WO2015052366A1 - Method, system, computing system and computer program product for restricting the calculations to be performed in a raster model of a territory used in a geographic information system (gis) - Google Patents

Abstract

The invention relates to a method for restricting calculations to be performed in a raster model of a territory used in a geographic information system, dividing the raster model of the territory into a plurality of cells. The method comprises receiving data relating to different zones of movement which form the structure of the territory; receiving data relating to restrictions of movement between the different zones of movement; receiving data relating to at least one value assigned to each cell of at least one zone of movement of the different zones of movement; performing the calculations on the zones of movement that form the structure of the territory, bearing in mind the restrictions on movement between the different zones of movement and the at least one value assigned to each cell of at least one zone of movement of the different zones of movement.

Description

 Procedure, system, computer system and software product to restrict the calculations to be performed in a raster model of a territory used in a Geographic Information System (GIS) The present invention relates to a procedure to restrict the calculations to be performed in a model raster of a territory used in a Geographic Information System (GIS), dividing the raster model the territory into a plurality of cells.

The invention also relates to a system, a computer system and a computer program product for restricting the calculations to be performed in a raster model of a territory used in a Geographic Information System, suitable for carrying out this procedure.

The invention is applicable in different phenomena of dispersion, accessibility, mobility or displacement that may occur on the earth's surface. Thus, for example, the invention can make it possible to know the time necessary to reach a certain place (city, equipment, etc.) from the rest of places in a territory, or it may allow to know the propagation of, for example, a focus of pollution, a crop pest or a fire.

STATE OF THE PREVIOUS TECHNIQUE

It is known to use the raster format to represent a territory understood as a continuous space, in order to evaluate distances between any point of the territory. This distance evaluation is usually carried out using a spatial function to determine the accumulated cost in the displacement from one or several points (taken as origin) to the rest of the territory. The implementation of this spatial function is also known through the cost-distance procedure (or algorithm), in some of the most used GIS programs (ArcGIS, Sextante-gvSIG, Grass, etc.). For this reason, the cost-distance procedure is one of the most present in publications on accessibility works, such as eg [FARROW, A .; NELSON, A. Accessibility modeling in ArcView 3. International Center for Tropical Agriculture. 2001], [JULIAO, RP Measuring accessibility using GIS. 1998] or [PABLO, Federico; MUÑOZ, Carlos and MYRO, Rafael. An analysis of the effect of investment in infrastructures on the accessibility of the territory to the high capacity road network. XXIX Regional Studies Meeting. 2002].

The cost-distance procedure (or algorithm) is based on determining for each cell (raster) the value of the cost of moving from that point to another taken as a destination, considering that the displacements are influenced by the characteristics of the terrain through which it circulates . Although this procedure can be used in a way that allows calculating an anisotropic cost of the displacements according to the geographic direction that follows, it is normally used in order to calculate an isotropic cost.

In this procedure, the concept of distance is used in a similar way to that used in Euclidean functions, but other factors are allowed to assess other mobility costs. The territory on which the displacements are measured is characterized according to the resistance that each place offers to the movement according to its geographical or territorial characteristics, measured in different units (length, time, energy, money, etc.) according to the type of analysis that you want to perform. During the calculation process, the value of the cost accumulated in the displacements and the direction followed when crossing that cell to reach the previously indicated destination is obtained for each cell.

If desired, this cost-distance procedure also allows determining the path of shorter length between different origins and destinations, as well as assigning each point of the territory to the nearest destination, understanding proximity as the lowest cost necessary to reach it (proximity zoning ).

The execution of this procedure requires having a raster file that fixes the origin or destination places on which it is desired to have information on travel costs through the territory, from or to them. This file can be called a "source" file. You must also have a raster file that includes the cost of crossing each of the cells that make up the grid or matrix that represents the territory to be analyzed. This file can be called "cost area". Thus, the result of the execution of the cost-distance procedure is a new raster file in which each cell is assigned the lowest cumulative cost that is needed to arrive from it to the nearest destination cell among those specified as source , depending on the difficulties and resistance to the movements defined by the "cost area" file.

The process followed by this procedure can be based, for example, on considering the center of each cell as a node linked to the next eight by straight lines. Each link between two nodes carries an impedance that is based on the cost per unit of displacement associated with both cells and the distance that separates them. This distance can be obtained directly from the size of the cells or, what is the same, from the resolution of the raster file that contains them. The process is repeated iteratively, calculating the lowest accumulated cost for all existing cells.

Although the cost-distance procedure allows calculation between all the cells defined in a territory, it also has some drawbacks. In some cases, this procedure allows displacements between cells that are not really possible, which can lead to erroneous travel costs. For example, it can allow access to cells identified as Highway from bordering cells, regardless of whether or not there is a highway incorporation. In this case, if there is no such incorporation to the highway, a false cost could be generated, since this cost would refer to a displacement impossible to carry out in reality.

Procedures that are based on the use of data in vector format to perform transport network analysis are also known. However, the cost (temporary and economical) of obtaining vector data with sufficiently precise topology can be significantly high (much higher than eg the cost of obtaining data in raster format). In addition, the aforementioned vector format only allows accessibility values to be calculated in connection nodes and not at any point in the territory (which does allow eg raster format). EXPLANATION OF THE INVENTION

Therefore, there is a need for new procedures, software products and control units to restrict the calculations to be performed in a raster model of a territory used in a Geographic Information System (GIS), which solve at least some of the problems mentioned above. It is an objective of the present invention to satisfy said need.

This objective is achieved by providing a procedure to restrict some calculations to be performed in a raster model of a territory used in a Geographic Information System, dividing the raster model the territory into a plurality of cells, the procedure comprising:

 Receive data referring to different zones of displacement in which the territory is structured;

 - Receive data regarding travel restrictions between the different zones of movement in which the territory is structured;

 Receive data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured;

 - Carry out the calculations on the displacement zones in which the territory is structured, taking into account the displacement restrictions between the different displacement zones and the at least one value assigned to each cell of at least one displacement zone of the different displacement zones in which the territory is structured.

The establishment of different zones of displacement within the territory and the establishment of restrictions between these different zones of displacement can open new horizons of possibilities in geospatial analyzes. In this way, it could be considered not only to restrict or allow the execution of an algorithm but also to consider the execution of an operation or a different one depending on the areas of origin and destination, that is, depending on the cells belonging to areas that have previous characteristics that make recommended different treatments in the operations but that can be integrated during the same calculation process. In addition, this process according to the invention may allow different operations between two zones, depending on the origin zone and which the destination zone, being able to perform different operations between them depending on where or where the direction of travel occurs. The approach of setting restrictions on communication between cells can be achieved from a matrix of displacement conditions. In this matrix, the different types of displacement zones admitted in the analysis are sorted in rows and columns, so that it is possible to establish whether the displacement between each pair of zones is allowed or prohibited.

According to one embodiment, the method may comprise receiving data concerning at least one source from which the displacements originate.

According to another embodiment, receiving data referring to different zones of displacement in which the territory is structured may comprise:

 Receive a raster file that includes the different zones of displacement in which the territory is structured.

In accordance with another embodiment of the invention, receiving data regarding travel restrictions between the different travel zones in which the territory is structured may comprise:

 Receive a file that includes the travel restrictions between the different zones of movement in which the territory is structured. This file does not necessarily have to be raster type. It can also be of some other format, such as a text file.

In addition, receiving data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured can comprise:

Receive at least one raster file comprising data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured. According to another aspect, the invention provides a system for restricting the calculations to be performed in a raster model of a territory used in a Geographic Information System, the raster model dividing the territory into a plurality of cells, the system comprising:

 - Computer / electronic means to receive data referring to different areas of displacement in which the territory is structured;

 - Computer / electronic means to receive data regarding travel restrictions between the different zones of movement in which the territory is structured;

 - Computer / electronic means to receive data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured;

 - Computer / electronic means to execute calculations on the zones of displacement in which the territory is structured, taking into account the displacement restrictions between the different zones of displacement and the at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured. This system may also comprise computer / electronic means for receiving data concerning at least one source from which the displacements originate.

In accordance with yet another aspect of the invention, a computer system is provided comprising a memory and a processor, in which the memory stores computer program instructions executable by the processor, these instructions comprising functionalities for executing a procedure to restrict the calculations to be carried out in a raster model of a territory used in a Geographic Information System, as described above.

According to another aspect, the invention provides a computer program product comprising program instructions to cause a system to execute a procedure to restrict the calculations to be performed in a raster model of a territory used in a Geographic Information System, as described previously. Said computer program may be stored in physical storage media, such as recording media, a computer memory, or a read-only memory, or it may be carried by a carrier wave, such as electrical or optical.

On the other hand, the invention also provides a method for determining the accessibility of a territory, from a raster model of the territory used in a Geographic Information System, which divides the territory into a plurality of cells, this procedure comprising:

 - the procedure to restrict the calculations to be performed in a raster model of a territory used in a Geographic Information System as described above, in which:

 Receive data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured comprises:

 o Receive data regarding travel costs between the cells of any of the travel zones in which the territory is structured;

 - Perform calculations on the zones of displacement in which the territory is structured, taking into account the displacement restrictions between the different zones of displacement and the at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured includes:

 o Obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in which the territory is structured and the cost of cell displacement cost.

