FR2693012A1 - Visualisation procedure for synthetic images of volumes in real=time - by maintaining database of data relating to topological, geometric and photometric attributes of volumes in order to represent them as polyhedrons revealing hidden surfaces and to project images in two dimensions - Google Patents

Abstract

The procedure involves using database which represents the volumes as polyhedrons. The database comprises the topological attributes of their sides, the spatial coordinates of the extremities of these sides and the geometric and photometric attributes of their faces. This data is used to eliminate the hidden surfaces of the polyhedrons, to effect an alteration in the references of the faces to be revealed and to eliminate all obstructions between the observer and the front plane of truncation. It is also used to put the revealed surfaces into perspective in order to project them in two dimensions and to effect a vectorial truncation in two dimensions according to a pyramid of projection. ADVANTAGE - Avoids need for specialised processors and is simple to apply.

Description

i

IMAGE VISUALIZATION METHOD

  SYNTHETICS OF REAL-TIME VOLUMES

  The present invention relates to a method of

  s visualization of synthetic images of volumes in real time.

  A real-time synthetic image generator (that is,

  at a rate of at least 25 frames per second) has at least three types of computation stages: a geometric processor, a sampling processor, and a video processor. The computational power required for the real-time calculation is such currently used for each type of stage, a dedicated processor (specialized) Such a solution is expensive and when the structure is defined and realized, it is very difficult or impossible to change without changing a processor or

1 S even all processors.

  The subject of the present invention is a method for visualizing synthetic images of volumes in real time, which does not require for its implementation of specialized processors,

and that is simple to apply.

  The method according to the invention consists in storing in a database the data describing the volumes to be represented in the form of any polyhedra from their oriented sides, these data being the topological attributes of the sides of the polyhedra, the coordinates in the space of the extremities of these sides, and the geometrical and photometric attributes of the faces of these polyhedra, to eliminate the self-concealed faces of these polyhedra, to make a change of reference of the faces to be visualized, to eliminate all the objects situated between the observer and the truncation plane before, to put into perspective for projection in two dimensions, and to perform a truncation

  two-dimensional vector following a projection pyramid.

  This vector truncation is carried out for each of the planes delimiting the said polyhedra, and for each of these plans, it is carried out

  a truncation on each side of the faces of the polyhedra.

  The truncation and change of reference calculations are organized in a vectorial way so as to obtain the maximum performances, and allow an efficient parallelization of the

  calculation method used by the invention.

  The present invention will be better understood on reading

  the detailed description of an embodiment, taken as a

  non-limiting example and illustrated by the accompanying drawing, in which: Figure 1 is a schematic perspective view of an object to be viewed, which has been shown topological structure describing it; FIGS. 2 to 5 are schematic views of faces of an object to be displayed, used to define the conventions used for the

topological description of objects;

  Figure 6 is a table summarizing the data used by the method of the invention; Figure 7 is a schematic view of faces of an object, explaining how to determine self-hidden faces; Figure 8 is a schematic perspective view showing a truncation pyramid; Figure 9 is a diagram explaining a process of putting into perspective that can be implemented by the method of the invention; and FIG. 10 is a schematic perspective view showing a

  standardized truncation volume, used by the method of the invention.

  FIG. 1 schematically shows a topological structure 1 describing any object, which will be referred to below as "hyperfacette". This structure is composed of adjacent flat faces (facets) which correspond as closely as possible to the faces of the object. to represent Of course, if the faces of the object to be represented are plane, the correspondence is exact, but if they are curved, the correspondence is better as the facets of the structure are small Such a representation by polyhedra is based on the method described by BG BAUMGART in the article "A Polyedron Representation for Computer Vision", National Computer

Conference, 1975, pp. 589-596.

  A "hyperfacette" is described, in a database, by an unordered list of sides. Each side is characterized by its two ends (called "points"), its two adjacent faces 1 o (or its adjacent face), and its links with other sides. FIG. 1 schematically shows a hyperfacette 1 A flat facet of the hyperfacette 1 is referenced 2 This facet 2 is bordered by four sides referenced 3 to 6 The sides 3 to 5 are shared by two different facets They are said to be "shared" Note that one side can not be shared by more than two facets Only side 6 is not shared by two facets; so it belongs to the edge of the object figured by

the hyperfacette 1.

