EP1779306A2

EP1779306A2 - Method and system for identifying proximity areas between several digitally simulated geometrical objects

Info

Publication number: EP1779306A2
Application number: EP05792025A
Authority: EP
Inventors: Lionnel Joussemet; Flavien Maingreaud
Original assignee: Haption; Commissariat a lEnergie Atomique CEA
Current assignee: Haption; Commissariat a lEnergie Atomique et aux Energies Alternatives CEA
Priority date: 2004-07-22
Filing date: 2005-07-20
Publication date: 2007-05-02
Also published as: FR2873472A1; FR2873472B1; JP2008507056A; US7774180B2; US20080319718A1; WO2006018570A3; JP4829885B2; WO2006018570A2

Abstract

The inventive system for identifying proximity areas between several digitally simulated geometrical objects comprises (a) a memory (111) for storing data describing the geometry of objects, (b) an initialisation module (120) for creating a pawn population, (c) a central processing unit (140) consisting of at least (c1) one unit (141) for selecting the percentage of the pawn population to be exposed to a paired combat, (c2) a comparing and calculating unit (142) for evaluating the quality of each pawn, (c3) a marker unit (143) for identifying which pawn of a pawn pair exposed to combat won or lost for each session of a tournament, (c4) an iteration unit (144) for advancing the pawn which participated in at least one combat in association with at least one exploratory mutation operator and one redefinition operator and (c5) an extracting module (145) for retaining only the best pawns of population in order to determine the proximity areas between at least two objects.

Description

Method and system for identifying proximity zones between several numerically simulated geometric objects

The present invention relates to a method and system for identifying proximity areas and evaluating distances between several numerically simulated objects. An object is thus constituted by a geometry within a digital environment.

For example, interactive simulation of the real world in a digital environment is called "virtual reality" (VR). A virtual reality platform (Figure 1) includes interfaces 10 between the virtual environment and the operator (s) participating in the simulation. There are several types of interfaces, each for the stimulation of one of the senses of the operator or operators. It is thus possible to implement in an RV platform for example visual interfaces 11, auditory 12, haptics 13.

An RV platform also includes a dynamic simulator

20 whose function is to govern in real time the evolution of the components of the virtual environment according to the laws of physics, as well as their interactions. These interactions can be bilateral (mechanical links) or unilateral (collision).

A dynamic simulator 20 is comparable to a physical engine whose role will be to govern the evolution of a virtual world composed of objects having dynamic and geometric properties. This task can be broken down into two sub-tasks: the management of the dynamic of the virtual world (dynamic engine 21) and the management of the collisions that take place within it (collision engine 22).

The management of the dynamics of the virtual world makes it possible to govern the individual evolution of the objects contained in the virtual world according to the laws of physics. Figure 2 illustrates the operating diagram of a dynamic motor 21 in the case of a single object.

The first step 211 consists in taking stock of the forces applied to the virtual object. These efforts to which the subject is subject may be of several origins: gravity, joint constraints (also called bilateral links), operator manipulation. Their accumulation will make it possible to obtain a static torsor of effort. During the second step 212 will be determined the linear and angular accelerations of the object by applying the fundamental principle of dynamics (PFD). The new position and orientation are then directly determined by double integration during the third step 213. It seems interesting to observe that the fact of evolving in discrete time imposes to approximate the integration. For this, several methods are possible (Euler, Tustin, Runge-Kutta, ...). The last step 214 is simply to update the position and orientation of the object under consideration.

Collision engine 1 22 provides a task that is decomposable into two phases; collision detection and generation of contact forces. Collision detection can be carried out according to several techniques depending on the type of geometry used and the expected performance. In the context of the discrete methods, which constitute the great majority of the techniques used, this first phase consists in detecting the interpenetrations between the different pairs of objects at every moment. On the contrary, continuous methods detect the exact moment of the first contact between objects.

Whatever the method used, this first phase is the heaviest task to be performed by the dynamic simulator. Indeed, the amount of computations to be performed as part of this detection is directly related to the nature of the objects evolving within the virtual world, particularly in terms of geometric complexities. After this first phase of collision detection, it remains to determine the forces resulting from collisions between the pairs of solids concerned. These are usually decomposed into a normal reaction force and a tangential friction force. It is thus necessary to model these collisions. To do this, three methods are mainly used: penalty, impulse and constraint.

In the context of dynamic simulations intended to operate in real time, the management of unilateral constraints (collisions), whether in terms of detection or calculation of the contact forces, generates a limitation of the geometric complexity of the components of the virtual world ( nature, number and type of elementary entities). By nature of the object is meant all of its properties of convexity (convex / concave) and rigidity (infinitely rigid / deformable). The elementary entities allowing the geometric definition of an object can be of several types: meshes (triangles, quads), voxels, points, analytical surfaces. The main techniques for detecting collisions between dynamic objects are presented below.

The location of the areas likely to collide is found in conventional collision detection techniques and, more particularly, in the optimizations made to it. Thus, three major strategies that can meet this need emerge from the scientific literature: the calculation of the minimum distance between objects, the hierarchies of bounding volumes, the consideration of the volumes scanned during the movement.

The first technique will consist in calculating, at any time, the minimum distance between two objects E and E2 of polyhedral type and thus know the geometric elements el, e2 closest (see Figure 3). Several approaches have thus been implemented in order to obtain this minimum distance as well as the geometric elements concerned. Most of these techniques consider convex objects. These The latter can still be used in the context of simulations involving concave objects by decomposition of the latter into convex elements. A first method for determining this minimum distance and the elements concerned was introduced by Gilbert, Johnson and Keerthi. This method, based on the Minkowsky difference and the convex optimization, makes it possible to determine the distance between two convex envelopes of two sets of points El and £ -? and has at worst cases for complexity o {(n + mf), n and m being the number of points respectively contained in E1 and E2. However, it is possible to optimize this method based on the results obtained during previous iterations and thus reduce the complexity to o (n). This process does not take into account the nature of the considered objects and the evolution of their geometry. It is thus used in processes involving objects other than rigid and convex. Lin and Canny introduce a computation method allowing the determination, in linear time, of the two nearest points of two convex non-deformable meshes. This process is based on the concept of spatial and temporal coherence. Since the virtual world evolves according to a dynamic model, the displacement of an object during a time step is infinitesimal, which gives hope that, at a given cycle, the nearest points belong to the neighborhood of the points closest to the previous cycle. . This process implying a "continuous" change of the zones of interest on the considered meshes, it can be optimized via a multiresolution approach making it possible to accelerate the "displacement of the computation" within the mesh, such as that proposed by Dobkin and Kirkpatrick.