In this way, an improvement of the Cost-Distance model known in the state of the art is achieved by modifying its operability according to the specific restrictions or conditions of any of the input data. Basically, the objective of this procedure according to the invention is to be able to consider jointly in the displacements of a territory the contribution of different shared modes of transport or overlapping infrastructures in the same place. Thus, this procedure adds a system of conditions that allows the modeling and calculation of displacements on the raster model used in a Geographic Information System (GIS) to be adjusted to reality, offering greater flexibility and new possibilities when analyzing territorial accessibility with these systems.

Basically, the procedure described takes into consideration the different characteristics of mobility in the infrastructures or in the geographical spaces through which it could be traveled, being able to specify limitations in the passage from one to another if necessary. Depending on what is intended to be analyzed with the procedure according to the invention (hereinafter referred to as a cost-distance conditioned procedure), the displacement of a certain object, individual, natural or artificial object or phenomenon, having a behavior in its movements over the territory that can be modeled using a raster GIS.

The basis of this procedure can be based on two requirements. In the first place, it is allowed to impose a series of restrictions in the displacements between the different types of zones previously identified in the territory to be analyzed, fixing the permits and the prohibitions of communication between them, which are specified in a matrix of Displacement conditions. In addition, in this procedure it is allowed that a place has different travel costs to cross it according to the type of infrastructure or mode of transport used, so in this conditioned cost-distance procedure several cost surfaces can be used, which are specified in a surface of simple costs, similar to the only surface of costs used in the original model cost-distance, and the surfaces of conditioned costs that are necessary in function of the different ways of shared or superimposed displacement that are taken into account.

The establishment of conditions between the zones can not only indicate the possibility of communication between two places, but also imply an additional cost to that transit. In this way the displacement is penalized or favored between specific zones, which can be collected by means of a numerical factor that is applied to the cost of crossing these cells, or simply a value that adds to the cost calculated in that displacement. A possible example would be the fact of moving from a road trip to one on the ground, since it is necessary to park the car before going for a walk, so that time is penalized by increasing the cost calculated for crossing the road cell and the neighboring land cell.

With respect to the matrix of displacement conditions, if proper use is made of it it is possible to impose that the cells representing a highway, for example, cannot communicate with the neighboring cells unless they belong to the identified area as a node of the conditioned displacement space that defines the high capacity pathways. This matrix allows you to identify whether to calculate simple cumulative costs during travel, it is possible to move from one cell to another. In the event that the relationship between the value of the source cell zone and the destination cell zone is "TRUE", the calculation can be performed, since this communication is allowed. If, on the other hand, the relationship between the zones of the origin and destination cells has a value of "FALSE", the cost calculation cannot be carried out since the displacement between them will not be allowed. It is important to note that the restrictions imposed in this matrix of conditions only affect the operations that are carried out on the surface of simple costs, and that are stored in the CAS.

Therefore, it is clear that this conditioned cost-distance procedure requires more information than in the cost-distance model, and also obtains more result files. While the cost-distance model uses only one data to locate the sources of displacement and a cost area to assess that mobility through the territory, this conditioned cost-distance procedure uses a file that collects all the zones of displacement, in addition of the source places that originate the displacements; several files with the cost surfaces according to the types of conditioned mobility to be studied, which include a simple cost surface similar to that used in the cost-distance model, in which all the cells have value; and at least one surface of conditioned costs, where only cells that present two types of mobility will have value. On the other hand, such as already described, this conditioned procedure needs to establish a matrix of displacement conditions that sets the communication compatibility for the calculation of the simple accumulated cost of the displacements between the zones defined in that territory.

Obviously, the final result of the procedures (the cost-distance versus the conditioned cost-distance) also differs, since the cost-distance model comes to a unique result of the cost accumulated from each source to any point of the studied territory, while the conditioned cost-distance procedure obtains the simple accumulated cost, similar to the previous one, and in addition the conditional accumulated costs for each surface of conditioned costs used in the calculation, and finally, the final result of the calculation process that can be called accumulated cost global, because it will take into account the simple accumulated cost and all the conditional accumulated costs.

In summary, the cost-distance procedure conditioned according to the invention raises a new accessibility calculation procedure on a raster GIS to obtain the cumulative cost of travel on a territory characterized by different areas with movement restrictions between them, and considering conditioned displacements in certain spaces that allow several types of mobility at the same time, and that require connection nodes to ensure communications with the rest of the territory.

In addition, the execution of this displacement analysis procedure involves the calculation of a simple accumulated cost, the conditional cumulative costs that are required and a global cumulative cost for each of the cells considered in the analysis.

According to an embodiment of the invention, the source may comprise at least one cell of the raster model of the territory.

According to another embodiment, the displacement zones can be selected from a single displacement zone; conditioned displacement zone; zone of displacement of the links or node. In the cost-distance procedure, the territory is classified into different zones of displacement that determine the ease of movement of an element or phenomenon to travel through each geographical place, as well as the way in which these areas can be related to each other. The ease of mobility will be understood as the cost of crossing the territory of each zone, as in the cost-distance model. This cost is generally represented as the time taken to cross these areas, although other types of costs such as energy, economic, or any other that consider the difficulty of going through these places could also be considered. However, the zones of displacement and the restrictions in the movements are own and exclusive of the procedure cost-distance conditioned according to the invention.

It is possible to define a zone of displacement as those geographical places that have similar characteristics of their own, that determine mobility over them. Each zone can have particular displacement conditions that establish the costs involved in crossing those areas.

When a zone of displacement represents geographical zones with similar characteristics in which an unrestricted displacement is allowed to interact with other zones, this space will be considered a zone of simple displacement, since it only requires a zone of displacement. The cells that represent it will have, in general, the time resulting from applying the maximum possible travel speed in them, depending on the means of transport used. An example could be to consider the conventional road network as a zone of displacement, which has a different speed of movement depending on the structural conditions of each road. In this area, communication restrictions with other border areas are not considered, as a user can, in principle, stop the vehicle at any point to move to another territorial area where there is no road, so it is possible to consider it as a space of simple displacement.

If the zone of displacement presents intrinsic restrictions in the movements that communicate it with the neighboring zones, it will be necessary to have another zone that allows its communication with the rest of the territory, constituting both zones of displacement a composite space that can be referred to as conditioned displacement space. A conditioned displacement space allows various types of displacement to coexist in those places, including transport modes with restricted displacement or with particular characteristics in its route. These conditioned displacement spaces necessarily have to be composed of at least two displacement zones: one that represents the conditioned displacement zone that determines the scope occupied by the type of transport infrastructure with access limitations or with specific displacement modes; and another zone, defined as a node, to enable the connection with the rest of the displacement zones that define a territory. This node will be the geographical area where it is possible to transform a conditional cumulative cost into a simple accumulated cost, and vice versa. These conditioned displacement spaces contemplate the possibility of sharing modes of transport in their conditioned areas, as well as the superposition of several zones in the same place. To represent these circumstances, a surface of conditioned costs associated with each conditioned displacement space is required, where only those cells that represent the conditioned displacement zone or that allow various types of displacement will have value. In this case, the conditioned cost assigned to these cells will have the value corresponding to the time spent traveling at the maximum possible speed to cross them considering the mode or means of transport associated with that conditioned travel space. In general, this conditioned cost is different from the displacement cost considered normal for that area, and which in turn is included in the Surface of Simple Costs.

An example of conditioned displacement space can be a highway, since the user can only leave it to other places in the territory at the links or at specific points along its route. In this case, the conditioned displacement space is formed by the high capacity path, understood as a conditioned displacement zone, and by the displacement zone of the links, which acts as a node of that composite space. To characterize the highway, a specific speed for longitudinal displacement is applied, but in viaducts or passageways, another transverse displacement is allowed on that infrastructure, in principle with a very different speed, which refers to the conventional road with which the high capacity road is crossed at different levels. Thus, on the same geographical location in the plant it is possible to have two different displacement zones, and therefore, two different costs to cross them. In order to continue maintaining the mobility of conventional roads that cross the highway by means of overpasses or subways, different travel costs must be considered in these places, as it circulates on the highway (conditioned cost) or by the conventional road that crosses it ( simple cost).

The conditioned cost-distance procedure allows these steps to be taken into account, assigning conditioned costs conveniently to the cells involved within the surface of conditioned costs associated with the conditioned displacement space of the highways. In these points two types of accumulated costs are obtained: one the simple accumulated cost corresponding to the transit through the same by the conventional road, and another the accumulated cost conditioned due to the displacement by the highway. This cumulative conditioned cost that is calculated in the steps at different levels and in the rest of the highway layout, is only transferred as a simple accumulated cost to the rest of the territory in the areas characterized as a node of that conditioned displacement space. In this way, this conditioned cumulative cost is prevented from influencing the calculations outside this high capacity or high performance infrastructure, except for the links, thus responding to the actual behavior of the displacements in this type of road.

The location of the zones of displacement on the territory can be assigned by means of a specific raster file, in which all the zones that will be used in the procedure are differentiated. The parameters that define each zone of displacement can be:

• CLASS: Sets the integer numerical value that the cells of each type of displacement zone will have in the specified raster file, which allows them to be differentiated and operated with them individually (integer numerical value of the displacement zone file); • NAME: this is an optional, recommended field, indicating a descriptive designation of the zone of displacement or the type of infrastructure that allows communications through a territory (for example, with a text-type field format);

 · CONDITIONED DISPLACEMENT SPACE (EDC): Identifies the conditioned displacement space to which an area belongs, if necessary, that will be represented by the only surface of conditioned costs associated with that conditioned displacement space;

 · EDC NODE: Indicates whether this zone of displacement allows a communication between that space and the rest of the territory, avoiding the restrictions associated with that EDC. (Possible values: TRUE / FALSE). At least one of the displacement zones within an EDC must have a value of "TRUE". These zones that function as a node within an EDC allow to calculate conditional accumulated costs (calculated using the proposed algorithm) from simple accumulated costs (obtained with the normal distance cost calculation procedure), and vice versa.