  A point is always shared between at least two sides.

  If a point was the end only on one side, the side bordered by this side would not be closed, which is forbidden for a topological structure Thus, for example, in structure 1, point 7 is shared by the sides 3, 6 and 8 (it constitutes one of the ends of

  each of these sides The point 9 is shared by the sides 10 and 1 1.

  According to another convention, the sides of the facets are oriented. One side of a point P1 is oriented towards the point P 2. FIG. 2 shows such a side 12 divided by two faces 13, 14, and the normals 15 are shown. , 16 to these faces (by convention, these normals are directed towards the outside of the object to be represented) The faces 13 and 14 are respectively called left face and right face The sides of the faces 13 and 14 sharing the point P1 are referenced 17, 18 and called respectively upper left side and upper right side The sides of the faces 13, 14 sharing the point P 2 are referenced 19, 20 and respectively

  called lower left side and lower right side.

  According to the convention, two faces having a shared side must be oriented in the same way: their normals must point to the same half-space inside or outside the object of which these two sides are part. This rule facilitates the graphic processing of the object: two faces having a shared side can not mutually occlude, while an elimination of the hidden parts would be necessary if this rule was not respected Thus, for example, there is shown in Figure 3 two faces 21, 22 side 23 is not a shared side within the meaning of this rule In fact, the respective normals to these faces, referenced 24, 25 point one to the outer half-space to the object of which these faces, and the other towards the inner half-space to this object In fact, it would have been necessary

  consider the face opposite to one of the two faces 22 or 23.

  FIG. 4 shows an example of a "concave" face 26. A face is said to be concave when at least the extension of one of its sides the cut It is said to be convex in the opposite case Thus, the extension 27 of the side 28 where the

  extension 29 of the side 30 of the face 26 cuts this face.

  FIG. 5 shows an example of a rectangular concave perforated face 31 having four rectangular holes 32 to 35. The extension of any one of the holes 32 to 35 intersects the

face 31, which is well concave.

  FIG. 6 shows a table giving the three

  categories of elements defining the topology of a hyperfacette.

  These elements are the sides, the points (ends of the sides) and the faces of the hyperfacette For each category of elements one defines attributes: for the sides: these are the topological attributes, namely, for each side, the points Pl and P 2 and the left and right faces (or one of these faces if the side is not shared), and the links between sides; for the points: their geometrical attributes, that is to say their coordinates in space (X, Y and Z); and for the faces: their geometric attributes and their photometric attributes The geometric attributes are the equations, in

  space, planes of the faces (of the form Ax + By + Cz + D = 0).

  Their photometric attributes include: their color, their

texture and their transparency.

  A first step of the method of the invention consists in eliminating the self-hidden faces, in order to simplify the treatments

  subsequent geometrical processors.

  When we observe an object, we can not see some faces unless we are in a particular angle of view. We use this property to say that if a face is not oriented in the direction of the observer, it can not be seen by it, and it is then said autocachée In Figure 7, there is shown on the right the position X of an observer and two faces 36, 37, and the normals 38, 39, respectively, to these faces The normal 38 is in the half-space (delimited by the plane of the face 36) seen from X, while the normal 39 is in the half-space (delimited by the plane of the face 37) not seen of X Mathematically, the visibility of a face is determined in the following way: either Ax + By + Cz + D the equation of the face in question and lxo, yo, zo I the position of the observer Si

  Ax O + Byo + Czo + D <O, so this face is auto-hidden.

  When the position of the observer varies, the objects, and in particular their points undergo a change of reference, resulting in a rotation and / or a translation This change of reference is made by a geometric processor according to the following formula, which allows to express the absolute coordinates of each point (xm, Ym, Zm) in the observer's coordinate system (xo, yo, zo) lxol r 11 '12 '13 ml x yo = r 21 r 2 r 23 Ym + ty (1) sZo r 1 12 r FX 1 L_ JL 22 32 33 j Lm, + lt (1 scale factors can be added to this matrix, if any) In this equation, the coefficients r 11 to r 33 relate to rotations and coefficients tx, ty, tz to

  translations These calculations are done in a vectorial way.

