Programming of one-dimansional and two-dimensional tokens for tokenization of land plots
The use of blockchain tools that allows spliting virtual objects into parts is considered. Examples of practical use of the developed algorithms are presented. The concept of one-dimensional and two-dimensional tokens representing one-dimensional and flat objects is proposed. Algorithms for the impl...
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pp_isofts_kiev_ua-article-6052024-04-27T17:06:49Z Programming of one-dimansional and two-dimensional tokens for tokenization of land plots Програмування одновимірного та двовимірних токенів для токенізації земельних ділянок Strutynskyi, S. V. Yalanetskyi, V. A. Blockchain; EVM; smart contracts; NFT; fractional tokens UDC 621.09.04 блокчейн; EVM; смарт-контракт; NFT; фракційні токени УДК 621.09.04 The use of blockchain tools that allows spliting virtual objects into parts is considered. Examples of practical use of the developed algorithms are presented. The concept of one-dimensional and two-dimensional tokens representing one-dimensional and flat objects is proposed. Algorithms for the implementation of one-dimensional tokens are developed, and the peculiarities of their practical application are considered. A designed smart contract allows to conduct a basic list of operations with one-dimensional tokens. Algorithms, providing implementation of two-dimensional tokens, are proposed. Peculiarities of presenting territories of virtual worlds and land plots are suggested. A comparative analysis of the use of NFT and two-dimensional tokens for presenting the Earth surface areas is performed. Methods that ensure ownership of tokens at different levels are proposed.Prombles in programming 2024; 1: 38-47 У публікації розглянуто ключові аспекти застосування блокчейн-інструментів, що дозволяють оперувати частинами віртуальних об’єктів. Для вирішення практичних задач пропонується використовувати одновимірні та двовимірні токени. Розроблено алгоритми та програмно реалізовано одновимірні токени на базі існуючих платформ смарт-контрактів. Запропоновані рішення дозволяють розділяти одновимірні об’єктів на частини та проводити транзакції із цими фрагментами. Розроблено алгоритми реалізації двовимірних токенів та розглянуті особливості їх застосування для представлення земельних ділянок та віртуальних територій. Визначено основні переваги двовимірних токенів у порівнянні із NFT при їх використанні для представлення ділянок земної поверхні. Розроблено алгоритми, що забезпечують володіння віртуальними об’єктами на різних рівнях.Prombles in programming 2024; 1: 38-47 Інститут програмних систем НАН України 2024-04-01 Article Article application/pdf https://pp.isofts.kiev.ua/index.php/ojs1/article/view/605 10.15407/pp2024.01.038 PROBLEMS IN PROGRAMMING; No 1 (2024); 38-47 ПРОБЛЕМЫ ПРОГРАММИРОВАНИЯ; No 1 (2024); 38-47 ПРОБЛЕМИ ПРОГРАМУВАННЯ; No 1 (2024); 38-47 1727-4907 10.15407/pp2024.01 en https://pp.isofts.kiev.ua/index.php/ojs1/article/view/605/655 Copyright (c) 2024 PROBLEMS IN PROGRAMMING |
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Blockchain EVM smart contracts NFT fractional tokens UDC 621.09.04 |
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Blockchain EVM smart contracts NFT fractional tokens UDC 621.09.04 Strutynskyi, S. V. Yalanetskyi, V. A. Programming of one-dimansional and two-dimensional tokens for tokenization of land plots |
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Blockchain EVM smart contracts NFT fractional tokens UDC 621.09.04 блокчейн EVM смарт-контракт NFT фракційні токени УДК 621.09.04 |
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Strutynskyi, S. V. Yalanetskyi, V. A. |
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Strutynskyi, S. V. Yalanetskyi, V. A. |
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Strutynskyi, S. V. |
| title |
Programming of one-dimansional and two-dimensional tokens for tokenization of land plots |
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Programming of one-dimansional and two-dimensional tokens for tokenization of land plots |
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Programming of one-dimansional and two-dimensional tokens for tokenization of land plots |
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Programming of one-dimansional and two-dimensional tokens for tokenization of land plots |
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Programming of one-dimansional and two-dimensional tokens for tokenization of land plots |