Therefore, the zones of simple displacement can define a space of simple displacement, which has associated a surface of simple costs that represents the value of the cost that is invested in crossing each cell belonging to the space of simple displacement.

In this way, receiving data regarding travel costs between the cells of any of the travel zones in which the territory is structured can include:

Receive the surface of simple costs associated with the space of simple displacement. On the other hand, to obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in which Structure the territory and the cost of cell travel cost may include: - Obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in which the territory is structured and the cost value that is invested in traversing the cell defined in the surface of simple costs.

According to one embodiment, each conditioned displacement zone in combination with a suitable node defines a conditioned displacement space, which has an associated cost surface that represents the value of the cost that is invested in traversing each cell belonging to the space of conditioned displacement.

Thus, receiving data referring to travel costs between the cells of any of the travel zones in which the territory is structured may include:

 Receive the surface of conditioned costs associated with each space of conditioned costs.

Therefore, to obtain, for each cell included in the raster model of the territory, the lowest accumulated cost of travel value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones where Structure the territory and the cost of cell travel cost may include:

 - Obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in which the territory is structured and the cost value that is invested in traversing the defined cell on the surface of simple costs and the cost value that is invested in traversing the defined cell in each surface of conditioned costs.

This stage of obtaining, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the restrictions of displacement between the different zones of displacement in which the territory is structured and the cost value that is invested in crossing the defined cell in the surface of simple costs and the cost value that is invested in crossing the defined cell in each surface of Conditional costs may include:

o Check if there is a source cell or a cell with minimum cumulative cost (CA _min ) unprocessed;

 In case of positive verification result,

 o For each cell and each surface of conditioned costs (SCC¡) to which this cell belongs, check if it is a destination cell (D) of a source cell (O) that does not have a conditional cumulative cost (CAC);

o If positive result verification process the cell considering the source cell (O) has a minimum accumulated cost conditioned (CAC _m¡n);

o In the case of a negative verification result, process the cell taking into account that the source cell (O) has a minimum conditional cumulative cost (CAC _min ).

This defined sub-procedure, therefore, must be performed iteratively until all the cells considered in the analysis are completed, so that they present the lowest possible accumulated cost values for the allowable displacements in the procedure.

According to one embodiment, processing the cell taking into account that the source cell (O) does not have a minimum conditional cumulative cost (CAC _min ) may comprise:

 o For each cell and each surface of conditioned costs (SCC¡) to which this cell belongs, verify if it has value in a surface of conditioned costs (SCC) and belongs to a zone of displacement (ZD) that is a node of the space of conditioned displacement (EDC) associated with this surface of conditioned costs (SCC);

o In case of positive result in this verification, calculate the cumulative conditioned cost (CAC) of this cell; o Check if the source cell (O) belongs to a zone of displacement (ZD ₀ ) that has no restrictions with the zone of displacement (ZD _D ) to which the cell belongs;

 o In case of a positive result in this verification, calculate the simple accumulated cost (CAS) of this cell.

Thus, calculating the cumulative conditioned cost (CAC _D ) of this cell can be performed according to:

LA L ^' _Q - L bn + ü * (Lb® + ^■ LL _Q ) in which:

CAC _D is the conditional cumulative cost of the conditioned displacement space (EDC) for the target cell (D);

CAS ₀ is the simple cumulative cost of the source cell (O);

d is the geometric distance between the source cell (O) and the destination cell (D);

CS ₀ is the simple cost associated with the source cell (O) within the surface of simple costs (SCS); Y

CC _D is the conditioned cost associated with the target cell (D) within the surface of conditioned costs (SCC).

On the other hand, calculating the simple accumulated cost (CAS _D ) of this cell can be done according to:

in which:

CAS _D is the simple cumulative cost of the target cell (D);

CAS ₀ is the simple cumulative cost of the source cell (O);

d is the geometric distance between the source cell (O) and the destination cell (D);

CS ₀ is the simple cost associated with the source cell (O) within the surface of simple costs (SCS); Y

CS _D is the simple cost associated with the target cell (D) within the simple cost area (SCS). According to another embodiment of the invention, processing the cell taking into account that the source cell (O) does not have a minimum conditional cumulative cost (CAC _min ) may comprise:

o For each cell and each surface of conditioned costs to which this cell belongs, verify whether it is a target cell (D) of a source cell (O) that does not have a conditional cumulative cost (CAC), and, or it has no value in a surface of conditioned costs (SCC) or it is not a node of the conditioned displacement space (EDC) associated to the surface of conditioned costs, and the origin cell (O) belongs to a zone of displacement (ZD ₀ ) that has no restrictions with the zone of displacement to which the destination cell (ZD _D ) belongs;

 o In case of a positive result in this verification, calculate the simple accumulated cost (CAS) of this cell.

Thus, calculating the simple cumulative cost (CAS _D ) of this cell can be done according to:

CáS _D = CÁ5 _S + d * iCS ₀ + CS _D )

in which:

CAS _D is the simple cumulative cost (CAS) of the target cell (D);

CAS ₀ is the simple cumulative cost (CAS) of the source cell (O);

d is the geometric distance between the source cell (O) and the destination cell (D);

CS ₀ is the simple cost associated with the source cell (O) within the surface of simple costs (SCS); Y

CS _D is the simple cost (CS) associated with the target cell (D) within the surface of simple costs (SCS).

On the other hand, processing the cell taking into account that the source cell (O) has a minimum conditional cumulative cost (CAC _min ) can comprise:

o For each cell and each surface of conditioned costs (SCC) to which this cell belongs, check if it is a destination cell (D) of a source cell (O) that has a cumulative cost conditioned (CAC), and has value in a surface of conditioned costs (SCC);

o In the case of a positive result in this verification, calculate the conditional cumulative cost (CAC _D ) of this cell;

o Check if the cell belongs to a zone of displacement (ZD _D ) that is a node of the conditioned displacement space (EDC) associated with the surface of conditioned costs (SCC); o In case of a positive result in this verification, calculate the simple accumulated cost (CAS) of this cell.

Thus, calculating the cumulative conditioned cost (CAC _D ) of this cell can be performed according to:

in which:

CAC _D is the conditional cumulative cost of the conditioned displacement space (EDC) for the target cell (D);

CAC ₀ is the cumulative conditioned cost of the conditioned displacement space (EDC) of the source cell (O);

d is the geometric distance between the source cell (O) and the destination cell (D);

CC ₀ is the conditioned cost associated with the source cell (O) within the surface of conditioned costs (SCC); Y

CC _D is the conditioned cost associated with the target cell (D) within the surface of conditioned costs (SCC).

In addition, calculating the simple cumulative cost (CAS _D ) of this cell can be done according to: € ^ÁS !> = ^{€ AC} + d * {C € ₀ + £ ¾) in which:

CAS _D is the simple cumulative cost of the target cell (D);

CAC ₀ is the cumulative conditioned cost of the conditioned displacement space (EDC) of the source cell (O);

d is the geometric distance between the source cell (O) and the destination cell (D); CC ₀ is the conditioned cost associated with the source cell (O) within the surface of conditioned costs (SCC); Y

CS _D is the simple cost associated with the target cell (D) within the simple cost area (SCS).

Finally, to obtain, for each cell included in the territory's raster model, the lowest accumulated cost of travel cost for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in which the territory and the cost value that is invested in traversing the defined cell on the surface of simple costs and the cost value that is invested in traversing the defined cell in each surface of conditioned costs may comprise:

 o Determine, for each cell, the minimum accumulated cost of travel value between the simple accumulated cost value and the at least one conditional accumulated cost value.

Thus, the cost-distance procedure conditioned according to the invention is based on the geospatial processing capacity of the raster GIS, so it is necessary to incorporate geographical data to start executing. As mentioned earlier, the input data in this model needs to incorporate more information than the one demanded in the known cost-distance model. Thus, in the present conditioned procedure that is proposed, the following types of input data are precise:

 • Displacement Zones (ZD): raster file that collects the different types of zones through which specific displacements can be established;

• Locations source of the displacements (FD): raster file where the cells that will be taken into account to generate the displacements and therefore to start the calculation process in the algorithm are specified with value "0";

 · Surface of Simple Costs (SCS): raster file that represents the cost that is invested in crossing each one of the cells belonging to the defined zones of displacement.

• Conditional Cost Surfaces (SCCi): set of raster files, as many as conditioned displacement spaces are defined in the model, which will represent the costs involved in crossing each of the specific cells that identify the zones of conditioned displacement.

Once all the precise input data to execute the procedure is defined, the accumulated costs are calculated according to the established displacement conditions, and following a mathematical process similar to that specified in the cost-distance model, although including a series of conditions and checks that will vary the way this calculation is executed to make it more versatile. The calculation process starts from the source cells of displacements that are set in the corresponding raster file. The proposed operations are always established between two cells, the origin cell (O) and any of the eight destination cells (D) that surround the origin cell, and towards which it can be moved from O (see figure 4). The calculation is performed iteratively until all the cells considered in the analysis are completed, so that they present the lowest possible accumulated cost values for the allowable displacements in the process.