A second approach taking into account a hierarchy of enclosing volumes is to partition the spaces occupied by the objects composing the scene. Thus, each object will be approximated by a bounding volume itself decomposed into a tree of subvolumes (generally of similar topology to the enclosing volume "root"). The strategy is to spatially locate areas that may be interpenetrating. In practice, the presence of overlapping bounding volumes of distinct objects is tested, and then, in the event of an overlap, a similar recursive test is performed at the level of the sub-volumes they contain. This strategy avoids a multitude of irrelevant tests and is widely used within existing physical engines. However, these overlap tests can be very numerous in some cases (plan / plan for example) and thus compromise the performance of the simulation. In addition, updating these volumes (movement, deformation) can be expensive.

Several types of geometries can be used as part of this spatial segmentation. The most commonly used are spheres 1, isothetic bounding boxes 2 (AABB) and oriented bounding boxes 3 (OBB) (see Figures 4a, 4b, 4c).

Each of these types of bounding volumes is more or less adapted according to the geometry considered and the expected level of performance. Thus, the all-encompassing spheres have the main advantage of the simplicity of the overlap tests. Indeed, the test of overlap of two spheres is limited to a comparison between the distance separating their center and the sum of their respective rays. However, the spheres generally give a less optimal approximation of the geometry considered, in comparison with the OBBs for example which, despite much heavier overlapping tests (theorem of the separator axes), limit the execution of non-relevant tests by a minimum encompassed volume.

Architecturally, the enclosing volume hierarchies are in the form of trees, often binary in order to optimize their course. We also talk about Octrees (8 branches / node), or Quadtrees (4 branches / node more suited to 2D geometries). The volume swept by a moving solid during a time interval corresponds to the union of the zones of space that it has occupied during this period. This geometric tool has several application domains: robotics workspace evaluation, geometric modeling in CAD. The volume swept by a sphere during a translation is illustrated by way of example in FIGS. 5a and 5b which respectively illustrate the initial 4 and final 5 positions of the object and the corresponding swept volume 6.

Considering the kinematics of the rigid objects that evolve within the simulation at a time t _{0 as} well as their geometry, it is conceivable to evaluate the volumes they are likely to scan at a horizon t _n , n> 0, and thus anticipating their interactions by determining the intersections between their respective scanned volumes.

Several processes are described in the literature. For example, the numerous works of K. Abdel-Malek et al. A particularly interesting method is also presented by Y J. Kim et al. The latter makes it possible to rapidly and robustly identify the volume swept by a polyhedron of relatively large complexity (thousands of facets). In addition to a sophisticated algorithmic, he uses the hardware which allows him to achieve a very high level of performance and usable in the context of a real-time simulation. Voxels are sometimes used to discretely define any geometry. The principle is to identify and encompass areas of space occupied by matter using cubes of varying sizes depending on the degree of resolution expected (see Figure 6). The above techniques of hierarchy of bounding volumes and scanned volumes are also applicable in the context of optimization of this type of voxelic approach.

We can mention in particular a technique based on a hybrid discretization using voxels (or "voxmap") and the combination of point cloud (or "shell point") and normals. This technique is illustrated in Figures 7a and 7b. Figure 7a shows a first original object 8 represented as voxels 8a and a second original object 9 represented as a cloud of points and normals 9a.

FIG. 7b shows the detail of an interaction between a voxel 8a of a static surface of the object 8 and the cloud of points of the object 9 with the tangent plane 9b to the static surface and the force vector 9a according to the normal to the point cloud of object 9.

This hybrid discretization technique requires a relatively long pre-computation phase but allows complex geometric data to be managed.

According to an analytical approach, two other types of models include implicit surfaces and parametric surfaces. The former use implicit functions that define shapes in space. Implicit surfaces are the set of points for which 0, the interior of the model being the points for which / (χ,>', - :) <0.

For these two modeling methods, solving collision problems amounts to manipulating these functions. These types of geometric definitions are used very little. Any objects (not from primitives) and complex are seen in fact very difficult to represent in this way, particularly in the case of protruding areas (discontinuity) very present in mechanical parts for example.

Once the zones of interpenetration identified, it remains to determine the contact forces, that is, in other words, the efforts of "repulsion" that will allow to bring the interpenetrated objects to a simple state of contact. To do this, three methods emerge from the scientific literature: the stress method, the impulse method and the penalty method. The constraint method consists in explicitly taking into account the constraints of non-interpenetration at the level of the equations of movement specific to each object. This constraint is expressed as follows: p (t) = / {force) C (P (O)> 0 where the first equation characterizes the movement of each object according to the forces applied to it and the second the constraints of no -interpénétration.

This method is particularly interesting in the case where the collisions are not very frequent (the collision calculation, the determination of C {ρ (ή, is expensive) and in the absence of friction, it has the advantage of not not have any adverse effects on the stability of the overall system.

The pulse method is a kinematic approach that equates the interaction between two rigid objects to an impact. The collision is thus considered as a quasi-instantaneous event generating a significant effort (called impulse) on the objects concerned. We thus have the following relationship between the speeds before and after impact:

V ₀ ≈ -e V _{1 where} e is called coefficient of restitution : elastic collision, : plastic collision). e is computable via the Poisson hypothesis: e = ^

When two objects are close enough, the pulse is calculated to separate them into a single iteration. It is often the condition that the objects concerned have a ballistic trajectory in order to optimize the calculations.

The penalty method makes it possible to manage repulsion efforts between rigid or deformable objects. It consists in applying to colliding objects 14, 15 a force proportional to the depth of interpenetration (we speak of stiffness). The "mechanism" of repulsion is thus often equated with a system 16 of derivative proportional type (see Figure 8). This method requires knowing the penetration vector (which can be expensive) and often generates instabilities (especially in cases of multi-point collisions). It follows from the foregoing that the evaluation of distances and the identification of proximity zones, and where appropriate the detection of collisions, between geometric objects evolving within a digital environment, is seen as an essential step in a a large number of disciplines, such as virtual reality or the scripting of robotic system movements.

However, particularly because of their cost in terms of computing time, the various processes used to date are often unusable in the context of simulations involving complex geometries and requiring high levels of performance. The present invention aims at remedying the drawbacks of the prior art and at making it possible to respond to most of the recurring problems in the evaluation of distances or the identification of proximity zones, and in particular in the detection of collisions by providing solutions. with reduced computation times compatible with real-time applications, with a high degree of performance and simplicity of implementation, even when the interacting objects have complex geometries or different natures or qualities.