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programming of one-dimansional and two-dimensional tokens for tokenization of land plots |
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Програмування одновимірного та двовимірних токенів для токенізації земельних ділянок |
| description |
The use of blockchain tools that allows spliting virtual objects into parts is considered. Examples of practical use of the developed algorithms are presented. The concept of one-dimensional and two-dimensional tokens representing one-dimensional and flat objects is proposed. Algorithms for the implementation of one-dimensional tokens are developed, and the peculiarities of their practical application are considered. A designed smart contract allows to conduct a basic list of operations with one-dimensional tokens. Algorithms, providing implementation of two-dimensional tokens, are proposed. Peculiarities of presenting territories of virtual worlds and land plots are suggested. A comparative analysis of the use of NFT and two-dimensional tokens for presenting the Earth surface areas is performed. Methods that ensure ownership of tokens at different levels are proposed.Prombles in programming 2024; 1: 38-47 |
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Інститут програмних систем НАН України |
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2024 |
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https://pp.isofts.kiev.ua/index.php/ojs1/article/view/605 |
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| fulltext |
Прикладне програмне забезпечення
38
UDK 621.09.04 http://doi.org/10.15407/pp2024.01.38
S. V. Strutynskyi, V. A. Yalanetskyi
PROGRAMMING OF ONE-DIMENSIONAL
AND TWO-DIMENSIONAL TOKENS FOR TOKENIZATION
OF LAND PLOTS
The use of blockchain tools that allows spliting virtual objects into parts is considered. Examples of practical use
of the developed algorithms are presented. The concept of one-dimensional and two-dimensional tokens repre-
senting one-dimensional and flat objects is proposed. Algorithms for the implementation of one-dimensional
tokens are developed, and the peculiarities of their practical application are considered. A designed smart con-
tract allows to conduct a basic list of operations with one-dimensional tokens. Algorithms, providing implemen-
tation of two-dimensional tokens, are proposed. Peculiarities of presenting territories of virtual worlds and land
plots are suggested. A comparative analysis of the use of NFT and two-dimensional tokens for presenting the
Earth surface areas is performed. Methods that ensure ownership of tokens at different levels are proposed.
Keywords: Blockchain, EVM, smart contracts, NFT, fractional tokens.
Introduction
Blockchain technologies proved their
effectiveness within creating distributed data-
bases. They found many applications, including
cryptocurrencies; tokenized assets presenting
fiat currencies, shares, property and other finan-
cial instruments; non-fungible tokens repre-
senting digital objects; decentralized domain
name databases [1].
Some of the tools and solutions based on
blockchain technologies have been successfully
implemented. Algorithms and software tools
that have proven their suitability for practical
use and resistance to attacks have been
developed. However, current tools have limited
capabilities preventing the creation of
specialized blockchain-based solutions.
One of the long-term areas of using
blockchain technologies is the implementation
of database of land plots. Decentralized
applications will allow transactions with real
estate, land plots and virtual territories. The
implementation of solutions, providing an
opportunity to perform specialized transactions,
requires the deployment of new blockchain
tools. An infrastructure that is optimized for
working with land plots and virtual territories
are to be created.
The tools that are necessary for real
estate transactions are at the initial stage of
development. There are algorithms and
simplified solutions that, if customized, could
be widely used.
Analysis of recent research
and publications
Cryptocurrencies, tokens and other
virtual assets are characterized by different
tokennomics. Virtual assets could be generated
once within startup or periodically after certain
time intervals. NFTs might have more complex
emission mechanisms. Most cryptocurrencies
and tokens have a variable volume of emission.
If the number of coins in circulation fluctuates
significantly, this leads to some difficulties, e.g.
when determining the current asset
capitalization.