The source cell has a minimum accumulated cost value, which allows starting the operation towards the destination cell to calculate its accumulated cost based on the following aspects:

 Cumulative cost of the source cell (in the case of being a source cell, this will be zero, since no travel cost has yet been accumulated). As cells are being traversed, the costs that have been invested in that displacement accumulate, so that crossing the target cell will increase the previous accumulated cost.

Geometric distance that separates the centers of both cells. For raster files based on square cells, as is the general case, the distance in horizontal and vertical displacements will be the dimension of the cell side, and for diagonal displacements, that distance will be the diagonal of the grid.

 Costs associated to the displacements through the two cells, indicated in the corresponding cost surfaces, both for simple costs and for conditional costs.

Prerequisites established in the displacement zones to which the cells belong, according to their belonging to displacement spaces conditioned, and considering the restrictions that are included in the displacement conditions matrix for the calculation of the simple accumulated cost. As the accumulated cost in a cell is calculated, it acquires the active cell condition, while until then it is considered as a latent cell in the calculation process. The accumulated costs that are calculated on the new active cells are stored in the corresponding accumulated cost list, depending on whether it is a simple accumulated cost (CAS) or a conditional cumulative cost (CAC). The CAS list will always exist, and there will also be a CAC list associated with each conditioned displacement space (EDC), just as there was a conditioned cost area linked to each EDC.

When a cell has the lowest accumulated cost value of all those calculated and stored in the existing accumulated cost lists (regardless of the list in which it is found), that active cell acquires the closed cell condition, and its value is assigned to the file that collects the final result of the corresponding accumulated cost, either CAS or CAC. From that cell, the accumulated costs in the cells adjacent to it are calculated, complying with the marked displacement conditions, obtaining an accumulated cost value in the cells that did not already have it, or changing it when the new calculated cumulative cost was less than existing in the target cell. These new values of the accumulated costs will be simple or conditioned according to the operative criteria of the procedure, storing their value in the corresponding accumulated cost list, together with the other CAS or CAC values calculated up to that moment of the procedure.

The procedure continues iteratively until all the cells are provided with the condition of "closed cells", that is, obtaining in each cell the lowest possible accumulated cost value adjusted to the calculation requirements established by the conditioned cost-distance procedure. . The simple accumulated cost (CAS) obtains value in practically all evaluable cells (except those defined as without value or "NoData" in the cost area or those that impose complete restrictions for some zone of displacement). For their part, the Conditional cumulative costs (CAC) will only have value in cells where the conditional cost surfaces (SCC) associated with the same conditioned displacement space (EDC) have value. The operability of the calculations is different if the source cell O has a minimum value of CAS or CAC. Whatever the minimum value starts the operative process of the procedure, but according to CAS or CAC, the minimum of all the accumulated costs that have been calculated up to that moment, and are stored in the accumulated cost lists, the operations to be carried out will vary.

In the case that cell O has a minimum value in the CAS (CAS _m¡n ), the first thing that checks the procedure is whether the target cell D has value in any SCC. If so, it is analyzed whether cell O belongs to a displacement zone (ZD) defined as a node of the specific conditioned displacement space (EDC¡) for that SCC¡. If so, the source cell O has the ability to provide CAC to cell D, so it is calculated using the formula, as discussed above: £ .4 ¾ = CÁSQ + & * {CSQ + £ Ti > J in which,

CAC _Í D is the Conditional Accumulated Cost of the EDC¡ for the destination cell D

CAS ₀ is the Simple Accumulated Cost of the source cell O

d is the geometric distance between cell O and cell D

CS ₀ is the Simple Cost associated with cell O within the Surface of Simple Costs (SCS)

CC _/ o is the Conditional Cost associated with cell D within the SCC¡ Then the same check would be done that is necessary in the event that the destination D has no value in any SCC¡, or if the source cell does not belong to a zone of displacement considered as a node. In these cases, it is checked in the displacement conditions matrix (MCD) if the zone of the source cell O and the zone of the destination cell D are compatible (that is, there are no restrictions between them). In the event that communication is allowed between the two zones, the CAS of the destination cell D is calculated using the formula, as previously mentioned:

where,

CAS _D is the Simple Accumulated Cost of the destination cell D

CS _D is the Simple Cost associated with cell D within the SCS When calculating the simple cumulative cost, it is verified whether the target cell D has a value in another area of conditioned costs other than the one already verified. If so, for each cell value in an SCC _j , this entire process would be repeated. If D had no value in more SCQ, a new target cell D would be searched for the source cell O considered. As soon as it had operated with all possible D cells around O, then a new source cell would be searched associated with the lower value of the accumulated costs already calculated. In any case, if the target cell corresponds to a cell defined as "source", then the cost is not calculated, since these cells start the calculation procedure and will therefore always have a zero value for their accumulated cost.

If the minimum accumulated cost calculated and stored in the lists it corresponds to the costs arising Cost Accumulated Conditional any of the spaces Conditioning Displacement (EDC¡) defined in the analysis, the cell containing the minimum value CAC¡ _m¡n be now the source cell O in the calculation. The first check we do is check whether the target cell D has value in the SCC¡ associated with EDC¡ linked to CAC¡ _m¡n. If cell D has value in SCC, then we calculate its CAC with the formula, as previously mentioned:

where,

CAC _Í D is the Conditional Accumulated Cost of the EDC¡ for the destination cell D

CAC _Í O is the Conditional Accumulated Cost of the EDC¡ of the source cell OR

d is the geometric distance between cell O and cell D CC _Í O is the Conditional Cost associated with cell O within the Conditional Cost Surface (SCC¡)

CC _/ o is the Conditional Cost associated with cell D within the SCC¡ It would then be operated in the same way as if the destination cell D had no value in SCC¡, then checking if the destination cell D belongs to a displacement zone defined as Node the EDC¡ associated with CAC¡ _m¡n. If so, the cell would allow to obtain the CAS from the CAC, so the following formula would be calculated, as previously mentioned: LΛ QT ti * ¾ ..! -, QTL ¿} where,

CAS _D is the Simple Accumulated Cost of the destination cell D

CS _D is the Simple Cost associated with cell D within the SCS

If the displacement zone of the destination cell is not an EDC node, then a new destination cell associated with the source cell O is searched, repeating this calculation process until all the cells surrounding the source cell O are checked. When this happens, the source cell is replaced by another that has the lowest value of the accumulated cost among all those calculated up to that moment.

When the accumulated cost lists do not have any value, the calculation process will be over. All cells will be assigned the lowest value resulting from the cost of travel between them and the closest source cell among all those established in the analysis, according to the type of cumulative cost considered, CAS or CAC.

In this way, the final result obtained with this procedure of conditioned cost-distance is more adjusted to the reality generated by certain types of transport infrastructure with access restrictions, which allow a specific mobility adjusted to the layout of its structural platform, and that it only interacts with other mobilities throughout the rest of the territory, at certain points along its route. This implies that in the near environment of places belonging to these specific infrastructures, there may be very different values in the travel costs associated with the analysis of the accessibility of a territory, Well, there really are notable differences in the mobility behavior of each of the zones.

The execution of the conditioned cost-distance procedure according to the invention entails the generation of a multitude of calculations and operations of which only the final values obtained in the simple accumulated cost and in each of the conditional accumulated costs associated with each one are interested of the conditioned displacement spaces defined in the analysis. These results are specified in different raster files that in general will have values in the same cells that have non-zero value in the respective files corresponding to the cost surfaces. Thus, the CAS will have value in virtually all cells with value in the SCS. Only those displacement zones that have displacement restrictions with all contiguous zones will not be valuable. On the other hand, the CACi will have value in the cells that have value in their respective SCCi associated to the corresponding EDCi.

To finalize the algorithm, the calculated cumulative costs are unified, so that a single value is obtained per cell, which can be referred to as CAG global cumulative cost. This cost corresponds to the lowest value of all the costs calculated for each cell, as it indicates the minimum time taken to reach it from any of the source cells considered. This minimum value represents the potential of that place to be reached with a certain cost regardless of the conditions of conditioned displacement that have been considered, nor the means of transport used to access it from the predetermined displacement generating points. This CAG file is the final result of storing in each cell the minimum value of all the accumulated costs calculated in it.

CA G = ini CAS; CA C

In this way, a generic result of the Conditional Distance Cost Model is obtained, a value in each cell, which expresses the lowest cost that must be used to arrive from it to the nearest source cell, among all those established in the accessibility analysis considered .

Therefore, the results of the procedure are understood as: • Simple accumulated cost (CAS)

 • Conditional cumulative cost (CAC¡) for each conditioned displacement space (EDC¡) defined;

 • Global cumulative cost (CAG) as a minimum value of all accumulated costs obtained.

On the other hand, the invention also provides a system for determining the accessibility of a territory, from a raster model of the territory used in a Geographic Information System, which divides the territory into a plurality of cells, this system comprising:

 - the system to restrict the calculations to be performed in a raster model of a territory used in a Geographic Information System as described above, in which:

 - the computer / electronic means for receiving data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured comprises:

 or computer / electronic means to receive data regarding travel costs between the cells of any of the travel zones in which the territory is structured;

 - the computer / electronic means to execute calculations on the zones of displacement in which the territory is structured, taking into account the displacement restrictions between the different zones of displacement and the at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured include:

or computer / electronic means to obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in the that the territory and the cost of travel of the cell are structured. In addition, the invention also provides a computer system comprising a memory and a processor, in which the memory stores computer program instructions executable by the processor, these instructions comprising functionalities for executing a method for determining the accessibility of a territory, from of a raster model of the territory used in a Geographic Information System, as described above.