These objects are achieved, according to the invention, by a method of identifying proximity zones between at least first and second digitally simulated objects, characterized in that it comprises the following steps:

(a) providing data describing the geometry of each of the first and second digitally simulated objects and storing the data in memory,

(b) creating a population consisting of a set of N individuals called pions each defined by first and second nucleons themselves. same defined as points belonging respectively to the geometries of each of the first and second objects,

(c) Tournament sessions are organized within the Npions of the created population, where during each session a percentage of the population is subjected to combat during which it is evaluated for each pair of pawns submitted to a fight. , based on an assessment of the quality defined by an aptitude criterion, which has won and which has lost and the winner and the loser are identified by marking which is different at the end of each session of the tournament, (d) after the tournament, an exploratory mutation of the pawns having lost during a first session is carried out, the pions which have lost during a second session are replaced by crossing randomly chosen pions and a redefinition is carried out random pieces lost during a third session,

(e) for the exploitation of the pieces to be used to determine zones of proximity between the first and second objects, only the population of the victors of the combats,

(f) repeating steps (c), (d) and (e) are repeated, and (g) geometric information is retrieved on demand from an updated configuration of the pion population during repetitive execution.

During the geometric information extraction step, the distances between the identified proximity zones can be evaluated. The data for identifying areas of the space describing the geometry of at least one of the first and second numerically simulated objects may include polyhedral representations, voxel representations, parametric surface representations or point clouds. . According to one particular characteristic, the aptitude criterion for evaluating the quality of a pion is constituted by a measurement of the distance separating the first and second nucleons defining this pion, the the quaiity of the pawn being all the greater as the measured distance is smaller. This measurement of the distance may for example take into account the square of the distance separating the first and second nucleons defining the pion. The method according to the invention may further comprise, after the step (a) of providing data describing the geometry of each of the first and second digitally simulated objects, the following steps:

(a1) creating a connectivity map containing information defining the neighborhood properties between geometrical elements within the first and second objects and storing in memory the information of this connectivity map,

(a2) a proximity card is created containing information defining the proximity properties within the first and second objects and the information of this proximity card is stored in memory.

Advantageously, the mutation of the pions having lost during a session of the tournament generating exploratory mutations for lost pions consists in moving the first and second nucleons composing a pion on the surface of the first and second objects to which these first and second nucleons respectively belong.

According to a particular embodiment, during the mutation of a pawn having lost during a session of the tournament, generating exploratory mutations for the pions having lost, at least one of the first and second nucleons composing this pawn and belonging to the one of the first and second objects represented in a polyhedral form is subjected to a succession of discrete center facet displacements in the facet center by considering the information defining the neighborhood properties stored in memory.

According to another particular embodiment, during the mutation of a winning token during the tournament, at least one of the first and second nucleons composing this pion and belonging to one of the first and second objects represented in a polyhedral form is subjected to displacement on the same facet on a disk having as center the initial position of this point and for radius a maximum displacement amplitude which depends on the area of the facet on which the displacement is made.

According to yet another particular embodiment, during the mutation of a winning pawn during the tournament, at least one of the first and second nucleons composing this pawn and belonging to one of the first and second objects represented in a polyhedral shape is subjected to a "wormhole" displacement from one vertex of one facet to another vertex close to another facet that is not necessarily connected, considering the information defining the proximity properties stored in memory. According to yet another particular embodiment, during the mutation of a winning pawn during the tournament, the first and second nucleons composing this pion and respectively belonging to the first and second objects each represented in a polyhedral form with triangular facets, are positioned such that they delimit a segment defining the minimum distance between the two triangular facets to which these first and second nucleons respectively belong.

Advantageously, when replacing a pawn having lost during a session of the tournament generating for the pions having lost substitutions by crossing randomly selected pions, to define the new pawn resulting from the crossing of a first and a second selected pawns randomly, the new pion is considered to be composed of the first nucleon of the first randomly selected pawn and the second nucleon of the second randomly selected pawn. The invention relates more generally to a method applied to a set of P objects simulated numerically with P> 2, characterized in that it comprises the following steps: (a) provides data describing the geometry of each of the P graphically simulated objects,

(b) creating a population consisting of a set of N individuals called pions each defined by first and second nucleons themselves defined as points respectively belonging to the geometries of one of the P objects and another of the P objects ,

(c) Tournament sessions are organized within the Npions of the created population, where during each session a percentage of the population is subjected to combat during which it is evaluated for each pair of pawns submitted to a fight. , based on an assessment of the quality defined by an aptitude criterion, which has won and which has lost and the winner and the loser are identified by marking which is different at the end of each session of the tournament,

(d) after the tournament, an exploratory mutation of the pawns having lost during a first session is carried out, the pions which have lost during a second session are replaced by crossing randomly selected pions and a random redefinition of the pions is carried out. pions having lost during a third session, (e) for the exploitation of the pieces to be used to determine zones of proximity between two of the P objects, one considers only the population of the victors of the combats,

(f) repeating steps (c), (d) and (e) again, and

(g) Geometric information is extracted on demand from an updated configuration of the pion population during repetitive execution.

In the case where the data making it possible to identify areas of the space describing the geometry of the digitally simulated P objects comprise polyhedral representations, the method advantageously comprises the following additional steps after step (a) of providing data describing the geometry of the digitally simulated P objects:

(a1) creating a connectivity map containing information defining the neighborhood properties between geometrical elements within each of the P objects and storing in memory the information of this connectivity map,

(a1) a proximity card is created containing information defining the proximity properties within each of the P objects and the information of this proximity card is stored in memory.

The invention further relates to a proximity zone identification system between a number P of objects simulated numerically with P> 2, characterized in that it comprises;

(a) first memory means for storing data describing the geometry of each of the P objects,

(b) an initialization module for creating a population consisting of a set of N individuals called pions each defined by first and second nucleons themselves defined as points respectively belonging to the geometries of one of the P objects and another of the P objects,

(c) a central processing unit comprising at least:

(c) means for selecting a percentage of the population of the N pions to be subjected to pairwise combat during a session of a tournament, (c2) means of comparison and calculation for evaluating during a session of a tournament, for each pair of pawns submitted to a fight, the quality of each pawn of the pair of pawns based on an aptitude criterion,

(c3) marking means for identifying at each session of the tournament which pieces of a pair of pions subject to a fight has won, and which of the pieces of the said pair of pawns submitted to a fight has lost,

(c4) iteration means for producing an evolution of the pions that have undergone at least one combat, these iteration means being associated at least with an exploratory mutation operator of the pions having lost during a first session of the tournament, at a replacement operator of the pawns having lost during a second session of the tournament by crossing randomly selected pawns and to an operator of redefinition of the pawns having lost during a third session of the tournament, and

(c5) an extraction module for retaining only the best pions of the population according to the aptitude criterion, for determining the proximity zones between at least two of the P objects. The system may further include:

(a1) second memory means for storing information representing a connectivity map and defining the properties of the neighborhood between geometrical elements within each of the P objects, (a2) of the third memory means for storing information representing a map of proximity and defining the proximity properties within each of the P objects.

The central processing unit may comprise a set of computing units operating in parallel. The method and the system according to the invention are thus based on an evolutionary process based on a stochastic approach. This evolutionary process deals with populations of individuals defined by real components and not simply binary.