Coins in the Bitcoin network are issued
to pay miners who generate blocks [2]. The
exponential decay of the payment for the
creation of the block led to the fact that the
volume of funds in circulation ceased to change
significantly. The additional emission is
insignificant compared to the number of coins
in circulation.
Some cryptocurrencies are
characterized by constant emission. Payments
to miners or validators are conducted from
funds paid by customers for the performance of
transactions. Such an algorithm reduces
inflationary trends significantly.
There are also cryptocurrencies whose
emission volume is decreasing. The process is
implemented by burning virtual assets. The
source of funds could be commission fees, a part
©S.V. Strutynskyi, V.A. Yalanetskyi, 2024
ISSN 1727-4907. Проблеми програмування. 2024. №1
Прикладне програмне забезпечення
39
of which is withdrawn from circulation. An
example of the implementation of such an
algorithm is the Ethereum blockchain platform
[3]. After the activation of the London hard fork,
which includes EIP-1559 [4], a part of the
commissions is withdrawn from circulation. The
established algorithm is quite flexible, since the
volume of ETH emission could decrease or
increase according to external factors.
The proposal of stablecoins and
tokenized assets is determined by the
management company. Most often, their
emission of tokens depends on the market
demand for them.
Non-fungible tokens are put into
circulation through other algorithms. The
emission of tokens is implemented via smart
contract, which allows you to link NFTs with a
digital object. Most often, the token contains a
file hash. In this case, the file is not stored on
the blockchain, but the hash allows you to
identify the data-set and link it to the NFT. In
some cases, additional algorithms can be used
when performing operations with tokens. In
some cases, the author of the NFT can receive
royalties from the sale of the token [5].
Financial instruments based on
blockchain are characterized by different
volume of emission. Most often, the emission
of an asset is measured in millions, billions or
quadrillion units. A large volume of emission
provides customers with certain conveniences
when conducting small transactions.
Cryptocurrencies and ERC-20 tokens
[6] issued in EVM-compatible networks are
characterized by a large volume of emission, for
example1026. This is caused by current
limitations of Solidity programming language
when working with fractions [7]. Usually the
decimals parameter is used which means the
number of decimal places of the fractional part
of the token. As a rule, this parameter is chosen
equal to 18. In this case, one token contains
1018 parts.
The approach involves the use of
auxiliary units. For example, users can specify
the transfer amount in thousandths or billionths
of the token. Ethereum uses Finney, Gwei and
other units to represent fractional parts.
In the generalized case, the entire
volume of emission can be represented through
one token, and its parts can be used for
calculations among customers. A similar
replacement can be used for comparative
analysis of various blockchain-based financial
instruments.
The concept will also make it possible to
implement some applied algorithms. At the same
time, you can use the same approaches when
conducting operations with cryptocurrencies,
tokens and NFTs issued in a single instance. In
certain cases, the approach can simplify network
interaction and transaction processing.
However, difficulties might arise within the
implementation of the concept due to the need
for additional emission. Operations with land
plots require more complex algorithms for the
emission of tokens and other approaches in
determining the volume of the emission.
Current algorithms do not consider the
specifics of properties. A special approach for
land plots is used. It considers that each of the
objects is presented as a non-fungible token [8].
There is no possibility of simultaneous
ownership of the plot on several levels (by the
owner and sub-owners). However, such
decisions are necessary to ensure ownership of
the plot by a private person while this territory
will belong to the state. New algorithms will
make it possible to implement more complex
forms of real estate ownership. There is no
possibility of spliting land plots into fragments
of arbitrary area and configuration or
combining them in current solutions.
Non-fungible tokens can be linked to
cadastral numbers [9], which include infor-
mation about them. It is placed in an external
database. The cadastral number determines the
boundaries of the land plot and allows you to
get all the information about it. All data on the
territory are placed in the register. However, the
database is constantly changing. Additional en-
tries are made to it during registration of new
plots. The spliting or unification of territories
will be accompanied by a change in cadastral
numbers. Thus, storing data on properties in a
separate database creates certain difficulties
when synchronizing information in the land ca-
daster and blockchain.