Finally, the invention provides a computer program product comprising program instructions to cause a system to execute a procedure to determine the accessibility of a territory, from a raster model of the territory used in a Geographic Information System, as it is described above

Similarly, this computer program may be stored on physical storage media, such as recording media, a computer memory, or a read-only memory, or it may be carried by a carrier wave, such as electrical or optical .

DEFINITIONS

With the intention of avoiding confusion and facilitating the understanding of the different descriptions, some definitions of key concepts within the context of the present invention are detailed below. The term "raster" refers to a geographic data format implemented on a Geographic Information System (GIS), which is based on systematically dividing the entire territory to be defined, through a set of elementary units, called cells, which collect the value that describes that place, and that make up a mesh following a certain pattern from contiguous non-overlapping cells, and usually regular squares. The size of the cell, called resolution, determines the precision with which a variable is collected within a raster layer. Both the Cost-Distance model or procedure and the proposed procedure according to the invention are based on the use of raster data to perform the calculations and obtain the results. The term "source" refers to a cell, or set of cells, on which the iterative process of calculating the minimum cost accumulated in the displacements on the rest of the cells that make up the rectangular mesh that represents the territory of analysis begins. The source cells can be one or several, and they can be grouped together forming an area or scattered over different places of the mesh.

The term "Surface of Simple Costs" (SCS) refers to a raster layer where each cell has the value that represents, for the whole field of study, the friction or cost that it offers when being traversed.

The term "Surface of Conditional Costs" (SCC) refers to a raster layer where each cell has the value that represents the friction or cost it offers when being traversed, but only in those cells that make up the Conditional Displacement Space (EDC) at that represents that SCC. The values of the cells of an SCC will in general be different from the values of those same cells in the SCS, so that these places will have at least two different travel costs, and therefore at least two costs can be calculated in them accumulated different.

The term "zone of displacement" represents those geographical places that have similar characteristics of their own, which determine the particular conditions of displacement that will establish the costs involved in crossing these areas of mobility.

The term "conditioned displacement zone" determines the scope occupied by those places with specific displacement modes or by some type of territorial element, or transport infrastructure, with access limitations except at certain points of its geometry.

The term "Conditional Displacement Space" (EDC) represents the places composed of a conditioned displacement zone that presents intrinsic restrictions in the movements that communicate it with the neighboring displacement zones, and by the displacement zone, called Node, which allows Your communication with the rest of the territory. An EDC allows them to several types of displacement coexist in those places, including modes of transport with restricted displacement or with particular characteristics in its route. The term "displacement zone of the links" or "displacement or communication node" represents that or those places that allow the connection of a displacement zone conditioned with the rest of the displacement spaces that define a territory. This node will be the geographical area where it is possible to transform a conditional cumulative cost into a simple accumulated cost, and vice versa.

The term "origin" or "origin cell", during the iterative calculation process, refers to the cell that has the lowest cumulative cost of travel of all those existing at that time of the operation. From this source cell a new calculation is carried out to obtain the cumulative cost of its neighboring cells.

The term "destination" or "destination cell" refers to each of the neighboring cells at the time of interacting to establish the cost of travel with the source cell.

The term "displacement" refers to the action of crossing a territory from one place to another, and that in the raster format is represented by the passage from the center of one cell to the center of another different cell. Basically, the supported displacements are based on the connection of a source cell with the eight destination cells adjacent to it.

The term "latent cell" refers to any cell other than the source cells, with a value other than null, which belongs to a Cost Area, and on which a cumulative cost of displacement has not yet been calculated. A latent cell will participate in the accumulated cost calculation process.

The term "active cell" refers to any latent cell after calculating an accumulated cost of travel on it. The active cell will continue to participate in the calculation process until the lowest accumulated cost of travel is reached. The term "closed cell" refers to any active cell after calculating the lowest accumulated cost of travel possible. The value of that cell will participate in the final result of the accessibility calculation.

The term "Simple Accumulated Cost" (CAS) refers to the result of the process of calculating the procedure according to the invention, which represents for each latent cell of the Simple Cost Surface (SCS), the value of arriving from it to the nearest source cell (depending on the measurement parameter used - time, distance, etc.-).

The term "Conditional Cumulative Cost" (CAC) is the result of the process of calculating the procedure according to the invention, which represents for each latent cell of the determined Conditional Cost Surface (SCC), the value of arriving from it to the nearest source cell (depending on the measurement parameter used - time, distance, etc.-).

Finally, the term 'Global Cumulative Cost' (CAG) refers to the final result of the process of calculation of the procedure according to the invention, which represents for each cell of the Cost Surfaces, the minimum value of those obtained in the CAS and CAC, and that supposes the minimum cost of arriving from that cell to the nearest source cell (in the measurement parameter used - time, distance, etc.-), taking into account all the possibilities and conditions of displacement considered.

BRIEF DESCRIPTION OF THE DRAWINGS

Particular embodiments of the present invention will now be described by way of non-limiting example, with reference to the accompanying drawings, in which:

Figure 1 is a flow chart schematically illustrating a Conditional Distance Cost method according to an embodiment provided by the invention; Figure 2 is a flowchart that schematically illustrates a sub-process of processing an origin cell O that does not have a cumulative cost conditioned in the context of a procedure equal to or similar to that of Figure 1; Figure 3 is a flowchart that schematically illustrates a sub-process of processing an origin cell O that does have a cumulative cost conditioned in the context of a procedure equal to or similar to that of Figure 1; Y

Figure 4 schematically represents a source cell, its destination cells, and fundamentals that can be used in some embodiments to obtain the distance between the source cell and any of the destination cells.

DETAILED EXHIBITION OF MODES OF EMBODIMENT

In general, different embodiments of the method / system / software provided by the invention can be used to obtain movement costs in the context of any diffusion / dispersion / propagation process of an element (person, object, phenomenon, etc.) on a surface land. For example, embodiments can be used to obtain propagation costs and, therefore, the evolution of a fire, taking into account restrictions based on eg the types of vegetables existing in the territory (some vegetables are more combustible than others) , the humidity existing in different parts of the territory, etc. Similarly, the spread of pests on crop surfaces, the spread of polluting substances, etc. could also be estimated. For the sake of simplicity and compression of the invention, embodiments of the process are described below only in the context of movement through a territory by a person or vehicle. In some implementations, the Conditional Distance Cost procedure may be based on the geospatial processing capacity of the raster GIS, so it may require the incorporation of geographic data to begin execution. The input data in this model may require the incorporation of more information than that demanded in the known Cost Distance model. To execute this known procedure it is required to have an input file that mark the source places or generators of the displacements, and a raster file that represents the friction or cost surface associated with the displacements at each point of the scope of study. The following types of input data may be required in the proposed proposed procedure:

 - ZD Displacement Zones: which can be a raster file that collects the different types of zones through which specific displacements can be established.

 - Source places of the FD displacements: which can be a raster file in which the cells that will be taken into account to generate the displacements and therefore to start the calculation process in the procedure can be specified with value "0".

 - Surface of Simple Costs SCS: that can be a raster file that represents the cost that is invested in crossing each one of the cells belonging to the zones of displacement ZD defined.

 - SCC Conditioned Cost Surfaces: which can be a set of raster files, as many as EDC Conditioned Travel Spaces are defined in the model, which may represent the costs involved in crossing each of the specific cells that identify the zones of conditioned displacement ZDC

Once all the precise input data have been defined to execute the procedure, the accumulated costs can be calculated according to the established displacement conditions, and following a mathematical process similar to that used in the Cost Distance procedure, although including a series of conditions and verifications that will vary the way this calculation is executed to make it more versatile. The calculation process can start from the source cells of displacements (which can be set in eg the corresponding raster file). The proposed operations are always established between two cells, a source cell O and any of the (eg eight) destination cells D that surround the source cell, and towards which there may be a shift from the source cell O. The calculation It can be done iteratively until all the cells considered in the analysis are completed, so that they present the lowest possible accumulated cost values for the allowable displacements in the process. The source cell may have a minimum accumulated cost value, which may allow the operation to start towards the destination cell to calculate its accumulated cost based on eg the following aspects:

- Cumulative cost of the source cell (in the case of being a source cell, this may be zero, since no travel cost has yet been accumulated). As cells are being traversed, the costs that have been invested in this displacement may be accumulated, so that crossing the target cell may increase the previous accumulated cost.

- Geometric distance that separates the centers of both cells. For eg raster files based on eg square cells, the distance in horizontal and vertical displacements may be the dimension of the cell side (see figure 4), and for diagonal displacements, that distance may be diagonal of the grid.

- Costs associated with travel through the two cells, indicated on the corresponding cost surfaces, both for simple costs and for conditional costs.

 - Prerequisites established in the displacement zones to which the cells belong, according to their membership in Conditional Displacement Spaces, and considering the restrictions that can be included in a Displacement Conditions Matrix for the calculation of the Simple Accumulated Cost.

As the accumulated cost in a cell is calculated, it can acquire the active cell condition, while until then it can be considered as a latent cell in the calculation process. The accumulated costs that are calculated on the new active cells can be stored in a corresponding List of Accumulated Costs, depending on whether it is a Simple CAS Accumulated Cost or a CAC Conditional Accumulated Cost. The CAS list may always exist, and there may also be a list of the CAC associated with each EDC Conditional Displacement Space, just as there may be a

Conditional Cost Area linked to each EDC.