Other characteristics and advantages of the invention will emerge from the following description of particular embodiments given to As non-limiting examples, with reference to the accompanying drawings, in which:

FIG. 1 is a block diagram representing the functional architecture of a virtual reality platform; FIG. 2 is a flowchart showing the dynamic evolution diagram of an object contained in the virtual world according to the laws; of physics,

3 is a diagram illustrating a known method for calculating the minimum distance between two objects of the polyhedral type; FIGS. 4a, 4b and 4c show three examples of approximating an object by a bounding volume;

FIG. 5a illustrates initial and final positions of a spherical object in translation,

FIG. 5b illustrates the swept volume corresponding to the translation of the object of FIG. 5a,

FIG. 6 illustrates an example of a voxelic decomposition of an object,

FIG. 7a shows an example of hybrid representation of an object in the form of voxels cooperating with another object represented in the form of a cloud of points and normals,

FIG. 7b represents the detail of an interaction zone of the two objects represented in a hybrid manner in FIG. 7a,

FIG. 8 illustrates the representation of two objects subjected to repulsion efforts according to the penalty method; FIG. 9 is a diagram illustrating the genotype of an individual or pion used in the context of the invention,

FIG. 10 illustrates an example of discrete exploratory displacement of a point on a polyhedron, as part of a mutation,

- Figure 11 shows an example of an operating operator involved in a mutation,

FIG. 12a illustrates a process for identifying nearby elements in the context of objects represented in a polyhedral form, FIG. 12b illustrates an example of a path without wormhole in the object represented in FIG. 12a,

FIG. 12c illustrates an example of a path through a wormhole in the object represented in FIG. 12a; FIG. 13 illustrates the principle of the crossing of two pions,

FIG. 14 represents the three main phases of the process according to the invention,

FIGS. 15a, 15b and 15c illustrate three examples of geometrical configurations making it possible to materialize the segment defining the minimum distance between two triangles of polyhedral representations of objects, to which belong the two points composing a pion,

FIG. 16 illustrates the projection of ends of a segment on a plane containing a triangle as part of the determination of the segment defining the minimum distance between two triangles belonging to polyhedra representing two interacting objects,

FIGS. 17 and 18 illustrate, in the case of the process represented in FIG. 16, the determination of a segment defining a minimum distance, respectively in the case of segment-point and in the segment-segment case,

FIG. 19 represents the genotype of several pions defined between different polyhedra representing different objects,

FIG. 20 illustrates the random replacement of a pawn in the case of an object represented in polyhedral form; FIG. 21 illustrates the genotype of a pawn defined between two parameterized surfaces representing two objects,

FIG. 22 illustrates the genotype of a pawn defined between two point clouds representing two objects,

FIG. 23 illustrates the genotype of a pawn defined between two voxelic representations of objects,

- Figure 24 illustrates the function of a crossing operator, FIG. 25 represents hybrid pins defined between geometries of different types representing objects, and

- Figure 26 is a block diagram showing the main modules constituting an exemplary system according to the invention. The method and system according to the invention, described according to a particular embodiment, make it possible, starting from digitally simulated objects, or virtual objects, to identify, throughout a real-time dynamic simulation featuring geometrical representations of objects, the geometric zones likely to collide, regardless of the geometric complexity and nature (convexity, rigidity) of the objects.

To do this, the method according to the invention uses an evolutionary process. In general, it applies a strategy that consists of changing a population of individuals using variation operators (mutation, crossing) to converge this population to an optimal configuration.

The evaluation of the quality of an individual is done through a function called "objective function (" fitness ") to measure one or more qualitative criteria.This evolutionary process generating new individuals has a high efficiency and a simplicity of implementation.

In a first step, the method according to the invention which applies an evolutionary process to virtual reality, will be described with reference to objects represented by polyhedra, but the invention is more general and applies to objects whatever their geometric representation.

As already indicated, the basic strategy of the method according to the invention consists in changing a population of individuals using variation operators (mutation, crossing) intended to converge the population (set of individuals). to an optimal configuration. Figure 9 illustrates an exemplary definition of the 51 genotype of an individual (which subsequently will also be called "pin") which is defined as a pair of nucleons constituted by points belonging respectively to each of the two meshes Objeti and Object ₂ representing the first and second objects whose proximity we wish to evaluate.

The genotype 51 of a pawn can thus be expressed as:

where the Face indices (unsigned integers) represent the identifiers of the faces to which belong respectively the points defining the pion, a, and β _t the coordinates of the point belonging to the first polyhedron in the base O ₁ , e ₂ ) of the relevant face , and respectively for α ₂ and β ₂ in the base (e ^, e ^). (O≤α, <\, 0 <β _l ≤ι, α, + β _t ≤i).

The genotype defined above is intended to be used in the context of simulations of objects of the polyhedral type. It is important to point out that, more generically, a pion is simply defined by two nucleons belonging respectively to two objects of any kind. If we consider for example the case of implicit surfaces, in this case a pawn will be defined by the coordinates (* ,, y _x , z _x ) of the first point and the coordinates (x ₂ , y ₂ , Σ ₂ ) άu second. In the case of voxelic type geometries, the points may be defined by the index of the voxels concerned. Thus, the description of a pawn is directly related to the type of geometry used. It is also possible to define a pion between two geometries of different types, the coordinates of the points being systematically expressed in the Cartesian space at the time of the evaluation.

The objective function ("fitness") or aptitude criterion for evaluating the quality of a pion is constituted by measuring the distance separating the first and second nucleons defining the pion. This measure can advantageously be chosen as being the square of the distance separating the two nucleons composing the pion.

Let (x ,, ^ ₁₅ Z ₁ ) and (X ₂₅ ^ ₂₅ Z ₂ ) be the respective Cartesian coordinates of the nucleons composing a pion p _λ projected in the same frame. The expression of the fitness of this individual is the following: fitness (p _x ) = (x ₂ - x, f + (y ₂ - y _x f + (z ₂ - z _x f.

The use of the square of the standard is advantageous because the square root function is very expensive in terms of computation time.

It should be noted that the Quality quality (p) of an individual or p-p is inversely proportional to its fitness goal function (p).

The mutation is an evolution operator that is definable as a more or less important variation of the genetic heritage of an individual.

More particularly, in the context of the present invention, to mutate an individual consists in moving the points that compose it on the surface of the objects to which they belong.

Several displacement heuristics can be defined in the context of simulations involving polyhedra.

Thus, with an example of an exploration operator illustrated in FIG. 10, the points defining the individual concerned will be able to move over great distances on the surface of the objects. This operator generates discrete displacements of centers 52 of facets 53 in centers

52 of facets 53 by considering the connectivity of the considered objects, obtained by means of neighborhood maps of the pre-calculated polyhedra. The amplitude of these displacements, which corresponds to the number of jumps made during the mutation, is determined randomly. She is between 0 and σ _Eψhr , maximum displacement amplitude depending on the geometry of the object.