One of the features of NFTs is their in-
divisibility. The owner can only sell the token
as a whole, as it cannot be split into parts. The
widespread distribution of NFTs has led to an
increase in demand for them, as well as an in-
Прикладне програмне забезпечення
40
crease in their value. The price of some tokens
reaches millions of US dollars, which signifi-
cantly reduces the liquidity of these assets,
making them similar to precious stones, which
also have a large value and cannot be divided
into parts. However, the implementation of
non-fungible tokens on smart contract plat-
forms provides an opportunity to create more
flexible mechanisms for issuiance and interac-
tion with tokens.
The high prices on NFTs have led to the
emergence of new tools that allow you to split
tokens into parts and conduct transactions with
them. The simplest solution that enables NFT
splitting involves locking the token in a smart
contract. At the same time, the contract issues
ERC-20 tokens. When an NFT is locked, a cer-
tain number of fragments are created, for exam-
ple 100. These assets can be sold for a corre-
sponding part from the NFT's market value.
The number of fragments is small, and it re-
duces the risk of losing one of them.
The technical implementation of frac-
tional NFTs requires the use of additional algo-
rithms. There are several projects that allow you
to increase liquidity and split non-fungible to-
kens into parts, and each of the solutions has
certain features.
The NFTX trading platform allows you
to create repositories that hold multiple NFTs
[10]. An asset lock allows contract to release a
certain number of ERC-20 vTokens that
represent parts of the repository. The algorithm
allows the user to withdraw a random NFT from
the repository by burning a single vToken.
NIFTEX and Fractional.Art platforms
use more complex algorithms to split non-
fungible tokens. After locking the NFT, the
smart contract issues ERC-20 tokens. To trade
these parts, the developers suggest creating
cryptocurrency pairs on decentralized trading
platforms, such as UNISWAP.
To regain ownership on a locked NFT,
you must collect all the fragments and use a smart
contract to return the NFT. This splitting method
can lead to the fact that some fragments can be
lost, burned or frozen (reserved) by their owners.
If you do not know special algorithms, NFT may
remain locked in a smart contract forever.
The Fractional.Art platform involves
setting a certain price value for a non-fungible
token. This value is determined by voting, in
which only fragments' owners participate. An-
yone can buy a locked NFT at an auction if they
bid higher. However, the minimum value of a
non-fungible token cannot be lower than the
value determined during the voting. When re-
deeming, the fragments are burned, and their
owners receive a corresponding share of the
value of the non-fungible token.
The NIFTEX platform also provides the
possibility of redemption of fragments. The
algorithm allows any fragment owner to
redeem NFT. The initiator of the transaction
sets the redemption price, which requires him to
block the relevant funds. If any of the other
owners believe that the buyout price is low,
they have the option to buy out the ownership
share of the iniciator of the transaction at the
specified value. At the same time, the NFT
remains locked. Otherwise, the initiator
receives a non-fungible token, and other co-
owners get blocked funds.
Current ways of splitting NFT into
fractions provide necessary functionality, but
have certain limitations. Many algorithms
provide only splitting into fixed parts. The
technical implementation imposes certain
obligations and restrictions on each of the
fragment owners. In order to unlock an non-
fungible token, additional social and market
mechanisms are needed.
Current solutions do not consider the
type of non-fungible token when splitting it into
parts. If the NFT is a part of the virtual world or
a flat image, the token fractions will not be
associated with a specific area of that object.
Prospective solutions should provide the ability
to split a non-fungible token into arbitrary-sized
pieces that are associated with specific parts of
a digital object represented by an NFT. There is
also a requirement to ensure asset ownership at
multiple levels. Progressive algorithms should
provide more complex forms of ownership on a
virtual object, which will expand the scope of
their practical application significantly.
