FR2927449A1 - TRACE OF POLYGONAL LINES - Google Patents

Abstract

A method of drawing a polygonal line of a digital image from an ordered 2D or 3D set of vertices. For at least one given vertex (An) following a first neighboring vertex (An-1) and preceding a second neighboring vertex (An + 1) of said ordered set, a point (Bn) associated with the given vertex is determined, said associated point being located at a fixed distance from a straight line corresponding to the first neighboring vertex and the given vertex, and situated at the same fixed distance from a line corresponding to the given vertex and the second neighboring vertex, the point associated with the vertex being selected using the scheduling of the set of vertices. An ordered sequence of triangles is defined, the vertices of said triangles being defined at least according to the vertices of the set and the associated point, and the surfaces of the triangles of the ordered sequence of triangles are displayed.

Description

The present invention relates to the field of digital display of three-dimensional surfaces, and in particular to the drawing of polygonal lines. The invention is more particularly suitable for embedded applications, for example digital mapping, on mobile terminals, for example mobile phones, PDA or PDA etc. Such applications are for example implemented in mobile terminals able to communicate with a server. There are several ways to display a three-dimensional object on a screen. For example, you can display the texture of the surface of the object. The wired representation (or wireframe in English) allows a better visualization of the relief of the surface of the object. Of course, one can display both the structure via a wired representation, and the texture. A wired representation of a three-dimensional surface can be obtained by simply plotting the display primitives, whether triangles or quadrilaterals, for example. However, display primitives may include more complex polygons. For example, a football can be broken down into hexagons, a quadrilateral house, a mountain of arbitrary polygons. Display primitives can be coplanar or not coplanar. Also, it may be desirable to display other types of polygonal lines, such as open polygonal lines, to allow for viewing of roads for example. When the display is performed on a terminal in communication with a possibly remote server, the terminal receives display data from the server, and processes this data to be able to display the three-dimensional surface corresponding to these data. The display data typically includes the vertex coordinates of the display primitives, so that their transmission requires relatively little bandwidth.

When a polygon has four points or more, this polygon may not be coplanar. Some terminals relatively poor in memory and / or compute resources are unable to display non-coplanar polygons and are configured to process only triangles. For example, for a set of three point coordinates forming a triangle, a mobile phone is able to calculate the plane passing through the three points and display the part of the inner plane to the triangle. In addition, certain applications in mobile terminals for tracing three-dimensional surfaces, for example 3D graphics programming interfaces (APIs), are designed to make plots only from strip and / or fan triangles. An ordered set of strip triangles is such that each triangle of the set, starting from the second triangle in the order of the ordered set of triangles, has two vertices of the preceding triangle and a new vertex distinct from the vertices of the preceding triangles. . An ordered set of fan triangles is an ordered set in strip in which there is a vertex common to each of the triangles. Thus some applications are able to display only the internal surfaces of triangles, which in addition must sometimes be organized in strip and / or fan. It would be desirable to be able to display a polygonal line plot using these applications relatively poor in memory and / or compute resources. According to a first aspect, the subject of the invention is a method of drawing a polygonal line of a digital image, starting from an ordered 2D or 3D set of vertices, comprising the following steps, for at least one vertex given along a first neighboring vertex and preceding a second vertex adjacent to this ordered set: a / determining a point associated with the given vertex, this associated point being located at a fixed distance from a line corresponding to the first neighboring vertex and the given vertex , and located at the same fixed distance from a line corresponding to the given vertex and the second neighboring vertex, the point associated with the vertex being selected using the scheduling of the set of vertices, b / defining an ordered sequence of triangles, the vertices of these triangles being defined at least according to the vertices of the set and the associated point, c / displaying the surfaces of the triangles of the ordered sequence of triangles. Thus, the polygonal line is drawn through the display of triangles surfaces. A terminal relatively poor in memory and / or computation resources, able to display only the internal surfaces of triangles, is thus able to make this plot. The associated point is selected taking into account the order of the vertices. The associated point may be on one side or the other of the broken lines defined by the vertices in the order of these vertices in the ordered set. The coordinates of the vertices and the points can for example include a latitude, a longitude and an altitude in a repository (X, Y, Z), or other. The fixed distance may be one pixel for example, but any other distance value is possible. Advantageously, a vector associated with the given vertex, said normal vector, is defined and first and second projected are determined by orthogonally respectively projecting respectively the first and second neighboring vertices on the plane passing through the given vertex and orthogonal to the associated vector. The straight line of step a / corresponding to the first neighboring vertex and the given vertex passes through the first projected and the given vertex, and the right of step a / corresponding to the given vertex and the second neighboring vertex passes through the vertex given and the second projected. Thus, the associated point belongs to a tangent plane, which may be more relevant than the plane defined by the given vertex, the first neighbor vertex and the second neighbor vertex.