Figure 10 illustrates the discrete exploratory displacement of a point on a polyhedron with an amplitude of eight jumps, but this value is naturally given only as an example.

An exploitation operator that corresponds to another type of mutation, illustrated in Figure 11, is intended to refine the positioning of the points that make up the individual concerned. Unlike the case of the exploratory mutation, these displacements are defined metrically. Thus each point will perform a displacement on a disk of radius ^σ _FxP i _o , _t i maximum displacement amplitude, having as center the initial position of the point. The maximum displacement amplitude (expressed in meters) may be dependent on the area of the face 56 on which the displacement is performed. Thus, this amplitude is calculated during the pre-calculation phase for each facet 56.

Moving on the faces 61 of a polyhedral representation 60 of an object by considering only the connectivity (neighborhood properties) may be restrictive, particularly in the case of thin objects or strongly curved. Thus, according to another aspect of the invention, it is set up a second "map" based on the proximity of the vertices. During the pre-calculation phase, for each vertex 62, 63 is established a list of the nearest vertices 64, 65. When one of the points (63) that make up the mutating pion is on a vertex at from a displacement, it has the possibility (and not the obligation) to slide to a nearby vertex (64) not necessarily connected. This type of displacement can be called "wormholes", with reference to the Einstein-Rosen bridges (passages similar to shortcuts linking distant zones within a curved universe).

Figure 12a illustrates the polyhedral representation 60 of an object having faces 61.

According to a proximity card, the vertices 64, 65 are identified as being closest to the vertices 62, 63. Figure 12b illustrates an example of a path 66 without a wormhole, from the vertex 63 to a point 67.

Figure 12c illustrates an alternative path using the "wormhole" mutation operator. In this case, the path from the top 63 to the point 67 includes a passage 68 of the "wormhole" type outside the representation 60 of the object, between the vertices 63 and 64 identified as being close.

Mutation operators having functions similar to those of the three operators described above can be defined in the simulation framework involving other types of geometries.

The invention also implements a variation operator, called "crossover", which is intended to accelerate the convergence of the population (FIG. 13). The principle is to generate a pawn (child) by coupling two pawns coming from the population (spawners). The new pawn thus has genetic properties specific to its two parents. In practice, this operator can be used in the following way: the pawn "child" has for nucleon 1 that of the first spawner and for nucleon 2 that of the second.

The general scheme of the method according to the invention is illustrated in FIG. 14, with a first initialization phase 71, a second tournament phase 72 and a third evolution phase 73.

During the initialization phase 71, data is provided to identify points describing the geometry of each of the graphically simulated objects and stores these data in memory. During this same initialization phase 71, a connectivity map is also created containing information defining the topological neighborhood properties within the objects and the information of this connectivity map is stored in memory.

The initialization phase 71 also comprises the establishment of a proximity card containing information defining the proximity properties (wormhole) within the objects and the storage in memory of the information of this proximity card. Finally, during the initialization phase 71, a population consisting of a set of N individuals (which may be called pions) each defined by first and second nucleons constituted by points respectively belonging to the geometries of two objects is created. previously identified.

Phase 72 tournament consists of the organization of fights between individuals. A fight between two individuals or pions consists of evaluating which of the two pions proves to be of better quality, that is to say which of the two pions has a goal function (or aptitude criterion) "fitness" the weakest.

Thus, during phase 72 of the tournament, sessions are organized within the N pions of the created population where, during each of the sessions, a percentage of the population is subjected to fights during which it is evaluated for each pair of pieces. subject to a fight, based on a quality assessment defined on the basis of an aptitude criterion, which has won and which has lost and the winner and the loser are identified by a mark that is different at the end each session of the tournament.

The various sessions of the tournament phase 72 may for example comprise a first session Mut% consisting of fights of a percentage of the population which will then generate mutations, a second session Cross% consisting of fights of a percentage of the population which will then generate crosses and a third session Rand% consisting of fights of a percentage of the population which will then generate random redefinitions.

The first, second and third sessions, Mut%, Cross% and Rand% can take place in any order. At the end of the tournament phase 72, the winning pieces are identified by a marking that is different from that of the losing pieces. The marking of the pieces also differs according to the session during which they have undergone one or more fights. The evolution phase 73 consists in applying the previously defined variation operators to the population according to the results of the tournament and thus includes the mutation of the pieces having lost during the first session Mut% of the tournament, the replacement of the pieces having lost during the second session Cross% of the tournament by crossing randomly selected pieces, and the redefinition of the pieces having lost during the third session Rand% of the tournament. The exploitation of the winners of the combats which are supposed to be good elements makes it possible to determine zones of proximity between two objects. The process is iterative and phases 72 and 73 can be repeated without stopping. It is possible at any moment to exploit an improved configuration by exploiting the only pawns then marked as being winners.

The method according to the invention is little dependent on the geometric nature and the quality of the objects. It can be used in the context of simulations involving all types of geometries (polyhedra, voxels, parametric surfaces, etc.) as long as the appropriate variation operators are defined. In addition, it allows the mix of geometries, the points that make up the pions can evolve in a completely different way to the surface of the objects to which they respectively belong. The process is not sensitive to concavities, exploratory mutations and random redefinitions ensuring diversity of the population.

The quality of objects (orientation of normals, holes, ...) does not affect the operation of the process. This is a considerable advantage (the current physics engines are very sensitive to the quality of the objects, which often greatly affects their proper functioning ...).

The execution times of the second and third steps 72, 73 of the process (tournament, evolution) are not dependent on the number of elementary geometric entities, but only on the number of pions that are not dependent on the geometric complexity of the objects . In all cases, the counters are much less numerous than the entities elementary geometries. The process is therefore in total little dependent on the geometric complexity of the objects.

As already indicated, an individual or pion of a population of N individuals is composed of two points which can also be called nucleons.

It has been described above, more particularly in the case of objects represented in a polyhedral manner, a set of evolution operators or mutators intended to make the pions evolve within the polyhedra to which they belong. Another operator allows an optimal positioning of the nucleons constituting the individual concerned on the triangles that contain them in representations of objects of the polyhedral type.

This mutation operator makes it possible to minimize locally, according to a deterministic approach, the objective function (fitness) of the pion concerned. This mutation operator is intended to be applied to the elite of the individuals making up the population. It is intended to accelerate the convergence and increase the accuracy of the results resulting from the implementation of the method.

The goal of this operator is to position the nucleons that make up the pion concerned so as to materialize the segment defining the minimum distance between the two triangles to which they respectively belong.

Figures 15a, 15b, 15c show three different geometrical configurations with two triangles 81, 82; 83, 84 and 85, 86 respectively for which segment 87; 88; 89 respectively materializing the minimum distance between the two triangles corresponds to a vertex / face interaction, vertex / vertex and edge / edge.