When a cell has the lowest cumulative cost value of all those calculated and stored in the existing Accumulated Cost Lists (regardless of the list it is in), that active cell can Acquire the closed cell condition, and its value can be assigned to the file that collects the final result of the corresponding accumulated cost, either CAS or CAC. From that cell, the accumulated costs in the adjacent / adjacent cells can be calculated, complying with the marked displacement conditions, being able to obtain an accumulated cost value in the cells that do not yet have it, or changing it when the new calculated accumulated cost it was smaller than the one in the destination cell. These new values of the accumulated costs may be simple or conditioned as certain operational criteria of the procedure are met, being able to store their value in the corresponding List of Cumulative Costs, together with the other CAS or CAC values calculated up to that moment by the procedure . This process may continue iteratively until all cells are provided with the condition of "closed cells", that is, obtain in each cell the lowest possible accumulated cost value adjusted to the calculation requirements that the Conditional Distance Cost model can establish. The Simple CAS Accumulated Cost can obtain value in practically all evaluable cells (except for those that can be defined as worthless or "No data" on the Cost Surface or those that may impose full restrictions for some zone of displacement) . On the other hand, the CAC Conditional Accumulated Costs could only have value in the cells where the SCCs associated with the same EDC have value. The operability of the calculations may be different if the source cell O has a minimum value of CAS or CAC. Whatever the minimum value may start the operative process of the procedure, but the operations to be carried out may vary depending on the CAS or CAC the minimum of all the accumulated costs that may have been calculated up to that time, and may be stored in the Lists of accumulated costs.

Figure 1 is a flow chart schematically illustrating a Conditioned Cost Distance method according to an embodiment provided by the invention. In this embodiment, the procedure begins at a start stage 100. Then it goes on to step 101, in which it checks if there is an FD source cell or active cell with a minimum cumulative cost CA _min . If this verification produces a positive result S (if there is an FD cell or active cell with a _minimum CA), proceed to step 1 02. If this verification produces a negative result N (there is no FD cell or active cell with a CA _min ), go to step 1 05, in which the procedure ends.

In step 102, the source cell FD or active cell with the minimum cumulative cost CA _min is closed and then it goes to step 1 03. In this stage 103, the closed cell is assumed / marked as source cell O and then proceed to step 1 04. In this step 1 04, it is verified whether the minimum accumulated cost CA _min of the source cell O is a cumulative conditioned cost minimum CAC _min . If this verification 1 04 produces a positive result S (the CA _min of cell O if it is a CAC _min ), it is passed to step 107, which comprises a sub-procedure of processing the source cell O taking into account that it has a cumulative cost conditioned minimum CAC _min . If this verification 104 produces a negative result N (the _min AC of cell O is not a CAC _min ), it is passed to step 106, which comprises a sub-procedure of processing the source cell O taking into account that has a minimum accumulated cost CAC _m¡n conditioned. A transition from step 1 07 to step 1 01 is also reflected in Figure 1. This transition occurs when step 107 has already completed the processing of the current FD or active (with CAC _m ) source cell, so that step 1 01 determines and starts the processing of a new FD source cell or active (with AC _min , whether conditioned or not). Details are provided on the processing performed by step 1 07 in other parts of the description with reference to the figure

3.

A transition from step 1 06 to step 101 is also reflected in Figure 1. This transition occurs when step 106 has completed processing of the cell or active source FD (without CAC _m¡n) current, so that the step 1 January determine and start processing a new source cell FD or active (with AC _min , whether conditioned or not). Details are provided on the processing performed by step 1 06 in other parts of the description with reference to Figure 2. Figure 2 is a flowchart that schematically illustrates a subprocess of processing an origin cell O that does not have a cumulative cost conditioned at least CAC _min in the context of a procedure equal to or similar to that of Figure 1. The sub-process begins in step 200 when step 104 produces a negative result N, which indicates that the aggregate cost of the minimum CA _min cell origin O is not a minimum accumulated cost CAC conditioned _m¡n (see Figure 1) . In step 200, it is checked whether there is a destination cell D not yet processed adjacent to the source cell O, and if said destination cell D has value in some SCC conditioned cost surface. If this verification 200 produces a positive result S (there is unprocessed cell D adjacent to cell O and with value in some SCC), it is passed to step 201. If this verification 200 produces a negative result N (there is no unprocessed cell D adjacent to cell O and with value in some SCC), it is passed to step 203. In step 201, it is verified if the source cell O belongs to a ZD Offset Zone defined as the Node of the EDC Specific Conditioned Offset Space for that SCC conditioned cost surface. If this verification 201 produces a positive result S (cell O does belong to a ZD defined as the EDC Node for that SCC, which means that a cumulative cost conditioned CAC can be attributed to cell D), it is passed to the stage 202. If this verification 201 produces a negative result N (cell O does not belong to a ZD defined as the EDC Node for that SCC, which means that a cumulative cost conditional CAC cannot be attributed to cell D), it is passed to stage 203.

In step 202, the CAC conditioned cumulative cost for the target cell D is calculated, which can be obtained by applying the following formula:

THE € _$ = L ^' AS _Q + d. * {LSQ + ^■ CL _S ) in which:

CAC _D is the cumulative CAC conditioned cost of the EDC for the target cell D; CAS or is the simple cumulative cost of the source cell O;

d is the geometric distance between the source cell O and the destination cell D (see figure 4); CSo is the simple cost associated with the source cell O within the surface of simple costs SCS; Y

CC _D is the conditioned cost associated with the target cell D within the surface of conditioned costs SCC.

Once step 202 has been completed and, therefore, the cumulative cost conditioned CAC for the destination cell D has been calculated, it is passed to step 203.

In step 203, it is verified whether the ZD Offset Zones of the source cell O and of the destination cell D are compatible, that is, if communication between both ZD Offset Zones is allowed. This can be done by consulting an MCD Displacement Conditions Matrix. If this verification 203 produces a positive result S (the ZD of cell O and cell D are compatible according to the MCD), it goes to step 204. If this verification 203 produces a negative result N (the ZD of the cell O and cell D are not compatible according to the MCD), go to step 205.

In step 204, the simple accumulated cost CAS of the destination cell D is calculated by the following formula:

€ AS _D = € ÁS _Q + d »(CS _G ÷ € 5 _D ) in which:

CAS _D is the simple accumulated cost CAS of the target cell D;

CAS or is the simple cumulative cost of the source cell O;

d is the geometric distance between the source cell O and the destination cell D (see figure 4);

 CSo is the simple cost associated with the source cell O within the surface of simple costs SCS; Y

CS _D is the simple cost CS associated with the target cell D within the surface of simple costs SCS.

Once step 204 has been completed and, therefore, the simple accumulated cost CAS of the destination cell D has been calculated, it is passed to step 205. In step 205, it is verified whether the destination cell D has value in another surface of conditioned costs SCC not yet considered. If verification 205 produces a positive result S (cell D does have value in another SCC not yet considered), it is returned to step 201 in order to repeat the process (from said step 201) for the value of the destination cell D in this other SCC. If verification 205 produces a negative result N (cell D has no value in another SCC not yet considered), it is passed to step 206.

In step 206, it is verified whether the source cell O has an adjacent destination cell D pending processing. If this verification 206 produces a positive result S (cell O does have an adjacent cell D pending processing), it is returned to step 200 in order to repeat the process (from said stage 200) for this other adjacent destination cell D pending processing. If this verification 206 produces a negative result N (cell O does not have an adjacent cell D pending processing), it is returned to step 101 in order to process a new source cell FD or active cell with a minimum cumulative cost CA _min (see figure 1).

Figure 3 is a flowchart that schematically illustrates a sub-process of processing an origin cell O that does have a cumulative cost conditioned in the context of a procedure equal to or similar to that of Figure 1. The sub-procedure begins in step 300 when step 104 produces a positive result, which indicates that the minimum cumulative cost CA _min of the source cell O is a cumulative cost conditioned minimum CAC _min (see Figure 1). In step 300, it is checked whether there is a destination cell D not yet processed adjacent to the source cell O, and if said destination cell D has value in some SCC conditioned cost surface. If this verification 300 produces a positive result S (there is unprocessed cell D adjacent to cell O and with value in some SCC), it goes to step 304. If this verification 300 produces a negative result N (there is no cell D no processed adjacent to cell O and with value in some SCC), it is passed to step 301.

In step 301, it is verified whether the destination cell D belongs to a ZD Offset Zone defined as the Node of the EDC Specific Conditioned Offset Space for that SCC conditioned cost surface. If this verification 301 produces a positive result S (cell D does belong to a ZD defined as the EDC Node for that SCC, which means that a simple accumulated cost CAS can be attributed to cell D), it is passed to step 302. If this verification 301 produces a negative result N (cell D does not belong to a ZD defined as the EDC Node for that SCC, which means that a simple accumulated cost CAS cannot be attributed to cell D), it is passed to step 303.

In step 302, the simple accumulated cost CAS of the target cell D is calculated by the following formula:

] _ or € AS _S - = CÁ € _g ^{■ a} «CC _Q + ^■ £ ¾) in which:

CAS _D is the simple accumulated cost CAS of the target cell D;

 CACo is the Conditional Accumulated Cost of the EDC of the source cell O;

15 d is the geometric distance between the source cell O and the destination cell D (see figure 4);

 CCo is the conditioned cost associated with the source cell O within the SCC conditioned cost surface; Y

CS _D is the simple cost CS associated with the target cell D within the surface of 20 simple costs SCS.

Once step 302 has been completed and, therefore, the simple accumulated cost CAS of the destination cell D has been calculated, it is passed to step 303.