The purpose and tasks
of research
The purpose of this article is the
research of specialized tools of EVM-
compatible networks that implement the
splitting of tokens into parts, tokenization of
Прикладне програмне забезпечення
41
properties and establishing the features of the
practical application of the proposed algorithms
for solving applied problems.
The research objectives include
substantiation of the need for one-dimensional
and two-dimensional tokens to represent linear
and flat objects and conduct operations with
them.
The tasks include the research of
algorithms that allow entering data on the
parameters of land plots directly the blockchain
and the specifics of their application. The work
includes the development and analysis of
algorithms that ensure the splitting of objects,
in particular, virtual territories into parts of an
arbitrary configuration and the unification of
these parts.
Tasks include the analysis of algorithms
that allow ownership of territory at different
levels and control over transactions by the
issuer establishing the features of the practical
application of the proposed solutions.
1. The concept of one-dimensional
tokens
Let's consider the geometric
interpretation of a one-dimensional token, the
emission volume of which is one unit. It can be
represented as a segment of unit length in one-
dimensional space.
One of the ends of the segment is selected
as a reference point. According to this
interpretation, the shares belonging to the owners
will be represented by parts of the segment, which
are determined by the coordinates of the
beginning and end. For example, Alice owns
0.45; Bob - 0.15; Carol - 0.25; Dave - 0.05; and
Ed – 0.1 token (Fig. 1). Unlike ERC-20 tokens,
customers own plots defined by two coordinates
(for example, Bob will own plot [0.45; 0.6]). At
the same time, plots equal in size will not be
identical and fungible.
Fig. 1. A geometric interpretation of the one-
dimensional token with a segment
Fig. 2. Geometric interpretation of the one-
dimensional token with a circle
A circle of unit length might be used for
the geometric interpretation of the token instead
of a line segment. It is divided into sectors of
different sizes with corresponding angles (Fig.
2). It is necessary to choose a reference point on
the circle, in relation to which the boundaries of
the plots belonging to customers are
determined. According to this interpretation,
the units of measurement can correspond to
radians or degrees.
The initial emission involves the
transfer of token fragments to one or more
customers. Fragmentation of the segment and
token will be observed after performing a
number of operations. After the redistribution
of ownership shares, some customers may
own several parts (Fig. 3). For example, Alice
owns the parts [0; 0.3] and [0.65; 0.8], Bob –
[0.3; 0.4] and [0.8; 1.0], and Carol – [0.4;
0.65].
Fig. 3. Fragmentation of the one-dimensional
token
The implementation of a one-
dimensional token does not depend on a
geometric interpretation (segment, circle or
another curve). It is necessary to set its initial
coordinate and its increment for each plot,
which determine the share of ownership of the
customer. In the case the customer has several
plots, it is necessary to specify the parameters
of each of them.
Прикладне програмне забезпечення
42
If only the share of ownership are to be
determined, a one-dimentional token will
function similarly to ERC-20 token. Each
customer will own a certain part of the total
emission volume. In this case, the order of
location of plots, as well as their number, is not
important. To find the property of the subject, it
is more appropriate to use the initial coordinate
of the plot and the increment of the coordinate.
An alternative option is to specify the
coordinates of the beginning and end of the
segment directly.
Since a customer can own a large
number of plots, several sources of assets can
be used to perform transactions. A similar
algorithm has been successfully implemented
in Bitcoin [2] and other cryptocurrencies. The
technical implementation of Bitcoin requires
the use of one or more unspent transaction
outputs (UTXO) to perform the transfer. At the
same time, data on the sources of assets is
included in the transaction. One-dimensional
tokens can be implemented in EVM-compatible
networks, and customers can send several plots
in a single transaction (Fig. 4).
Fig. 4. Transfer of several fragments within
one transaction
When transferring, the customer sends
previously received plots (Input Plot 1, Input
Plot 2, ...), accordingly, it is necessary to check
the ownership rights to them. The transaction
requires the address of the receiver and the
parameters of the source and transferred plots
(Output Plot 1, Output Plot 2, ...).