These different cases can be taken into account with the determination method described below. In order to determine in a short time the optimal positioning of the nucleons composing the pion concerned, the triangle / triangle case is decomposed into 6 segment / triangle cases as expressed below, thus covering all the geometric configurations previously defined.

P ₁₁ ⁽⁽ A ₁ B, AMA B ₂ A ⁾⁾ ([C ₂ ^, B ₂ AU ₁ - BrA)) I

Where yτ _s , (S, T) and ψ _n (T _x , T ₂ ) respectively determine the segments representing the minimum distance in the cases segment / triangle and triangle / triangle. The determination of the minimum segment in the segment / triangle case itself breaks down into two phases:

- Identification of possible geometrical configurations and elements concerned (segments, points, faces).

- Determination of the minimum segment. The first phase consists of orthogonally projecting the ends of the segment onto the plane containing the triangle. The combination of the positions of their projected relative to the triangle will make it possible to identify the possible geometrical configurations and the potentially affected elements. The positions of the projected relative to the triangle are formalized by their belonging to one of the plan portions defined by the straight lines bearing the sides of the triangle. For example, in the case illustrated in FIG. 16, the projections Pi, Qi of the ends Pet Q of the segment belong respectively to the zones Z ₂ and Z ₄ of the plane containing the triangle (A, B, C). Thus there are 49 possible combinations:

{(Z ,, Z _y ), l ≤ / ≤ 7, l </ ≤ 7}.

The following table describes the potential bearing pairs of the minimum segment for each of the combinations where ψss ([Pi Qi], [P2 Q2]) _and and _ps (M, [PQ]) respectively determine the segments representing the minimum distance. in the case segment / segment and point / segment

The second phase will consist of determining the optimal counter. Thus in this part we define the set of functions mentioned above.

The point / segment case is illustrated in Figure 17 and corresponds to

Ψ _P s (M, [PQ])

The goal is to determine the coefficient λ such that: Λe [0, l], V // e [0, l] (X-PQ) M <(μ-PQ) M ^

After putting into equation:

PW = X-PQ

PQ MM '= 0

we obtain four equations for four unknowns:

^X M '~ ^X p ~'^' \ ^X _Q ~ Xp)

z _M , -z _F = X- (z _Q -z _p )

( ^χ _Q - ^X p) - (** ^• - ^χ u) + (y Q -y _P ) - (y M- - y _M ) + ( ^z υ - ^z ,>) - (^ - ^Z M) = °

From which we deduce:

X = ( ^χ _L ) - ^χ p) - ( ^χ ,> -%) + (yo -y _P ) - (yp - y M) + (% - ^Z P) ^• O _f - ^Z M

(x _o - x _p f + (y _o - y _j , f + (z _o - z _p f

In order to ensure the membership of M 'to [PQ] ₁ we saturate the coefficient X, that is to say that if X <0, then we give X the value 0 if X> 1, then we gives f the value 1

The segment / segment case is illustrated in Figure 18 and corresponds

The goal is to determine the coefficients X and μ such that:

/ te [0, l], // e [0, l], V (tf, /?) € [0, l] ² , (XP ₁ Q ₁ ) (MP ₂ Q ₂ ) <(a P ^) (PP ₂ Q ₂ )

After putting into equation:

P ₂ M ₂ = μ P ₂ Q ₂ P ^ Q ₁ -M ₁ M ₂ = O

Υ & ₂ -M ^~ M ₂ = 0

we obtain eight equations for 8 unknowns:

y M, - y ι \ = ^λ <yQ _ï -y ^p) ² _M1 - _P1 = ² ά- (z _{(-z Jι} _Pι) x M ₂ ~ Xp ⁼ ₂ ^ ^{^(x} o ₂ ^{~ X} P ₂₎ y _M1- y _P1 = A- (J _Q1 -y _h )

² _M2 - ² _P2 = A '(z _(Ji- Z _Pi )

(XQ ₁ - ^x n) - ( ^χ M ₂ -XM ₁ ) + (y Q ₁ - y P ₁ ) ^• (y M ₂ -y _Mt ) + ( ² _Ql - ² n) ^• ( ² M ₁ - ² M ₁ ) = ° (XQ ₂ - ^χ p ₂ ) ^• ( ^χ M ₂ - ^χ _M ,) + (y Q ₂ - y P ₂ ) ^• (y M ₁ -> v,) + ( ² Q ₂ - ² P ₂ ) - (% ₂ - ² M ₁ ) = ⁰

From which we deduce:

^ P ₁ P ₁ + ² O ₁ P ₁ ^'2 P ₂ P _X )

in order to ensure the membership of M ₁ and M ₂ respectively to [R ₁ Q ₁ ] and [P ₂ Q ₂ ], the coefficients are saturated! and μ as before.

In the case of the numerical simulation of objects involving several moving objects with respect to each other, it is possible to create a population of pions for each pair of objects. This approach can be adopted in the case where the number n of objects is relatively small, but can be expensive in computing time if the number n of objects is much greater than 2. The invention can be implemented using a single population of N individuals or pions that applies to all the representative geometries of objects present within the simulation.

In this case, the pions of the same population can evolve not only on one of the pairs of geometries contained in the simulation, but on all the pairs of geometries (or meshes) contained in the simulation.

In order to privilege the relevant combinations, however, we do not take into account the pairs of objects that can not come into contact, that is to say in particular rigidly bound objects or very distant.

If we consider the polyhedral case, the genotype of a pion is expressed in the following way, with MeSh ₁ and Mesh ₂ which represent the identification of the meshes (polyhedra) of the objects to which the two points (nucleons) component belong. a pawn :

mesh

Face, α, β.

Mesh ₂

Face ₂ α ₂

P ₂

where the indices Mesh and Face (unsigned integers) respectively represent the identifiers of the polyhedra and faces to which belong the nucleons defining the pion, α _x and β _x the coordinates of the point belonging to the first polyhedron in the base (e ,, e ₂ ) of the face concerned, and respectively for a ₂ and β ₂ in the base (e \, e ' ₂ ). (0 ≤ ₁ ≤ 1, 0 ≤ β, ≤ 1, a ₁ + β ₁ ≤ 1).

The mutators defined previously are not affected by this mode of operation. Inter-geometry "jumps" of the nucleons are performed during the random replacement phase that covers the entire space to be traveled and not just one of the geometries.

The general application of the method to a population of Pioni PiOn ₄ pions covering Meshi to Mesfi4 geometrical representations of objects is illustrated in Figure 19 for case n = 4 and N = 4.

The genotypes of the four pions in the example of Figure 19 are as follows;

Pion _x

The invention is equally applicable to simulations involving polyhedral geometries, which are commonly used in a large number of fields of application such as virtual reality or computer graphics, or to simulations involving non-linear geometries. polyhedral.