For example, in the case of an ordered set of vertices corresponding to a road, it may be wise to choose a normal vector in a fixed direction, typically the vertical direction. In another example, the vector associated with the given vertex is obtained from vertices located in a neighborhood of the given vertex. The tangent plane to which the associated point belongs is defined by the neighborhood of the given vertex. The vertices in this neighborhood may include other vertices than the first neighboring vertex and the second neighboring vertex. Of course, the invention is not limited by this projection step in a plane orthogonal to a normal vector. The right of step a / corresponding to the first neighboring vertex and the given vertex can pass through the first neighboring vertex and the given vertex, and the right of step a / corresponding to the given vertex and the second neighboring vertex can pass by the given summit and the second neighboring summit.

It can be predicted to determine a midpoint of the segment having as ends the given vertex and the point associated therewith; and a symmetrical point of the midpoint is determined with respect to this given vertex. The vertices of the triangles of the ordered sequence of triangles include this midpoint and the symmetrical point.

Thus, the line to trace covers the segments connecting the vertices of the ordered set. In particular, this embodiment can be interesting in the case of an open line, for which there is no particular reason to draw the line on one side or the other of the segments. Advantageously and non-limitatively, for each vertex of a plurality of vertices of the set, a respective point is associated according to step a /; and the vertices of the triangles of the ordered sequence of triangles are defined at least according to the vertices of the set and the associated points. Advantageously and in a nonlimiting manner, each triangle from the second triangle according to the order of the ordered sequence of triangles comprises two vertices of the triangle which precedes it in the order and a distinct vertex of the vertices of this triangle which precedes it.

The vertices of the triangles of the ordered sequence advantageously include, but are not limited to, the vertices of the set and the associated point (s) determined according to step a /. According to another aspect, the subject of the invention is a module adapted for drawing a polygonal line of a digital image, from an ordered 2D or 3D set of vertices, comprising: calculating means for determining an associated point (Bn) at a given vertex (An) of the ordered set, this associated point being located at a fixed distance from a straight line corresponding to the preceding vertex (An_I) in the ordered set the given vertex and at the vertex given, and located at the same fixed distance from a straight line corresponding to the given vertex and the next vertex (An + 1) in the ordered set the given vertex, the point associated with the given vertex being selected using the scheduling of the set of vertices; means for defining an ordered sequence of triangles, the vertices of said triangles being defined at least according to the vertices of the ordered set and the associated point. means for displaying the surfaces of the triangles of the ordered sequence. This module makes it possible to implement the method according to one aspect of the invention. The display means may for example comprise a graphical interface suitable for 3D plotting of surfaces by means of strip triangles which are indicated to it by the ordered sequence of the vertices of these triangles. The module may comprise or be part of a terminal in communication with a server. The terminal receives data from the server, for example coordinates of the vertices of the ordered set. The data can be prioritized in different levels of precision.

According to yet another aspect, the subject of the invention is a computer program comprising instructions for implementing the steps of a method according to an embodiment of the invention, during execution of the program by means treatment.

