (rotation, mirroring, etc.),

 Work with text,

 Hand drawing (a pen, a pencil).

The ability to use a computer and graphic software

(being able to use at least the basic tools) and knowing

the principles for creating vector graphics are the

prerequisites for doing so. In order to be able to create

a graphic object, one needs to know how to work with

graphic objects and what tools can be used when

working with curves.

The following are the basic tools used in vector

graphics instruction:

 Selection tool,

 Node point transformation tool,

 Tool for creating basic geometric shapes,

 Hand drawing tool (a pen, calligraphic pen, brush,

pencil, etc.).

The selection tool is the default tool of every

graphic editor. It allows the user to select, move, rotate

and change the size of objects. The node point

transformation tool enables the user to change:

 The position of node points,

 Properties of node points (e.g. a smooth or corner

Algorithmization in a Computer Graphics Environment

469

node point),

 The number of node points in an object.

The node point transformation tool enables the

user to influence the final shape of an object or a curve.

Depending on the software, the node point

transformation tool has different names:

 Object shaping (Zoner Callisto),

 Curve editing at node level (Inkscape),

 Direct selection tool (Adobe Illustrator),

Figure 7: (1a) Object Selection and Editing tool, (1b) Object

Shaping tool, Zoner Callisto; (2a) Select and transform

objects (2b) Edit path nodes or control handles, Inkscape;

(3a) Selection tool, (3b) Direct Selection tool, Adobe

Illustrator.

In this paper, we use the name “direct selection tool”.

The tool for creating basic geometric shapes allows

the user to create circles, ellipses, starfish, rectangles

and other polygons (see Figure 8).

Figure 8: Basic geometric shapes (Zoner Callisto 5/ Adobe

Illustrator/ Inkscape).

3.4 Algorithmization in Creating Vector

Graphics

The paper is aimed at an algorithmic expression of the

basic process of creating graphic objects through the

following:

 Creating basic geometric shapes (rectangles,

circles, ellipses, polygons, etc.),

 Modifying basic geometric shapes using logical

operations based on Boolean logic (mathematical

operations – amalgamation, division, difference,

penetration, etc.).

 Modifying basic geometric shapes using a tool

for creating and modifying node points.

An example will show the creation of graphic objects

through:

 Verbal description,

 A flowchart,

 Visual instruction.

The individual steps in creating a graphic object will

be demonstrated on the following picture of a robotic

toy.

Figure 9: Graphic object – robotic toy.

3.5 Working with Basic Geometric

Shapes

The proposed graphic file consists of graphic sub-

elements such as the robotic toy’s body, eyes,

eyebrows, etc., which together form the final image.

Generally speaking, every graphic sub-element is a

part of a complex problem (see Figure 10).

Figure 10: Graphic sub-elements as parts of a problem.

The pupil’s ability to interpret the basic shapes and

curves which constitute a particular graphic file has an

impact on their creativity, making it a prerequisite for

creating graphic objects. Therefore, this skill should be

developed. Considering time allocation and pupils’

age, it is natural that the time they spend with vector

graphics is limited. Nevertheless, the instruction needs

to be systematic. However, the difficulty of a graphic

object should be adequate to the pupil’s age. The

method of creating shapes can be used in vector

graphics instruction.

3.5.1 Creating Graphic Objects through the

Use of Basic Shapes

The basic and at the same time easiest way to create

graphic objects is using a tool for creating geometric

shapes which is part of every graphic editor. The

following picture shows the basic shape of circles (no

further changes are required).

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470

Figure 11: Basic shape of circles.

A verbal description of an algorithm for creating

graphic objects using a tool for creating basic shapes is

one of the ways of using algorithmization for

interpreting a process that leads to a solution:

1. Use the tool for creating basic shapes (in this case,

it is a tool for creating circles) to create the basic

shape of an object.

2. Does the shape of the correct size/ position/

proportion? (If not, activate the selection tool to

change the shape’s size and/or position and/or

proportion; If so, proceed to step 3)

3. Has the shape of well-defined contour and filling?

(If not, use the selection tool and define the contour

and filling of object, then repeat step 3).

The default assumption of each algorithm is a new

document (referred to as canvas), in which the situation

is drawn.

A flowchart does not require any conditions. It could

look as follows:

Figure 12: A flowchart – Case 1.

Since the algorithm is trivial, it would be

meaningless to express it through a visual instruction.

It would be more difficult to create an interestingly

shaped object (which could be accomplished by using

more elements to create a single object).

3.5.2 Creating Graphic Objects through

Mathematical Operations

Another way to create graphic objects is to use the

Pathfinder tool to create shapes that consist of two or

more objects through mathematical operations. Those

are:

 Unification,

 Difference,

 Intersection,

 Exclusion,

 Division.

When solving a problem, graphic sub-elements

representing an image could be created this way. The

images are created by unifying (the left image) and

differentiating (the right image) two circles.

Figure 13: Object as compound shape.

The following verbal expression for an algorithm

can be used when creating graphic objects through

Boolean algebraic operations where node anchor

points do not need to be changed:

1. Use the tool for creating shapes to create the

required number of the object’s basic shapes.