The genotypes and mutation operators adapted to polyhedral geometries have already been described in the examples given above. An example of a mutator proceeding to the random replacement of a nucleon 91, 91 'on the facets of a polyhedral structure is shown in FIG.

Some examples of implementation of the invention involving non-polyhedral geometries will be described below.

Figure 21 illustrates the case of objects represented by parametric surfaces (Bézier, B-Spline, ...) called "patch".

In this case, the definition of each of the nucleons of a pion includes the identifier Patchi, resp. Patch ₂ of the parametric surface to which it belongs and the coordinates U ₁ Vi resp U ₂ V ₂ of this nucleon within this parameterized surface Patchi, resp Patch ₂ to which it belongs.

The genotype of a pawn is then the following:

In Figure 21, Mi and M ₂ are the mathematical expressions that respectively define Patchi and Patch ₂ .

As regards the mutators used with parameterized surfaces, it can be noted that the evolution of a nucleon on a parametric surface will consist of stochastically modifying its coordinates within the latter (ie (w, v) => (w + Δ _u , v + Δ _v )). Thus, the choice of the maximum values of the coefficients of variation A _tι and Δ _{v will} condition the type of mutation (exploration or exploitation).

A random repositioning of a nucleon can be done by randomly changing its coordinates. The case of objects represented in the form of point clouds is illustrated in Figure 22 with two representations of objects referenced Nuagei and Nuagβ2.

In this case, to determine the genotype of a pin, one defines each of nucleons by the identifier pi resp p ₂ from the point to which it belongs, as follows:

Cloud, p,

Cloud ₂

As far as mutation operators are concerned, the evolution of a nucleon within a cloud of points will consist of making it jump to the points around the one to which it belongs. For this, it is necessary to limit the computation time to generate in the pre-calculation phase a proximity card similar to that used in the polyhedral case. Setting up a random replacement mutator is trivial. It simply consists in randomly updating the parameters p _x and p ₂ .

Figure 23 illustrates the case of objects represented by voxelic geometries called Geometry and Geometry2.

To define the genotype of a pion, in the voxelic case, each of the nucleons is defined by the identifier υi resp υ ₂ of the voxel to which it belongs as indicated below:

Geometry v, 1 Geometry _^

V _n

However, the previously defined genotype may be unsuitable in some cases (voxels of different sizes or too large). It may then be necessary to enrich the latter with the coordinates of the nucleons within their respective voxel.

In the voxelic case, mutators can be defined as follows; Discrete Exploration: The nucleon moves from voxel to voxel using a pre-calculated proximity map.

Continuous exploration; In the case where the voxels prove to be large, the nucleon can move on the surface of the voxel to which it belongs (stochastic variation of its coordinates within the voxel).

Stochastic Exploitation: Continuous exploration of restricted amplitude.

Deterministic Exploitation: The segment "materializing" the minimum distance between two cubes is trivially deterministically deterministic. Deterministic exploitation thus consists in locally minimizing a pawn within a pair of voxels.

Random Replacement: Random selection of new voxels.

It will be noted that the crossing operator previously defined with reference to polyhedral geometries also proves to be perfectly adapted to all the genotypes proposed with representations in the form of parameterized surfaces, point clouds or voxels.

Figure 24 represents in its generality the crossing operator to produce from two pawns Géniteuri and Géniteur a child pawn composed of the first nucleon Nucléoni of the pion Géniteur _! and second nucleon Nucleon ₂ the pin ₂ progenitor.

The genotypes and mutators that have just been defined are presented as formalisms adapted to the definition and the evolution of nucleons within the different types of selected geometries.

It may be noted, however, that in the implementation of the method, the evaluation of the quality of a pion is reduced to the evaluation of the Euclidean distance separating the nucleons that compose it.

As a result, it is quite possible to involve within the same simulation geometries of different types and to take into consideration hybrid pions consisting of nucleons of different natures, as illustrated in FIG. example, we see a polyhedral representation "Mesh" of a first object, a representation in the form of cloud of points "Cloud" of a second object, a voxelic representation "Vox" of a third object and a representation in the form of parameterized surface "Patch" of a fourth object, with a first Pioni counter of which the nucleons belong to the geometric representations "Vox" and "Patch", a second piece PiOn ₂ whose nucleons belong to the "Patch" and "Cloud" geometrical representations and a third piece P ₃ whose nucleons belong to the "Mesh" geometrical representations and "Cloud", which translates for these three pawns by the following genotypes:

pawn,

Figure 26 shows in block diagram form an exemplary proximity area identification system between a number P of graphically simulated objects, with P> 2, according to the invention.

This system comprises a memory unit 110 with at least memory areas 111, 112, 113.

A first memory area 111 makes it possible to store data describing the geometry of each of the P graphically simulated objects.

A second memory area 112 stores information representing a connectivity map and defining neighborhood properties within each of the P objects.

A third memory area 113 stores information representing a proximity map and defining the proximity properties within each of the P objects. An initialization module 120 makes it possible to create a population consisting of a set of N pions each defined by first and second points or nucleons respectively belonging to the geometries of one of the P objects and another of the P objects. A display screen 130 allows, if desired, to display the P simulated objects numerically.

A central processing unit 140 comprises at least the following subassemblies 141 to 145;

means 141 for selecting a percentage of the population of the N pions to be subjected to pairwise combat during a session of a tournament,

comparison and calculation means 142 for evaluating during a session of a tournament, for each pair of pions subjected to a fight, the quality of each of the pieces of the pair of pions based on a criterion of 'aptitude,

marking means 143, for identifying at each session of the tournament which pieces of a pair of pawns submitted to a fight have won, and which pieces of said pair of pions subjected to a fight have lost, means for iteration 144 to produce an evolution of the pawns that have undergone at least one fight,

an extraction module 145 for retaining only the best pions of the population according to the aptitude criterion, for the determination of the proximity zones between at least two of the P objects. The iteration means 144 are associated with at least one exploratory mutation operator of the pawns having lost during a first session of the tournament, to an operator replacing the pieces having lost during a second session of the tournament by crossing randomly chosen pieces and an operator redefining the pieces that lost during a third session of the tournament.

The reference 150 designates an optional interface such as a haptic interface making it possible to exploit the selected and selected pieces. during the repetitive execution of tournaments and the evolutionary process.

It will be noted that the invention avoids the sorting phases which are time consuming and, by virtue of the independence of the processing of the individuals, allows a process which is highly parallelizable with a possibility of distribution of the calculations on several microprocessors or microcontrollers, as well as for each nucleon of a pion the possibility of moving from one type of object geometry to another, which gives great flexibility of operation. Populations of individuals may include for example a few hundred individuals.