Other features and advantages of the invention will become apparent on reading the description which follows. This is purely illustrative and should be read with reference to the accompanying drawings in which: FIGS. 1A and 1B show two ordered sets of vertices and the plots corresponding respectively to these sets; FIG. 2 represents a polygon with holes; FIGS. 3A and 3B show two types of line plots obtained from sets of vertices arranged in opposite directions to each other; FIG. 4 illustrates a polygon line drawing method according to one embodiment of the invention; FIG. 5 represents a series of triangles that can be used in one embodiment of the invention. FIG. 6 illustrates a polygon line drawing method according to another embodiment of the invention; In one embodiment, the contour plot of a polygonal primitive is considered. For reasons of clarity of representation, it is better to assume the coplanar polygons. Nevertheless, the drawing method applies under any circumstances, for example for different faces of any polyhedron. The mode of drawing polygons depends essentially on the order of the vertices. Indeed, Figures 1A and 1B show that the plot of the ordered set (A, B, C, D) does not coincide with the plot of the set (A, B, D, C). Of course, the plot of the ordered set (A, B, C, D) where the vertices are given in the clockwise (or indirect) direction and the plot of the ordered set (D, C, B, A) where they are given counterclockwise (or forward direction) are similar. Similarly, the plots of the ordered sets (A, B, C, D) and (B, C, D, A), where the vertices are shifted by one position correspond to similar quadrilaterals. By convention, one can differentiate the polygons according to their orientation. Such a convention makes it possible to determine without ambiguity the areas to be filled and those to be emptied. It allows to define generalized polygons or polygon "with holes". Figure 2 illustrates the case of such a generalized polygon simply defined from two differently oriented quadrilaterals. The orientation used for filling intervenes for the drawing of a delimitation zone between the meshes, called wireframe in English. Such a contour in the form of a strip must not exceed the polygon "with hole" so that the faces of an object coincide edge to edge. FIGS. 3A and 3B show delimitation zones obtained for sets of vertex coordinates comprising the same vertices, but in reverse order of each other. Two orthogonal square faces are represented and the delimitation zones, or outlines, in the form of strips exceeding (FIG. 3B) or not exceeding (FIG. 3A) faces. We see that when the bands exceed, as in Figure 3B, it affects the readability of the drawing. In other words, the tape must always be inside the faces. In the example of Figure 2, the outline of (A, B, C, D) should be drawn inward while the outline of (E, F, G, H) should be drawn out. In both cases, the contour should be drawn to the indirect normal to the contour. Closed Polygon In the case, first of all, of a polygon of the space defined by the ordered set (A o, • • • • .4N-1) where N> 3, for the sake of simplification, we arbitrarily assumes that all vertices are cyclically extended. In other words, we write Ao = AN, A-1 = AN-1 and more generally T "Z. An + w ù An_ Then we consider the three consecutive points of the polygon An-1, An and = ~ n + 1 around a given vertex An. As (.Ao, • • •, -AN-1) defines a polygon, we know that AA, and AnAn + 1 are not collinear. We now see in + 1 / 2 the vector 'n`-tn + I / • -tn + 1An- Therefore, the three consecutive points around An define a plane with the base consisting of the vectors in-1/2 and in + 1/2. The meaning of these vectors derives from the ordering of the vertices in the ordered set of vertices, the objective being to determine the point Ba associated with the point An so that the polygon (Ba ... 'BN-1) is exactly at a distance of one pixel from the polygon (Ao, -, .A N-1) in accordance with FIG. 4. We place ourselves in the reference defined by the point Aa and the vectors

: n-1, 2 and iin + 1 f2 We note xi, and yn the coordinates of Bn in the reference then the vector An Bn. Therefore, it is checked: = snlln-1, + 2 + YnUn + 1 f2 The distance condition of a pixel is written using the equations: 1 = d ([An_1, An], Bn) = 11 n-an-1/2 '/ en-1 / 21I = II' n-1/2 + Ynt = n + 1/2 - (mnjin-1/2 + Yniin + 1/2, iin-1/2 / t1n-1 / 2II IIrni1'n-1/2 + Yni1n + 1/2 n-1/2 + tln-1/2) tin-1/2 - Yn (5n + 1 / 2.21n_1 / 2) 1 / 2Il = IIYnitn + 1/2 - Un + itn + 1/2 'Un_1 / 2;) iin-1 / 2II = lYnl X Iliin + 11`2 i'n + 1/2 / iin-1 / 2Il 1 = d1 [An, An + 1], Bn)