2. Is the shape the correct size/ position/ proportion?

(If not, activate the selection tool and edit the size/

position or proportion of the object; if so, proceed

to step 3).

3. Apply the selection tool for multiple selection of all

objects.

4. Apply the specific logical mathematical operations

tool.

5. Is the shape of well-defined contour and filling? (If

not, activate the selection tool and define the

contour and filling the shape).

When drawing two or more homogenous objects

(e.g. circles), Step 1 can be generalized by using he

command “duplicate”.

The following set of images can be used to describe

the aforementioned process:

Figure 14: Compound shapes – Pathfinder.

Start

Activate the tool for

create a basic shape

and draw the shape.

End

Activate the selection

tool and edit the size/

position or proportion.

Does the shape

of the correct size/ position/

proportion?

Yes

Has the shape of

a well-defined color fill and

outline?

Activate the selection

tool and define the

color fill and outline.

Yes

Algorithmization in a Computer Graphics Environment

471

The flowchart may take the following form.

Figure 15: A flowchart – Case 2.

3.5.3 Creating Graphic Objects through the

Use of Tool for Creating and Modifying

Node Points

There is also a third way of creating graphic objects

where it is necessary to modify anchor points in the

path segment in order for the curve to have the required

shape. The Layout of anchor and control points affects

the resulting shape of the object. Using the Direct

Selection tool, we can modify the position of the nodes,

convert the smooth node to the anchor (and vice versa),

or change the number of nodal points that are in the

path of the object. Most graphics software has the

function of adding new or removing the original

anchor point as a separate feature (e.g. Adobe

Illustrator). Conversely, for example, Inkscape allows

you to insert a new node on the path where you double-

click the mouse. In order to simplify this process

generalize and call this an "Edit path nodes" using the

Direct Selection tool. For this case, consider these

shapes.

Figure 16: Object with modified anchor points.

This option includes sub-elements and therefore

requires experience in vector graphics on the user’s

part. The following is a flowchart describing the

aforementioned situation.

The creation of a graphic object can be described

by an algorithm (see Figure 17) for creating and

modifying the basic shape through a transformation of

anchor points:

1. Activate the required tool for create a shape and

draw a basic shape.

2. Does the shape have the desired shape? (If so,

proceed to step 3; if not, activate the Direct

Selection tool and edit path nodes, then repeat the

step 2).

3. Does the shape of the correct size/ position/

proportion? (If not, activate The Selection tool

and edit the size/ position or proportion of the

graphics object; if so, proceed to step 4).

4. Has the shape of well-defined color fill and

outline? (If not, activate the selection tool and

define the color fill and outline of object).

By dividing an illustration into graphic sub-

elements (sequential steps), the pupil learns of how

many shapes the final illustration will consist (see Fig.

18).

Naturally, sometimes a situation may occur when

one needs to combine all four methods. However, such

a situation would require experience beyond that of an

elementary school pupil.

This algorithm may show discrepancies, depending

on the software used. This case is designed for

Inkscape. The form of the flowchart could be the

following:

Figure 17: A flowchart – Case 3.

Start

Activate the tool for

create a basic shape.

The shape will be

the same as the previous

shape.

You need to draw

another basic shape?

Yes

Activate the selection

tool and edit the size/

position or proportion.

End

Draw the basic

shape of the object.

Does the sha pe

of the correct si ze/ position/

proportion?

Yes

Activate the

selection tool and

select all created

shapes.

Activate a tool

Pathfinder and

select a specific tool.

Has the shape of

a well-defined color fill and

outline?

Yes

Activate the

selection tool and

define the color fill

and outline.

Start

Activate the tool for

create a basic shape

and draw the shape.

Does the object have

the desired shape?

Yes

Activate the selection

tool and edit the size/

position or proportion.

Does the shape

of the correct size/ position/

proportion?

End

Activate the direct

selection tool and

edit path nodes.

Yes

Has the shape of

a well-defined color fill and

outline?

Activate the

selection tool and

define the color fill

and outline.

Yes

CSEDU 2019 - 11th International Conference on Computer Supported Education

472

Figure 18: Process of transforming objects by modifying

nodes.

ACKNOWLEDGEMENTS

This paper was supported by the Student Grant

Competition of the University of Ostrava. Project

Title: Using interactive learning objects to develop

problem-solving competencies.

4 CONCLUSION

The paper is aimed at algorithmic description of the

process of creating vector graphics through the method

of drawing geometric shapes. This method can be used

in elementary school instruction when pupils work

with predefined shapes such as circles, squares,

rectangles, polygons, etc.

The presented methods were algorithmically

described using a verbal algorithm, a flowchart and

visual instructions. Computer graphics instruction can

benefit from all these methods as they complement one

another. While a verbal description of an algorithm

provides information about the process and the tool,

visual instructions provide information about the

results of individual steps, i.e. they capture the process

of the transformation of the basic shape into the

required shape.

Even though elementary school pupils have no

previous experience with vector graphics, they should

be encouraged to develop their algorithmic thinking.

The pupil should be able to analyze a problem, divide

it into sub-problems and use their creative thinking to

find a solution. Moreover, they should further develop

their creative skills in the next stages of education.

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