Claims

REVENPICATÏONS

A method of identifying proximity zones between at least first and second digitally simulated objects, characterized in that it comprises the following steps:

(b) creating a population constituted by a set of N individuals called pions each defined by first and second nucleons themselves defined as points belonging respectively to the geometries of each of the first and second objects,

(f) repeating steps (c), (d) and (e) again, and (g) Geometric information is extracted on demand from an updated configuration of the pion population during repetitive execution.

2. Method according to claim 1, characterized in that during the step of extracting the geometrical information, the distances between the identified proximity zones are evaluated.

3. Method according to claim 1 or claim 2, characterized in that the data for identifying areas of the space describing the geometry of at least one of the first and second numerically simulated objects comprise polyhedral representations.

4. The method of claim 1 or claim 2, characterized in that the data for identifying areas of the space describing the geometry of at least one of the first and second numerically simulated objects comprise voxelic representations.

The method of claim 1 or claim 2, characterized in that the data for identifying areas of the space describing the geometry of at least one of the first and second numerically simulated objects comprise representations by surfaces. set.

The method according to claim 1 or claim 2, characterized in that the data for identifying areas of the space describing the geometry of at least one of the first and second digitally simulated objects include point clouds. .

7. Method according to any one of claims 1 to 6, characterized in that the aptitude criterion for evaluating the quality of a pion is constituted by a measurement of the distance separating the first and second nucleons defining this pawn. , the quality of the pawn being all the greater as the measured distance is smaller.

8. Method according to claim 7, characterized in that the measurement of the distance constituting the aptitude criterion for evaluating the quality of a pion takes into account the square of the distance separating the first and second nucleons defining this pawn. .

9. The method according to claim 1, characterized in that it further comprises, after the step (a) of providing data describing the geometry of each of the first and second digitally simulated objects, the following steps:

10. Method according to any one of claims 1 to 9, characterized in that the mutation of the pions having lost during a session of the tournament generating exploratory mutations for the lost pions, consists in moving the first and second nucleons composing a pawn. on the surface of the first and second objects to which these first and second nucleons respectively belong.

11. The method according to claims 3, 9 and 10, characterized in that during the mutation of a pawn having lost during a session of the tournament, generating exploratory mutations for the pawns having lost at least one of the first and second nucleons composing this pion and belonging to one of the first and second objects represented in a polyhedral form is subjected to a succession of discrete center facet displacements in the facet center by considering the information defining the neighborhood properties stored in memory.

12. Method according to claims 3, 9 and 10, characterized in that during the mutation of a winning pawn during the tournament, at least one of the first and second nucleons composing this pawn and belonging to one of the first and second objects represented in a polyhedral form is subjected to displacement on the same facet on a disc having as a center the initial position of this point and for radius a maximum displacement amplitude which depends on the area of the facet on which is made the move.

13. The method of claims 3, 9 and 10, characterized in that during the mutation of a winning pawn during the tournament, at least one of the first and second nucleons component pion and belonging to one of the first and second objects represented in a polyhedral form is subjected to a "wormhole" displacement from one vertex of one facet to another vertex close to another facet which is not necessarily connected, considering the information defining the proximity properties stored in memory.

14. Method according to claims 3, 9 and 10, characterized in that during the mutation of a winning pawn during the tournament, the first and second nucleons composing this pion and respectively belonging to the first and second objects each represented in one polyhedral shape with triangular facets, are positioned such that they delimit a segment defining the minimum distance between the two triangular facets to which these first and second nucleons respectively belong.

15. Method according to claim 1, characterized in that during the replacement of a pawn having lost during a session of the tournament generating for the pions having lost substitutions by crossing randomly chosen pions, to define the new pawn resulting from the crossing of first and second randomly selected pions, the new pion is considered to be composed of the first nucleon of the first randomly selected pawn and the second nucleon of the second randomly chosen pawn.

16. A method according to any one of claims 1 to 15, applied to a set of P objects simulated numerically with P> 2, characterized in that it comprises the following steps:

(a) provides data describing the geometry of each of the P graphically simulated objects,

(d) after the tournament, an exploratory mutation of the pawns having lost during a first session is carried out, the pions which have lost during a second session are replaced by crossing randomly chosen pions and a random redefinition of the pions is carried out. pieces having lost during a third session, (e) for the exploitation of the pieces to be used to determine zones of proximity between two of the P digitally simulated objects, one considers only the population of the victors of the combats,

(f) repeating steps (c), (d) and (e) again, and (g) geometric information is extracted on demand from an updated configuration of the pion population during repetitive execution,

Method according to claim 16, characterized in that the data for identifying areas of the space describing the geometry of the digitally simulated objects P include polyhedral representations, and that the method further comprises, after the step (a) of providing data describing the geometry of the digitally simulated P objects, the following steps:

(a1) creating a connectivity map containing information defining the neighborhood properties between geometric elements within each of the P objects and storing in memory the information of this connectivity map, (a2) creating a proximity map containing information defining the proximity properties within each of the P objects and the information of this proximity card is stored in memory.

18. System for identifying proximity zones between a number P of objects simulated numerically with P> 2, characterized in that it comprises:

(a) first memory means (111) for storing data describing the geometry of each of the P objects,

(b) an initialization module (120) for creating a population constituted by a set of N individuals called pions each defined by first and second nucleons themselves defined as points respectively belonging to the geometries of one of the P objects and another of the P objects,

(c) a central processing unit (140) comprising at least: (cl) means (141) for selecting a percentage of the population of the N pions to be subjected to pairwise combat during a session of a tournament,

(c2) comparison and calculation means (142) for evaluating during a session of a tournament, for each pair of pawns submitted to a fight, the quality of each of the pieces of the pair of pions from 'an aptitude criterion,

(c3) tagging means (143) for identifying at each session of the tournament which pawns of a pair of pawns in combat has won, and which of the pawns of said pair of pawns in combat have lost,

(c4) iteration means (144) for producing an evolution of the pions which have undergone at least one combat, said iterative means (144) being associated at least with an exploratory mutation operator of the pions having lost during a first session of the tournament, to an operator replacing the pieces having lost during a second session of the tournament by crossing randomly chosen pieces and to an operator of redefinition of the pieces having lost during a third session of the tournament, and (c5) a module of extraction (145) to retain only the best pions of the population according to the aptitude criterion, for the determination of the proximity zones between at least two of the P objects.

19. System according to claim 18, characterized in that it further comprises

(a1) second memory means (112) for storing information representing a connectivity map and defining the properties of the neighborhood between geometric elements within each of the P objects, (a2) third memory means (113) for storing information representing a proximity map and defining the proximity properties within each of the P objects.

20. System according to claim 18, further comprising a display screen for viewing digitally simulated objects.

21. System according to claim 20, characterized in that it further comprises a haptic interface (150).

22. System according to any one of claims 18 to 21, characterized in that the central processing unit (140) comprises a set of calculation units operating in parallel.