15 = I.Cnl x Il iln-1/2 - (1n-1 / 2.2 / n + 1/2 / 11n + 1 / 2Il.) A first refinement of the coordinates of Bi is deduced in the reference: rn = II1 [n-1/2 - ;, ten-112 21n + 11'2% i1n-1-1 / 2Il and Jn IIi0n + lj2 - \? ln_1 / 2, idn + 1/2 ~} tln - 112II Indeed we logically find four solutions corresponding to the four half-bisectors of the angle defined by the three points in the plane, and we then impose a condition using the order of the set of vertices: the point Bn must be the indirect norm of the vectors Un-1/2 and he, 1 to 2 The condition of orientation towards the indirect norm is written using the determinants:

I1 .Tn det (t1n-1/2, t'n) = 0 Un = + end> 0 and det • (tln + 1 f2, en) = = ùSn `i0 We deduce the exact coordinates of Bä in the reference: .C, y = Ilrtn-1/2 ù {.? Gn-1/2, a + 1/2) ttn + 1 / 2II and yn = + Ilttn + 1/2 ù (in-1/2 ttn) +1/2 Finally, to draw the outline, it is enough to pass the ordered list (BO, AO, ..., BN-1, AN-1, BO, A0) in strip or strip An ordered sequence of triangles is then defined ((Bo, Ao, A1), (Bo, B1, A1), (Al, B1, A2) ...) from the vertices of the ordered set and the points associated with these vertices. continuation is represented on the

Figure 5. Then the surface of each triangle of the ordered sequence is displayed, according to a known method.

Open polygonal line In this embodiment, the plot of a path represented by an open polygonal line is considered. The principle of the process is substantially identical to the framing of the polygons. However, it is best if the path is not affected by the orientation of the path. In addition, the process is slightly different for the first point and the last point. We first consider a polygonal line of the space defined by the ordered points (.4o, •

• .4 -1) where N> 2. In the polygon frame, the point Bä is calculated in the plane defined by the three consecutive points around An. For points Al, AN-2, it is possible to use to the process described above. However, this is not the case for the points Ao and AN-1 since the polygonal line is open, it is not possible to define cyclically the points A-1 and AN. Consequently, this method does not make it possible to calculate the coordinates of points Bo and BN-1. DTD: The embodiment described uses a normal vector, for each vertex at which a point is to be associated. An example of a normal vector choice is described below. Let an ordered list of normal vectors (No, •. • -1). For indexed points n such that 0 <n <N - 1, the points An_1 and An + 1 are well defined. We call consecutive points around An orthogonal to A'n the points t`in.n-1-An.n and An, n + 1 defined as the orthogonal projections of tn-1 An and An + i on the plane Tn passing through An orthogonal to, \ 'n. We can notice on the one hand that the point An, n coincides exactly with the point An whatever the vector gn. On the other hand, we can notice that the points An, n1 and An, n + 1 coincide with the points An_i and An-0 if the vector, \ 'n is orthogonal to the plane (.-L-1, An, An + 1). We can now calculate the point Bn.n from the three consecutive points Ann - 1. An.n and An, n + 1, according to the method described above in the context of drawing the line of a closed polygon. We can finally notice that the point B ,,,,, coincides exactly with the point Bn if we take for example as A'n vector the vector product Anù1An x -AnAn + i To avoid a plot affected by the orientation (possibly arbitrary ) of the path, the point Cn is defined as being the middle of the segment [An, Bn.n] and the point Con is defined as being the symmetry of Con with respect to An, as illustrated in FIG. 6, which amounts to from a computational point of view, to: 1 nBn.n and AnCn = ùAnBn, n • AnCn + = To overcome the problem of the extremities, one specifically defines Co and Co-. Thus, the vectors 1oCQ and .tr, are the semi-unitary vectors of the plane Po directly and indirectly orthogonal to: -10: -11. We can notice that they can be deduced almost directly from the vector product AQA 1 x Nô One defines in the same way the points C ^ 7-1 and CN-1 Finally to trace the path, it is enough to pass the ordered list (( For example, it is important to note that passing the inverted list in the CULLING_NONE mode will give the same result, but with this process it is sufficient to choose the most suitable normal vectors. For example, the pavement of a road being horizontal, it is therefore sufficient to always take the same normal vector k = (1, 0.0), (0,1,0) or (0,0,1) according to the conventions. Of course, it is also possible to define an associated vector, called "normal vector", at the vertices of an ordered set corresponding to a closed polygon.This taking into account of the normal vector makes it possible to place the associated point Ba in a plane more the plan defined by the vertices An_1, An, An + 1. oordonnées vertices useful pseudo-wired representation of polygons or paths are relatively inexpensive in computing time.