According to the technical
implementation, sending a part of a one-
dimensional token will be similar to the transfer
of a ERC-20 virtual asset, but it will require two
parameters that determine the beginning and
end of the fragment.
2. Peculiarities of technical
implementation and practical
application of one-dimensional tokens
A one-dimensional token (1DT) does
not conform to ERC-20 , so its implementation
on an EVM-compatible network requires
specialized algorithms and functions. It is
recommended to choose a token emission equal
to 1018. If you use the value of the decimals
parameter equal to 18, then the volume of emis-
sion will correspond to one token. In this case,
the minimum plot size is limited. If we consider
fragments of unit length, they can be placed
sequentially from zero to the maximum value.
In fact, each plot will be unique.
To implement the token in an EVM-
compatible network, it is necessary to develop
a smart contract and declare two arrays
Beginning_of_the_Fragment and
Fragment_Length, which are created with the
mapping tool. The first array determines the
coordinates of the starting point of the plot, and
the second is used to specify its size (Fig. 5a).
a)
b)
Fig. 5. Implementation of a one-dimensional
token in an EVM-compatible network
Arrays are created for each address
with a non-zero balance. If the customer owns
only one plot, the arrays contain one record
each. In other cases, data structures include
information about a large number of
fragments. Elements of arrays can contain
zeros that appear after complete transferring a
plot to another customer.
Implementation of a one-dimensional
token in an EVM-compatible network requires
the use of specialized functions. The
GetSummaryBalance() function (Fig. 6) allows
you to find the total length of all fragments
belonging to the customer. The algorithm adds
the lengths of the fragments and finds the share
Прикладне програмне забезпечення
43
of ownership corresponding to a certain
address.
Fig. 6. Implementation of the function Get-
SummaryBalance()
The GetPlotsParameters() function
(Fig. 7) displays two arrays of data that show
the parameters of the fragments belonging to
the customer. The first array represents the
coordinate of the beginning of the plot, and the
second denotes its length. The function does not
display null array elements. The result of
GetPlotsParameters() can have the following
form (Fig. 5b).
Fig. 7. Implementation of the function Get-
PlotsParameters()
To transfer a plot to another customer,
you can use the function Transfer (Sender,
Recipient, Beginning of the Fragment,
Fragment Length) (Fig. 9). The procedure
involves the creation of additional elements in
the arrays of the recipient represented by the
Recipient address. The resulting ownership
share of the sender varies depending on which
part of the fragment is being sent. At the same
time, three transfer options are possible:
▪ The plot is transferred in full. Elements
of the Beginning of the Fragment and
Fragment Length arrays corresponding
to the specified area are reset to zero.
▪ The sender transfer a part of the plot that
is at the beginning or end of the source
fragment. In this case, the algorithm
change the values of array elements that
determine the beginning of the fragment
or its length.
▪ The sender transfer a fragment that
divides the source plot into three parts.
The first and third parts remain with the
owner, and the second (middle) is
transferred to the recipient. In this case,
the parameters of the source fragment
are changed on the sender's side. An
additional element of the Beginning of
the Fragment and Fragment Length
arrays is also created. It includes the
parameters of the third part.
The increase in the number of customers
and transactions will lead to significant
fragmentation of the one-dimensional token. In
some cases, one customer will own several
adjacent plots. If the fragments are placed in
such a way that the end of one of them coincides
with the beginning of the next, then it will be
more appropriate to combine them. To perform
this operation, the Defragmentation() function
is used (Fig. 8). It allows you to find adjacent
areas and combine them into one. Since the
operation requires gas consumption and also
changes the parameters of the arrays that
determine the ownership of the customer, it can
be carried out only by the owner.