  When the coordinates of the points of the objects are calculated in the observer's coordinate system, a truncation is performed in the space, in order to eliminate all the elements between the observer and a truncation plane called the front truncation plane. This plane, perpendicular to the direction of observation, can be between the observer and the projection plane or beyond this projection plane. The facets truncated by the front truncation plane are cut off and then closed by the addition of one side, as described below for 2 D truncation, but here it is done in 3 D If necessary, the same procedure is followed with the rear truncation plane, which is

  example the visibility limit plan (horizon line).

  FIG. 8 shows the observation pyramid 40 relative to an observer 41, that is to say the pyramid whose edges join the observer 41 (supposedly punctual) to the vertices of the projection plane 42. observation Zobs is perpendicular to the plane of projection 42 is shown the clipping plane before 43, generally parallel to the plane 42, located between this

  plane 42 and the observer, and a rear clipping plane 44, located at

  The truncated pyramid of viewing is the portion of the pyramid 40 between the clipping plane 43 and the projection plane 42, or possibly between the two clipping planes 43, 44. also in figure 8 the angles of horizontal view Ox and vertical Oy. Once this "clipping" in three dimensions carried out, one carries out a perspective in order to visualize on the flat screen, thus in two dimensions (2 D), the objects three-dimensional (3 D), while maintaining the visual effect of these three dimensions The simplest projection is that using the Thales theorem, and is illustrated in Figure 9 It shows, in side view, a object 45 (in 3 D) to be displayed on a viewing window 46, the observer 47 supposed to be punctual looking in the direction of view 48 perpendicular to the window 46 or 49 any point of this object The straight line 47 to 49 intersects the window to be at 50 We call Hi and H 2 the respective distances of the points 49 and 50 to the line 48, and L1, L2 the respective distances from the observer 47 to the height Hi and to the window 46 According to the Thales theorem, We have: LI / H1 = L2 / H2 It is therefore easy to determine the location on the screen 46 of the point 50 which is the perspective projection of the point 49 on the screen 46.

  the same way for all the points of the object 45.

  By convention, and for reasons of efficiency, at the same time, we standardize the coordinates xe, Ye of any point of the screen 46:

-1 xe <1 and -1 Ye <1-

  FIG. 10 shows the "normalized clipping volume" defined between the point observer 51 and the normalized screen 52. The aiming direction 53, perpendicular to the screen 52, passes through its center 54 (with coordinates 0, 0 55 to 58 are referenced the middle of the sides of the screen 52, of respective normalized coordinates (0, 1,), (1, O), (0, -1), (-1, O). from point 51 to points 55 to 58 are respectively referenced 59 to 62 The angles formed by the edges 59, 61 on the one hand and 60, 62 on the other hand have a normalized value of 900. To perform the setting in perspective, it is used the following parameters dpp: distance between the observer and the projection screen, H 1/2 half height of the screen, L 1/2 half-width of the screen, e Ox 'L 1/2 Fx = cotéy) = d: normalization factor in x, (Oy '11/2

  Fy = cot =: normalization factor in y.

  k Z} dpp The following projection equations are then obtained xx O e Zo Fx e Zo Fy Once the geometrical information has been determined in the two-dimensional screen reference, all the equations providing the other information necessary for the visualization depth, texture, are projected. Shading To project the plane of facets, we use the following projection equations Axm + B Ym + C Zm + DO lBI Normal vector of the normalized plane (2) CS Distance from the origin point of the absolute reference to the plane The equation below above is defined in the absolute spatial coordinate system. To transform it into the observer's coordinate system (A ', B', C ', D'), we use the following matrix transformation FA rl, r 12 r 13 Ai i 'r 21 = l 2 rr 23 c (3) D '= D Atx Bty Ctz We calculate the depth z, or more precisely its inverse N = 1 / z, from the normalized values Xe and Ye using equation A 'Fx B'F c' X xx y 'D' e Dl e Dl Parameters other than geometrical, of which we know the equations in the three-dimensional reference, are transformed in the following way during the projection on the screen Let K be the value of any one of these parameters (texture, shading, luminance,) The equation giving K in the three-dimensional world coordinate is of the form: K = Px + P Ym + y Zm + (5) To perform the projection, we make the coefficients (a, ô, y and 5) undergo the transformations of equation 3, which gives new coefficients (a ', Pf', Y and 3 ') The equation giving the parameter K as a function of the normalized screen coordinates Xe and Ye is: K = A'F B' 't 6 A Fxxe e + C' Xx y, + 5 'D' e D Ye D 'ax'Fx + 13' F ye + YI = + 'According to the invention, a three-way clipping is carried out

  dimensions, by the display pyramid as defined above.

  above with reference to Figure 8, in order to eliminate anything that exceeds

  the edges of the projection screen.