25 In step 303, it is verified whether the source cell O has an adjacent destination cell D pending processing. If this verification 303 produces a positive result S (cell O does have an adjacent cell D pending processing), it is returned to step 300 in order to repeat the process (from said stage 300) for this other adjacent destination cell D pending processing. If this verification 303 produces a

30 negative result N (cell O does not have an adjacent cell D pending processing), returns to step 101 in order to process a new source cell FD or active cell with a minimum cumulative cost CA _min (see Figure 1 ).

In step 304, the CAC conditioned cumulative cost is calculated for cell 35 destination D, which can be obtained by applying the following formula: LAC¡¡¡ = LA CQ + íí * \ C ^' LQ - ¥ L ^' CJJ in which:

CAC _D is the cumulative CAC conditioned cost of the EDC for the target cell D; CACo is the Conditional Accumulated Cost of the EDC of the source cell O;

d is the geometric distance between the source cell O and the destination cell D (see figure 4);

 CCo is the conditioned cost associated with the source cell O within the SCC conditioned cost surface; Y

CC _D is the conditioned cost associated with the target cell D within the surface of conditioned costs SCC.

Once step 304 has been completed and, therefore, the conditional cumulative cost CAC has been calculated for the destination cell D, it is returned to step 301 in order to verify whether a simple accumulated cost CAS can be attributed to the cell D and, if so, proceed to its calculation (in step 302), as described above.

The global procedure (illustrated in Figures 1 - 3) ends when all the cells have been assigned the lowest value resulting from the cost of travel between them and the closest source cell FD among all those established in the analysis, according to the type of cost accumulated considered, simple accumulated cost CAS or cumulative cost conditioned CAC. The final result obtained with this Cost Distance procedure

Conditioned is more adjusted to the reality generated by certain types of transport infrastructure with access restrictions, which allow specific mobility adjusted to the layout of its structural platform, and that only interacts with other mobilities throughout the rest of the territory, at certain points of its route. This will entail that in the near environment of places belonging to these specific infrastructures, there may be very different values in the travel costs associated with the analysis of the accessibility of a region, since there are really notable differences in the mobility behavior of each of the zones. The execution of the Conditional Distance Cost model entails the generation of a multitude of calculations and operations that will only be of interest in preserving the final values obtained in the simple accumulated cost CAS and in each of the CAC conditional cumulative costs associated with each of the spaces of EDC conditioned displacement defined in the analysis. In some embodiments, these results can be specified in different raster files, which in general will have values in the same cells that have non-zero value in the respective files corresponding to the cost surfaces SC. Thus, the simple accumulated cost CAS will have value in virtually all cells with value in the SCS. Only those ZD displacement zones that have displacement restrictions with all contiguous zones will not have value. On the other hand, the cumulative CAC conditioned costs will have value in the cells that have value in their respective SCC conditioned cost surfaces associated with the corresponding EDC conditioned displacement spaces.

To complete the procedure, the calculated cumulative costs can be unified, so that a single value per cell is obtained, which can be called the CAG global cumulative cost. This cost corresponds to the lowest value of all the costs calculated for each cell, as it indicates the minimum time taken to reach it from any of the source cells FD considered. This minimum value will represent the potential of that place to be reached with a certain cost regardless of the conditioned displacement spaces that have been considered, nor the means of transport used to access it from the predetermined displacement generating points. This CAG file is the final result of storing in each cell the minimum value of all the accumulated costs calculated in it.

CAG = mm {£ AS; CACA In this way it is obtained as a generic result of the Cost Distance Model

Conditioned, a value in each cell, which expresses the lowest cost that must be used to arrive from it to the nearest FD source cell, among all those established in the accessibility analysis considered. Therefore they can be understood as results of the Model. Simple accumulated cost CAS

 CAC conditioned cumulative cost for each EDC conditioned displacement space defined in the model

 CAG global cumulative cost as a minimum value of all accumulated costs obtained

Figure 4 schematically represents a source cell, its destination cells, and fundamentals that can be used to obtain the distance between the source cell and any of the destination cells, in some embodiments. All cells shown (origin O and destination D) have a quadrangular shape, that is, with four sides of identical length d1. The source cell O is the one that occupies the central position and the destination D are those that surround (are adjacent) to it. The center point of each of the cells (origin O and destination D) is also shown. The length d2 refers to the distance between the respective center points of the source cell O and any of the destination cells D vertically adjacent to the source cell O. The length d3 refers to the distance between the respective center points of the cell origin O and any of the destination D cells horizontally adjacent to the origin O cell. The expert will easily understand that the distances d1, d2 and d3 are identical because of the quadrangular configuration and arrangement of the cells.

Even with reference to Figure 4, the length d4 refers to the distance between the respective center points of the source cell O and any of the destination cells D adjacent "diagonally" to the source cell O. The expert will easily understand that This length d4 can be obtained by the following formula:

Thus, the geometric distance between the source cell O and any of the destination cells D can be obtained in accordance with the above fundamentals. In particular, it may be considered, in some embodiments, that d1 (according to the definition above) is the geometric distance between the source cell O and any of the destination cells D adjacent horizontally or vertically to the source cell O, and that d4 (according to the previous calculation) is the geometric distance between the source cell O and any of the destination cells D adjacent "diagonally" to the source cell O.

Although only some particular embodiments and examples of the invention have been described herein, the person skilled in the art will understand that other alternative embodiments and / or uses of the invention are possible, as well as obvious modifications and equivalent elements. In addition, the present invention encompasses all possible combinations of the specific embodiments that have been described. The scope of the present invention should not be limited to specific embodiments, but should be determined only by an appropriate reading of the appended claims.

In spite of the fact that the described embodiments of the invention with reference to the drawings comprise computer systems and processes carried out in computer systems, the invention also extends to computer programs, more particularly to computer programs in or on carrier media, adapted to be The invention in practice. The computer program product may be in the form of source code, object code or intermediate code between source code and object code, such as in partially compiled form, or in any other form suitable for use in the implementation of the processes of according to the invention. The carrier medium can be any entity or device capable of carrying the program.

For example, the carrier medium may comprise a storage medium, such as a ROM, for example a CD ROM or a semiconductor ROM, or a magnetic recording medium, for example a floppy disc or a hard disk. In addition, the carrier means may be a transmissible carrier medium such as an electrical or optical signal that can be transmitted via electrical or optical cable or by radio or other means.

When the computer program product is contained in a signal that can be transmitted directly by a cable or other device or medium, the carrier medium may be constituted by said cable or other device or medium. Alternatively, the carrier means may be an integrated circuit in which the software product is encapsulated (embedded), said integrated circuit being adapted to perform, or to be used in the realization of, the relevant processes.

On the other hand, the invention can also be implemented by computer systems, such as personal computers, servers, a computer network of computers, laptops, tablets or any other programmable device or computer processor. In addition or alternatively, programmable electronic devices can also be used, such as programmable logic controllers (ASICs, FPGAs, programmable controllers, etc.).

Accordingly, the invention can be implemented in both hardware and software or firmware, or any combination thereof.

Claims

one . Procedure to restrict some calculations to be performed in a raster model of a territory used in a Geographic Information System, dividing the raster model the territory into a plurality of cells, the procedure comprising:

 Receive data referring to different zones of displacement in which the territory is structured;

 Receive data regarding displacement restrictions between the different zones of displacement in which the territory is structured;

 Receive data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured;

 Perform calculations on the zones of displacement in which the territory is structured, taking into account the displacement restrictions between the different zones of displacement and the at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured.

2. The method according to claim 1, comprising:

 Receive data concerning at least one source from which the displacements originate.

3. Method according to any one of claims 1 or 2, wherein receiving data referring to different zones of displacement in which the territory is structured comprises:

 Receive a raster file that includes the different zones of displacement in which the territory is structured.

4. A method according to any one of claims 1 to 3, wherein receiving data regarding travel restrictions between the different zones of movement in which the territory is structured comprises:

Receive a file that includes the travel restrictions between the different zones of movement in which the territory is structured.

5. Method according to any one of claims 1 to 4, wherein receiving data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured comprises:

 - Receive at least one raster file comprising data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured.

6. System to restrict the calculations to be performed in a raster model of a territory used in a Geographic Information System, dividing the raster model the territory into a plurality of cells, the system comprising:

 - Computer / electronic means to receive data referring to different areas of displacement in which the territory is structured;

 - Computer / electronic means to receive data regarding travel restrictions between the different zones of movement in which the territory is structured;

 - Computer / electronic means to receive data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured;

 - Computer / electronic means to execute calculations on the zones of displacement in which the territory is structured, taking into account the displacement restrictions between the different zones of displacement and the at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured.

7. System according to claim 6, comprising:

 - Computer / electronic means to receive data referring to at least one source from which the displacements originate.

8. Computer system comprising a memory and a processor, in which the memory stores computer program instructions executable by the processor, these instructions comprising functionalities to execute a procedure to restrict the calculations to be performed in a raster model of a territory used in a Geographic Information System, according to any one of claims 1 to 5.

9. Computer program product comprising program instructions to cause a system to execute a procedure to restrict the calculations to be performed in a raster model of a territory used in a Geographic Information System, according to any one of claims 1 to 5.

10. Computer program product according to claim 9, which is stored in recording media.

eleven . Software product according to claim 9, which is carried by a carrier signal.