Fig. 8. Implementation of the function
Defragmentation()
Прикладне програмне забезпечення
44
Fig. 9. Implementation of the function Transfer()
Fig. 10. One-Dimensional Token (1DT) smart contract
The One-Dimensional Token (1DT)
smart contract corresponding to the proposed
algorithms is deployed on the Fantom network
[11] at the address:
0xdfe84Ed9BD78db87C13C7137Ea1a365885
734420 (Fig. 10).
The functions of reading the smart
contract allow you to get general information
about the token, determine the share of
ownership and set the parameters of the plots
owned by the customer. Record functions
enable owners to transact and unify adjacent
plots. There are also tools that provide the
possibility of transferring plots using a third-
party smart contract.
The plot transfer is implemented
through the transfer() function and involves
entering three parameters: the address of the
recipient, the initial coordinate of the plot and
its size. When transferring a plot, it is
recommended to set the gas limit to more than
274000 units. Since the 1DT does not comply
with the ERC-20 standard, it is possible to
find out the current balance of the customer
only using the corresponding reading
function.
Прикладне програмне забезпечення
45
One-dimensional tokens have a number
of differences compared to ERC-20 virtual
assets and NFTs. These include the possibility
of splitting and unifying parts of the token. At
the same time, each of the fragments is unique
and is defined by two parameters. The one-
dimensional token allows us to demonstrate the
functionality of the solution and its capabilities.
3. Algorithms for the implementation
of two-dimensional tokens and their
application for solving applied
problems
A two-dimensional token is a virtual asset
defined in a two-dimensional coordinate system.
Graphical interpretation of an object – a section
of a spatial surface. In some cases, it is a part of a
plane, sphere or cylinder.
A token can represent an entire closed
surface, allowing it to be used for a sphere. In
other cases, the virtual asset corresponds to only
a part of the surface. For example, a token can
represent an area on a plane, bounded by a
polygon. When speaking about practical
application of the token, it is most appropriate
to use a rectangle. This plot is splited into
customer-owned fragments.
Two-dimensional tokens can be used to
represent areas of a flat or spherical surface,
assuming the use of identical algorithms. An
arbitrary fragment belonging to the customer can
be represented by a closed loop. The most optimal
is the use of a polygon, the parameters of which
are set by the coordinates of the vertices and the
order of their sequence.
Let’s consider the implementation of a
two-dimensional token on a spherical surface. It
is advisable to determine plot parameters in the
spherical coordinate system. In this case, the
position of a point in space is determined by two
angles and a radius. When the radius is constant,
it is enough to specify two angular coordinates.
To determine the location of the object on
the surface of the Earth, we use a geographic
coordinate system, and the parameters of the
point are determined by latitude and longitude.
For example, object coordinates can be specified
in the following form: 50.449214; 30.357773.
The number of characters after the separator
determines the accuracy of object positioning.
A territory of arbitrary shape on a
spherical surface can be represented in the form
of a polygon [12]. The order of passing the
vertices of the polygon determines its
configuration (Fig. 11).
Fig. 11. Representation of a land plot in the
form of a polygon
In certain cases, it is appropriate to
represent a polygon using the coordinate of one
vertex and increments that determine the
position of others. The algorithm allows to
reduce the amount of data recorded in the
blockchain. The parameters of a plot of
arbitrary shape (Area) can be set by an array
(Fig. 12). One of the vertices is selected as the
initial coordinate (Initial coordinate). The
coordinates of other points are set in the form
of increments in relation to the initial
coordinate (coordinate increment 1, coordinate
increment 2, ... coordinate increment n). The
Fig. 12. Representation of plot parameters
using an array
Прикладне програмне забезпечення
46
order of the vertices when passing a closed
circuit corresponds to clockwise movement.
The algorithm allows you to perform
operations with fragments of an arbitrary
configuration, to split and unify them. A special
configuration area may contain a void if its
interior belongs to another customer. In this
case, the territory can be represented by two
polygons that do not contain cavities, but have
common edges and vertices.