  This amounts to performing the clipping of a hyperfacette by

  a convex volume delimited by k planes (here k = 4).

  First, we search for the faces that must actually be clipped, that is to say that we eliminate automatically those who

  obviously should not be clipped: the auto-faces

  hidden, the faces being entirely outside the pyramid of clipping, and those being entirely inside this pyramid One marks (for example by a coding flag) and numbers the remaining faces, which must therefore be clipped. Then, for each of the k clipping planes, we examine in turn each of the sides of a hyperfacette cut by the clipping plane, and we calculate vectorially for each of them the point of intersection with the clipping plane. Then, we "shortened" the original sides to keep only their parts located inside the clipping pyramid, which amounts to practicing a line clipping We thus determine the points of intersection of these sides with the corresponding clipping plane, and we sort these intersection points by face number of the hyperfacette, then along the oriented clipping line (arbitrary orientation) Finally, we go through the sorted list of points of intersection and we connects them two by two, that is to say that we add sides between these points

to close the faces.

  The method for selecting faces to be clipped will now be described in detail. This selection uses a binary P-bit code assigned to each vertex of the hyperfacette, indicating its position relative to the P clipping planes. In this code, the bit k (k ranging from 1 to P) corresponding to the plane k is for example O if the vertex is in the inner half-space of this plane (the inner half-space is that containing the normal inside the plane, as shown in above with reference to FIG. 2) The selection of the faces to be clipped is carried out by means of logical tests on these binary codes: a face is entirely visible (is not to be clipped) if all its sides are inside the clipping pyramid In the following relation, "U" represents a binary OR: U codesoet = O (7) E faces a face must be clipped if at least one of its sides intersects or if all its sides surround the clipping pyramid The test is the following (in this relation, "A" is a binary AND) 3 side E face codesonmmet 1 ^ c desonmt 2 = O or U codesomnetl A codeset 2 = 111 (8) side E face To verify this relation, it is necessary and sufficient that one side of a face intersects the clipping plane (one of its vertices is

  in the inner half-space, and the other vertex in the half

  outer space), either the sides of the face must surround the pyramid (so that all the bits of the union of the codes of the intersections of the sides are at 1) This test is more complex than the simple intersection of the codes of each vertex of the face, but allows to eliminate the faces cut by one or more planes but

outside the pyramid.

  Of course, the other faces, which do not respond to these tests, are outside the pyramid and are not selected. The sides of the clipper faces being clipped in any order, it is necessary to sort the points of intersection before closing these faces. The sorting criterion (x or y coordinate of the points of intersection) varies, of course, according to the clipping plane concerned According to the method of the invention, these points are sorted

  intersection by clipping plane.

  For clipping in two dimensions, the edges of the viewing window are arbitrarily oriented, for example from left to right for the horizontal edges, and from top to bottom for the vertical edges. The sorting criterion is therefore the x-coordinate

or y from the point of intersection.

  For clipping in three dimensions, it must be taken into account that the line of intersection of the clipping plane and the plane of the face to be clipped can have any slope Thus, for example, in FIG. 11, there is shown a clipping plane 63 in the orthonormal coordinate system Oxyz (where Oz is the observation direction, at which the plane 63 is perpendicular, this plane being at a distance z = dpa from the observer). FIG. 11 shows three parts of faces intersected by the plane 63 and referenced 64 to 66 The parts of faces visible in FIG. 1 are those lying beyond the plane 63 (with respect to the observer) The respective intersection lines D1 to D3 have different slopes and any relative to the axes Ox and Oy So we can not decide to sort

  arbitrarily according to the coordinates in x or y.