12. Procedure to determine the accessibility of a territory, from a raster model of the territory used in a Geographic Information System, which divides the territory into a plurality of cells, this procedure comprising:

 - the procedure for restricting the calculations to be performed in a raster model of a territory used in a Geographic Information System according to any one of claims 2 to 5, in which:

 Receive data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured comprises:

 o Receive data regarding travel costs between the cells of any of the travel zones in which the territory is structured;

 Perform calculations on the zones of displacement in which the territory is structured, taking into account the restrictions of displacement between the different zones of displacement and the at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured includes:

o Obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different zones of displacement in which the territory is structured and the cost of displacement cost of the cell.

13. The method of claim 12, wherein the source comprises at least one cell of the raster model of the territory.

14. A method according to any one of claims 12 or 13, wherein the displacement zones are selected from:

 - Simple displacement zone;

 - Conditioned displacement zone;

 - Zone of displacement of the links or node.

15. A method according to claim 14, wherein the simple displacement zones define a simple displacement space, which has an associated simple cost surface that represents the value of the cost invested in crossing each cell belonging to the displacement space. simple.

16. The method according to claim 15, wherein receiving data referring to travel costs between the cells of any of the travel zones in which the territory is structured comprises:

 Receive the surface of simple costs associated with the space of simple displacement.

17. The method according to claim 16, in which, for each cell included in the raster model of the territory, to obtain the lowest accumulated cost of travel value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in which the territory is structured and the cost of displacement cost of the cell includes:

- Obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in which the territory is structured and the cost value that is invested in traversing the cell defined in the surface of simple costs.

18. A method according to any one of claims 16 or 17, wherein each conditioned displacement zone in combination with a suitable node defines a conditioned displacement space, which has a surface of associated costs associated with it representing the value of the cost that It invests in crossing each cell belonging to the conditioned displacement space.

19. The method according to claim 18, wherein receiving data referring to travel costs between the cells of any of the travel zones in which the territory is structured comprises:

 Receive the surface of conditioned costs associated with each space of conditioned costs.

20. The method according to claim 19, in which, for each cell comprised in the raster model of the territory, to obtain the lowest accumulated cost of travel value for the admissible displacements from the source, taking into account the displacement restrictions between the different displacement zones in which the territory is structured and the cost of displacement cost of the cell includes:

 - Obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in which the territory is structured and the cost value that is invested in traversing the defined cell on the surface of simple costs and the cost value that is invested in traversing the defined cell in each surface of conditioned costs.

twenty-one . Method according to claim 20, in which, for each cell comprised in the raster model of the territory, to obtain the lowest accumulated cost of travel value for the allowable displacements from the source, taking into account the displacement restrictions between the different zones of displacement in which the territory is structured and the cost value that is invested in crossing the cell defined in the surface of simple costs and the value of cost that is invested in crossing the defined cell in each surface of conditioned costs includes:

 o Check (101) if there is a source cell or a cell with minimum unprocessed cumulative cost;

 In case of positive verification result,

 o For each cell and each surface of conditioned costs to which this cell belongs, verify (104) if it is a target cell of a source cell that does not have a cumulative conditioned cost; o In the case of a positive result in the verification (104), process (106) the cell taking into account that the source cell does not have a minimum conditional cumulative cost;

 o In case of negative result in the verification (104), process (107) the cell taking into account that the originating cell has a minimum conditional cumulative cost.

22. The method of claim 21, wherein processing (106) the cell taking into account that the source cell does not have a minimum conditional cumulative cost comprises:

 o For each cell and each surface of conditioned costs to which this cell belongs, verify (200, 201) if it has value in a surface of conditioned costs and belongs to a zone of displacement that is a node of the conditioned displacement space associated with this surface of conditioned costs; o In the case of a positive result in this verification (200, 201), calculate the conditional cumulative cost of this cell;

 o Verify (203) if the source cell belongs to a displacement zone that has no restrictions with the displacement zone to which the cell belongs;

 o In case of positive result in this verification (203), calculate (204) the simple accumulated cost of this cell.

23. The method of claim 22, wherein calculating (202) the conditional cumulative cost of this cell is performed in accordance with:

CÁCQ = CASQ + á * (CS ₀ - $ - C € _D ) in which:

CAC _D is the cumulative conditioned cost of the conditioned displacement space for the target cell;

CAS ₀ is the simple cumulative cost of the source cell;

d is the geometric distance between the source cell and the destination cell;

CS ₀ is the simple cost associated with the source cell within the surface of simple costs; Y

CC _D is the conditioned cost associated with the target cell within the surface of conditioned costs.

24. The method according to any one of claims 22 or 23, wherein calculating (204) the simple accumulated cost of this cell is performed according to:

in which:

CAS _D is the simple cumulative cost of the target cell;

CAS ₀ is the simple cumulative cost of the source cell;

d is the geometric distance between the source cell and the destination cell;

CS ₀ is the simple cost associated with the source cell within the surface of simple costs; Y

CS _D is the simple cost associated with the target cell within the surface of simple costs.

25. A method according to any one of claims 21 to 24, wherein processing (106) the cell taking into account that the source cell does not have a minimum conditional cumulative cost comprises:

o For each cell and each surface of conditioned costs to which this cell belongs, check (200, 201, 203) if it is a target cell of a source cell that does not have a conditional cumulative cost, and, or does not have value on a surface of conditioned costs or is not a node of the conditioned displacement space associated with the surface of conditioned costs, and the source cell belongs to a displacement zone that has no restrictions with the displacement zone to which the target cell; o In case of positive result in this verification (200, 201, 203), calculate (204) the simple accumulated cost of this cell.

26. The method of claim 25, wherein calculating (204) the simple cumulative cost of this cell is performed according to:

in which:

CAS _D is the simple cumulative cost of the target cell;

CAS ₀ is the simple cumulative cost of the source cell;

d is the geometric distance between the source cell and the destination cell;

CS ₀ is the simple cost associated with the source cell within the surface of simple costs; Y

CS _D is the simple cost associated with the target cell within the surface of simple costs.

27. The method of claim 21, wherein processing (107) the cell taking into account that the source cell has a minimum conditioned cumulative cost comprises:

 o For each cell and each surface of conditioned costs to which this cell belongs, verify (300) if it is a target cell of a source cell that has a conditional cumulative cost, and has value in a surface of conditioned costs; o In the case of a positive result in this verification (300), calculate (304) the conditional cumulative cost of this cell;

 o Verify (301) if the cell belongs to a zone of displacement that is a node of the conditioned displacement space associated with the surface of conditioned costs;

 o In case of positive result in this verification (301), calculate (302) the simple accumulated cost of this cell.

28. The method of claim 27, wherein calculating (304) the conditional cumulative cost of this cell is performed in accordance with: in which:

CAC _D is the cumulative conditioned cost of the conditioned displacement space for the target cell;

CAC ₀ is the cumulative conditioned cost of the conditioned displacement space of the source cell;

d is the geometric distance between the source cell and the destination cell;

CC ₀ is the conditioned cost associated with the source cell within the surface of conditioned costs; Y

CC _D is the conditioned cost associated with the target cell within the surface of conditioned costs.

29. A method according to any one of claims 27 or 28, wherein calculating (302) the simple cumulative cost of this cell is performed according to:

CÁ5 _& = CAC _C ^■ + ^■ d * · {C € _D + € S _D in which:

CAS _D is the simple cumulative cost of the target cell;

CAC ₀ is the cumulative conditioned cost of the conditioned displacement space of the source cell;

d is the geometric distance between the source cell and the destination cell;

CC ₀ is the conditioned cost associated with the source cell within the surface of conditioned costs; Y

CS _D is the simple cost associated with the target cell within the surface of simple costs.

30. The method according to claim 29, in which, for each cell included in the raster model of the territory, to obtain the lowest accumulated cost of travel value for the admissible displacements from the source, taking into account the displacement restrictions between the different displacement zones in which the territory is structured and the cost value that is invested in crossing the defined cell on the surface of simple costs and the cost value that is invested in crossing the defined cell in each surface of conditioned costs comprises: o Determine, for each cell, the minimum accumulated cost of travel value between the simple accumulated cost value and the at least one conditional accumulated cost value.

31. System to determine the accessibility of a territory, from a raster model of the territory used in a Geographic Information System, which divides the territory into a plurality of cells, this system comprising:

 - the system for restricting the calculations to be performed in a raster model of a territory used in a Geographic Information System according to any one of claims 6 or 7, in which:

 - the computer / electronic means for receiving data referring to at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured comprises:

 or computer / electronic means to receive data regarding travel costs between the cells of any of the travel zones in which the territory is structured;

 - the computer / electronic means to execute calculations on the zones of displacement in which the territory is structured, taking into account the displacement restrictions between the different zones of displacement and the at least one value assigned to each cell of at least one zone of displacement of the different zones of displacement in which the territory is structured include:

 or computer / electronic means to obtain, for each cell included in the raster model of the territory, the lowest accumulated travel cost value for the allowable displacements from the source, taking into account the travel restrictions between the different displacement zones in the that the territory and the cost of travel of the cell are structured.

32. Computer system comprising a memory and a processor, in which the memory stores computer program instructions executable by the processor, these instructions comprising functionalities to execute a procedure for determining the accessibility of a territory, from a model raster of the territory used in a Geographic Information System, according to any one of claims 1 2 to 30.

33. Computer program product comprising program instructions to cause a system to execute a procedure to determine the accessibility of a territory, from a raster model of the territory used in a Geographic Information System, according to any one of claims 1 2 to 30

34. Software product according to claim 33, which is stored on recording media.

35. Software product according to claim 33, which is carried by a carrier signal.