Two-dimensional tokens can represent
areas of any flat or spherical surfaces. They can
be used in virtual worlds containing territories
owned by customers. The developed algorithms
can be used to represent areas of the Earth or
another celestial body.
Two-dimensional tokens can be used to
distribute NFTs or other virtual assets among
multiple owners. At the same time, each cus-
tomer can own a flat fragment of any
configuration.
If it is necessary to have sub-owners of
the first and second levels, then the process of
emission and transfer of the land plot will be
different. The first level sub-owner must issue
a token. In order to carry out operations with a
land plot, a second-level sub-owner must initi-
ate a transaction. However, to implement it con-
firmations from sub-owners of the first and sec-
ond levels are required. When using such an al-
gorithm, all transactions with virtual assets will
be controlled by all their owners.
When transferring, information about
the parties will not be disclosed, since only their
addresses are placed in the distributed database.
Blockchain technologies will provide
protection against unauthorized access,
eliminate the possibility of canceling a
confirmed transaction, and also prevent double
spending operations [14].
When creating and conducting
operations with large territories that include a
significant number of vertices of the bounding
polygon, a significant amount of information
must be entered into the blockchain. We can
reduce the amount of data by using a base
coordinate and coordinate increments for the
remaining vertices. It is advisable to use
abbreviated coordinates within operations with
small areas.
The use of two-dimensional tokens for
the tokenization of land plots will require
interaction with databases containing cadastral
numbers and other information about proper-
ties. It is more appropriate to place the specified
information in decentralized databases, e.g. by
using IPFS.
Conclusions
One-dimensional tokens are a powerful
tool for testing, creating arbitrary-sized plots and
conducting transactions. The developed smart
contract allows customers to own fragments of
any one-dimensional object and perform
operations with them.
2D tokens can be used to fragment
maps, flat images, and other 2D objects. They
have a number of advantages over NFTs when
used to represent land plots and virtual territo-
ries. Two-dimensional tokens allow you to cre-
ate fragments of arbitrary configuration, split
and unify them.
The developed algorithms can be used to
represent the territories of virtual worlds. Current
projects use fixed-sized plots, while two-
dimensional tokens provide greater flexibility by
allowing fragments of arbitrary configuration to
be operated on.
The technology can be applied to
spherical surfaces, including the Earth surface,
but it requires setting a reference point. The use
of two-dimensional tokens will require
interaction with external databases containing
data on cadastral numbers. At the same time, the
algorithm must be compatible with blockchain-
oracles that provide access to external state
databases that personalize the owners of
tokenized land plots.
Two-dimensional tokens can provide
ownership of a surface area at different levels. A
certain fragment can have one owner who is the
issuer and controls the operations with the virtual
asset and a sub-owner who conducts transactions
with the plot or its parts directly. Such an
algorithm provides an opportunity to implement a
model of ownership that is characteristic of the
land market of an individual country.
References
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Received: 01.12.2023
Про авторів:
Струтинський Сергій Васильович,
доктор технічних наук, професор кафедри
прикладної гідроаеромеханіки
і механотроніки Національного технічного
університету України
«КПІ імені Ігоря Сікорського».
Кількість наукових публікацій
в українських виданнях – понад 200.
Кількість наукових публікацій
в зарубіжних виданнях – понад 10.
Індекс Хірша – 5. https://orcid.org/0000-
0001-9739-0399
Яланецький Валерій Анатолійович,
старший викладач кафедри інформаційних
систем та технологій Національного
технічного університету України
«КПІ імені Ігоря Сікорського».
Кількість наукових публікацій
в українських виданнях – понад 30.
https://orcid.org/0000-0001-6163-0258
Місце роботи авторів:
Національний технічний університет
України «Київський політехнічний інститут
імені Ігоря Сікорського»,
проспект Берестейський 37,
Тел.: (044) 204-82-54,
E-mail: strutynskyi@gmail.com,
v.yalanetskyi@gmail.com
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