Normal Vector To represent "volumes" using 3D libraries (eg "OpenGL", "Direct3D" or "M3G"), the notion of normals can be used. Normal is defined locally. The tangent plane TMO (S) to a surface S at a point MO is the plane passing through MO which best approximates S in the neighborhood of MO. A vector g is said to be "normal" to a surface S at a point MO if it is orthogonal to the tangent plane TMO (S). The cases mainly considered are the following ones: • If the surface is a sufficiently regular submanifold of which one knows a local parametrization: M (s, t) = (x (s, t), y (s, t), z ( s, t)) such that MO = (x (0, 0), y (0, 0), z (0, 0)) then we get 1-2tiro (8) = (Mo; z ') with: cl û =: - (0,0) eté = r ~ _1 (0,0). Os vt It is then easy to deduce a direct normal vector by calculating the vector product g = é_ • If the surface S is a sufficiently regular submanifold of which one

knows a local equation: F (x, y, z) = 0 such that MO = (xO, yO, zO) (3) then we obtain a direct normal with: = (F (r0, y °, o), where (XQ, yO, ° 'o), ù (ro, ya, y 4 The notion of normality generally makes it possible to define how the

light must be reflected on the surface of the volume considered. Intuitively, it will be considered that the light can be effectively reflected orthogonally to the surface. Nevertheless, things are often more complex: • On the one hand surfaces are generally defined as

assemblies of triangles in space. To calculate a normal at a point, we can calculate the average of normals to the triangles to which the point belongs. Equivalently, this amounts to calculating the discrete derivative. • On the other hand, the surfaces considered are not necessarily

discretizations of regular subvarieties. Thus, even a very simple building of the shape of a parallelepiped is not necessarily regular at its edges. This results in different shades on both sides of the edges. For the drawing of surfaces with 3D libraries, this amounts to defining as many different normals on both sides of the edges for a