  The clipping plane being perpendicular to Oz, its equation is very simple, and the coefficients a and b of the equation of the clipped face directly characterize the slope of the line of intersection. The equation of this line is of the form fax + by + cz + d = O LZ = dpa is, after substitution y = ax + K (K = constant b We then determine the sorting criterion (in 3 D) as follows:

  if (lai <Ibi), we sort according to the x, otherwise we sort according to the y's.

  To finish the clipping, it is necessary to close the clipped faces.

  For this, it is necessary to determine which is the left face and which is the right face of the new side (joining the shortened sides) This new side is on the plane (or the right) of clipping It is thus not a shared side His second face is the right side or

  left of one of the clipped sides.

  For clipping 2 D, the orientation of the clipping line alone makes it possible to say whether it is the right face or the left face. FIGS. 12 and 13 are respectively represented, in accordance with the conventions described herein. above with reference to FIG. 2, the case where the visible face F is a left face (with respect to the segment oriented from Il to 12), and the case where the visible face F is a right face (always with respect to the segment oriented from He to 12). In the case of clipping 3 D, it is also necessary to know the direction of the normal (i) to the face to be clipped. FIGS. 14 and 15 show the two possible cases, with reference to the conventions established with reference to FIG. For these two cases, one clippes a triangular face F whose part lying on the right (as seen in the drawing) of the clipping plane 67 remains The case of Figures 14 and 15 are distinguished only by the orientation of the normal it to the face to clipper, so that in the case of Figure 14, we keep only the right side, and in the case of Figure 15, we keep only the left side The equation of this normal is to the form: ax + by + cz + D = OA a priori, one might think that the signs of the three parameters a, b, c and the sorting criterion can influence the final choice, which would require examining sixteen cases. after studying all these cases, we realize that by carrying out appropriate groupings, their number is reduced to two The first case occurs when the sorting must be done along the axis Ox and when b <0, or when a> O, and in this case, the left face must be preserved The second case arises when 'none of these two

  conditions are met, and the right face must be preserved.

  The visualization method described above is advantageously followed by a process of elimination of the hidden parts (process such as: "Z-Buffer", topological sort, scanning

of lines,).

Claims (8)

CLAIMS I   1 Method for visualizing synthetic images of volumes in real time, characterized in that it consists in storing in a database the data describing the volumes to be represented in the form of polyhedra from their oriented sides, these data being the topological attributes of the sides of the polyhedra, the coordinates in the space of the extremities of these sides, and the geometric and photometric attributes of the faces of these polyhedra, to eliminate the autocached faces of these polyhedra, to make a change of reference of the faces visualize, eliminate all objects between the observer and the front truncation plane, perform two-dimensional projection for perspective, and perform truncation   two-dimensional vector following a projection pyramid.   2 Process according to claim 1, characterized in that the truncation is carried out in a vectorial manner for each of the planes delimiting the said polyhedra, and for each of these planes, truncation is performed on each side of the faces of the   polyhedra, and the truncated faces are closed.   Method according to claim 1 or 2, characterized in that a face is self-hidden if: Axo + Byo + Czo + D <O, Ax + By + Cz + D being the face and lxo equation, yo, zol the position of the observer (Figure 7), these calculations being made from vector way.   4 Method according to one of the preceding claims,   characterized by the fact that the change of reference is done by rotation and translation in order to express the absolute coordinates of the   points of objects in the observer's landmark.   Method according to one of the preceding claims,   characterized by the fact that the perspective is done by   application of Thales theorem (Figure 9).   Method according to one of the preceding claims,   characterized by the fact that the truncation is performed in turn for each of the truncation planes, and in each plane, for each   each on all sides to truncate.   7 Process according to claim 6, characterized in that to perform the truncation of the sides, the sides to be truncated are selected, the point of intersection with the truncation plane is calculated for each of them, these sides are shortened, sorts the points of intersection by face on the truncation line, and we connect the points of intersection two by two with correctly oriented sides.   Method according to one of the preceding claims,   characterized by the fact that before performing the truncations, the faces which are to be actually truncated are searched for and marked.   Method according to one of the preceding claims,   characterized by the fact that it is followed by a process of elimination of hidden parts.