same summit. Indeed, if a building can not be seen as a regular subvariety, it can be seen as an assembly of regular subvarieties called faces. For a vertex belonging to two faces, the wire is calculated. normal to each of the faces and we attribute the "good normal" according to whether we consider that the vertex belongs rather to one face or rather to the other. For example: • A sphere consists of a single regular subvariety. Therefore for each point of the sphere, we define a single normal which coincides exactly with the direction of the ray passing through this point. • A cube consists of an assembly of six regular subvariety faces (six square faces). Each vertex of the cube belongs to three faces, in other words each vertex appears three times differently to build the cube. We must associate with each vertex a different normal depending on the face we are building. • The cylinder consists of an assembly of three regular subvarieties (two disc bases and a rectangle). Each point of the cylinder's edge belongs to a base and to the rectangle, in other words each vertex appears twice differently to build the cube. Again, we must assign each vertex a different normal depending on the face we are building. The use of normals is standard in all 3D display libraries. The choice of one or more normals per vertex depends on the regularity of the surface. When the surface is decomposed into polygonal display primitives, the notion of regularity depends on the choice of the developer. In order to highlight a "volume", one often has to draw the wireframe representation. In general, it is simply a matter of drawing the edges of the display primitives. In mobility applications, the only display primitives are triangles organized into bands ("triangle strip") under M3G, around a center ("triangle fan") or independent of each other ("triangles") under OpenGL or Direct3D. However, displaying all the edges of all triangles is not only not necessary but also resource intensive. In some cases, if the display primitives remain definitively triangles, the logical primitives or "faces" can be more complex polygons: • Case of the cube: one is led to consider its faces which are squares which will be then decomposed into triangles for the plot. Nevertheless, to obtain a satisfactory wire representation, it suffices to draw the edges of each square rather than those of the triangles. • Case of the classical approximate decomposition of a sphere: in hexagons as for a football. The logical primitives are the hexagons which will then be broken down into triangles for the plot. In this case, it is sufficient to draw the edge of each hexagon to have a satisfactory wire representation of the sphere. • Case of the approximate decomposition of a cylinder: each base is a regular polygon and the height band is a succession of rectangles. It suffices to draw the outline of the two bases and the contours of the rectangles to obtain a suitable wire representation. Following the principle of pseudo-wired representation, the lines are drawn in the form of bands of unit width. Nevertheless, if a strip has a width, it has no thickness, since it is the drawing of a two-dimensional object. In other words, depending on the point of view adopted, the band will be or will not be visible (a band observed on the "slice" is not visible). It is therefore necessary to draw enough bands so that they are connected to each other and a line is visible regardless of the point of view where the edge is actually observable. To draw the edges, we rely on the same principle as the normals of light. The pseudo-wired representation of an edge must be optimally visible when looking at the edge of the face. It is therefore necessary to draw the band in the plane orthogonal to the normal. When it comes to drawing a path in the general sense of the term (pedestrian path, road, etc.), they can also be seen as bands of width not necessarily unitary around a polygonal guideline. The method described above allows to trace such paths. Nevertheless, it remains to determine the good normals to determine the planes in which to draw the bands. It is quite realistic to impose the band to be locally in the horizontal plane, especially in the case of a road since the roads are generally substantially parallel to the ground. Visible bands are then obtained optimally from above. However, if the path is on the ground or on any other surface, then it may seem more appropriate to introduce a parameterization of this surface. Each point of the path must be associated with the normal from the point and orthogonal to the surface. The path then marries the shape of the surface that supports it. The use of normals is based on the topology of the surface to be plotted. The coordinates of the vectors associated with the vertices, called "normal", can also be received from a server with the coordinates of these vertices. In general terms, it is possible to provide a method of drawing a polygonal line of a digital image, starting from an ordered 2D or 3D set of vertices, comprising the following steps, for at least one given vertex of this set: determining a point associated with that given vertex, the associated point being located at a fixed distance from a line corresponding to the given vertex and another vertex of the ordered set, the given vertex and the other vertex being consecutive in the ordered set, defining an ordered sequence of triangles, the vertices of said triangles being defined at least according to the associated point. Thus, it is possible to use a method of displaying surfaces of triangles to draw the polygonal line. The other vertex can follow or precede the given summit.

Other constraints may be imposed on the associated point. For example, a neighboring first and second vertex framing the given vertex in the ordered set may be considered. The associated point may for example be determined so that it is located at the fixed distance from a line corresponding to a first neighboring vertex and the given vertex, and located at the same fixed distance from a line corresponding to the vertex given and at the second neighboring summit.

For a given vertex, it can be expected to determine more than one associated point. For example, two associated points, symmetrical with respect to each other, are determined, such as points CN-1 and GN-ID in FIG. 6. The ordered sequence of triangles can then comprise only triangles whose 5 vertices are associated points. Alternatively, we can predict that for two consecutive vertices (the given vertex and the other vertex) of the ordered set of vertices, we choose the point associated with one of these vertices (the given vertex) so that: the line passing through this associated point and this vertex is perpendicular to the straight line passing through the two consecutive vertices, the associated point is at a fixed distance from this vertex, the associated point is selected using the ordered set ordering of vertices. Such a method can be applied in particular to determine the point associated with a vertex corresponding to an open polygonal line end. One can also choose to apply this method to the other vertices of the ordered set. A vertex is then associated with one or two points, which multiplies the number of triangles of the ordered sequence of triangles. In general, the invention is not limited by the way in which the associated point is determined.

Claims (9)

A module adapted for drawing a polygonal line of a digital image from a 2D or 3D set of vertices comprising - computing means for determining an associated point (Bn) at a given vertex (An) of the ordered set, said associated point being located at a fixed distance from a line corresponding to the preceding vertex (An_1) in the ordered set to the given vertex and to the given vertex, and located at the same fixed distance from a straight line corresponding to the given vertex and the next vertex (An + 1) in the ordered set the given vertex, the point associated with the given vertex being selected using the set of vertices, means for defining an ordered sequence of triangles, the vertices of said triangles being defined at least according to the vertices of the ordered set and the associated point. means for displaying the surfaces of the triangles of the ordered sequence. 20 2. A method implemented by means for processing, drawing a polygonal line of a digital image on a screen of a terminal, from an ordered 2D or 3D set of vertices, comprising the following steps, for at least one given vertex (An) following a first neighboring vertex (An_.) and preceding a second neighboring vertex (An + 1) of said ordered set: al determining a point (Bn) associated with the given vertex, said associated point being located at a fixed distance from a straight line corresponding to the first neighboring vertex and the given vertex, and located at the same fixed distance from a straight line corresponding to the given vertex and the second neighboring vertex, the point associated with the vertex being selected using scheduling the set of vertices, b / defining an ordered sequence of triangles, the vertices of said triangles being defined at least according to the vertices of the set and the associated point, and cl displaying the surfaces of the triangles of the s an order of triangles on the terminal screen. 3. A method of drawing a polygonal line according to the preceding claim, further comprising the step of: defining an associated vector (Na) at the given vertex (An) and determining first (An, n_1) and second (An n + 1) projected by orthogonally respectively projecting the first (An_1) and second (An + 1) neighboring vertices on the plane (Pn) passing through the given vertex and orthogonal to the associated vector, and in which, in step a1: the line corresponding to the first neighboring vertex and the given vertex passes through the first projected and the given vertex, and the line corresponding to the given vertex and the second neighboring vertex passes through the given vertex and the second projected. 4. The method of claim 3, wherein the associated vector (Ç '') at the given vertex (An) is obtained from vertices located in a neighborhood of the given vertex. 5. A method according to any one of the preceding claims 2 to 4, wherein the step of determining a midpoint (C • â) of the segment having for its ends the given vertex (An) and the point is determined. (Bn, n) associated with it; and determining a symmetrical point (~ f72) of the mid point with respect to said given vertex; the vertices of the triangles of the ordered sequence of triangles comprising said midpoint and said symmetrical point. 6. Method according to claim 2 to 5 wherein, for each vertex of a plurality of vertices of the set associates a respective point according to step a /; and the vertices of the triangles of the ordered sequence of triangles are defined at least according to the vertices of the set and the associated points. 7. Method according to any one of claims 2 to 6, wherein each triangle from the second triangle in the order of the ordered sequence of triangles, has two vertices of the triangle preceding it in said order and a distinct vertex of vertices of said triangle which precedes it. 8. Method according to any one of claims 2 to 7, wherein the vertices of the triangles of the ordered sequence comprise the vertices of the set and the associated point (s) determined according to the step a /. 9. Computer program comprising instructions for implementing the steps of a method according to one of claims 2 to 8 during execution of the program by processing means.