Technical Field

The present invention relates to a computer-implemented method for remapping a texture of a three-dimensional graphic object, as a result of a remeshing procedure on such three-dimensional graphic object, while keeping the quality of the resulting texture substantially unchanged.

Background Art

As is well known, a three-dimensional (3D) graphic object consists of a surface mesh, i.e., a grid formed by regular polygons (usually triangles) arranged in 3D space, and a texture, i.e. a two-dimensional image, also subdivided into polygons, which is applied “like a sticker” on the surface mesh. Three-dimensional graphic objects are used in the most diverse software applications.

Three-dimensional objects must very often be properly manipulated before they are used.

Specifically, operations of various types, known as remeshing operations, are carried out which include, but are not limited to, operations to reduce the number of polygons constituting the object in order to reduce the weight thereof in memory or to increase such a number to improve the graphic definition thereof.

In particular, operations to reduce the number of polygons allow even very complex 3D objects to be simplified in important ways, making them more easily usable in applications of various kinds.

Clearly, when an object is simplified, the problem arises of appropriately transferring the texture of the original object to the simplified geometry. Specifically, UV texture coordinates are defined on the original object, the definition of which is lost after the modification processes for modifying the 3D mesh. Specifically, the process through which a two-dimensional image (the texture) is projected onto a three-dimensional mesh (the geometrically manipulated object) is called UV mapping. Generally, the process of reconstructing this mapping is carried out manually by graphic designers or, as an alternative, by anchoring the texture to the underlying mesh.

The texture is thus “dragged” throughout the remeshing process. This causes an irreparable change in the texture on the manipulated object, specifically the texture atlas of the object, which then requires an appropriate post-processing phase once remeshing is finished.

Description of the Invention

The main aim of the present invention is to devise a computer-implemented method for remapping a texture of a three-dimensional graphic object which allows such remapping to be carried out effectively after the remeshing operations on such an object, particularly in the case wherein such remeshing operations result in a reduction in the number of polygons constituting the object, while maintaining substantially the same quality of the final modified object.

Another object of the present invention is to devise a computer- implemented method for remapping a texture of a three-dimensional graphic object which allows the process of reconstructing the UV texture’s mapping (i.e., generating the function which associates the two-dimensional texture with the 3D mesh) to be automated.

Another object of the present invention is to devise a computer- implemented method for remapping a texture of a three-dimensional graphic object which allows significantly decreasing computational time to have simplified graphic objects directly usable in practice, thus avoiding any user intervention in a potential pre- or post-processing phase.

Another object of the present invention is to devise a computer- implemented method for remapping a texture of a three-dimensional graphic object which allows the texture atlas not to be modified during the remapping process, thereby considerably reducing the space allocated in memory for the graphic object of interest.

The aforementioned objects are achieved by the present computer-implemented method for remapping a texture of a three-dimensional graphic object according to claim 1.

Brief Description of the Drawings

Other characteristics and advantages of the present invention will become more apparent from the description of a preferred, but not exclusive, embodiment of a computer-implemented method for remapping a texture of a three-dimensional graphic object, illustrated by way of an indicative, yet non-limiting example, in the attached tables of drawings in which:

Figure 1 is a general block diagram of the method according to the invention; Figure 2 illustrates a possible example of a first 3D object provided with texture;

Figure 3 illustrates the mesh of the first object in Figure 2;

Figure 4 illustrates the texture applied to the first object in Figure 2;

Figure 5 illustrates the mesh of a second object without texture obtained as a result of a remeshing process of the first original object;

Figure 6 illustrates the second object in Figure 4 provided with texture and obtained using the computer-implemented method according to the invention; Figure 7 illustrates a mapping of the first UV texture coordinates of the first object;

Figure 8 illustrates a mapping of the second UV texture coordinates of the second object B, obtained by the computer- implemented method according to the invention.

Figure 9 schematically illustrates a projection phase of the method according to the invention applied to the first and second objects.

Embodiments of the Invention

With particular reference to Figure 1, reference numeral 100 globally indicates a computer-implemented method for remapping a texture of a three-dimensional graphic object.

The computer- implemented method 100 is used for remapping a texture of a three-dimensional graphic object in different applications, such as e.g. gaming, augmented reality (AR) and virtual reality (VR), medical applications and Industry 4.0.

The method 100 needs as input a first 3D object with texture (object A) and a second 3D object without texture (object B) where the first object A and the second object B represent the same three-dimensional graphic object.

The object B, generally, comes from mesh modification processes applied to the first original object A.

By way of example only, a possible object A, its mesh and texture are illustrated in Figures 2, 3 and 4, respectively.

Figure 5 shows the mesh of a second object B without texture, representing the same three-dimensional graphic object as the original first object A, obtained as a result of a remeshing process of the first object itself. In particular, as can be seen from a comparison between Figure 3 and Figure 5, the second object B is obtained as a result of a remeshing process aimed at reducing the complexity thereof and, therefore, the number of polygons.

On the contrary, Figure 6 shows, again as an example, the second object B provided with texture as obtained by means of the method 100 according to the invention.

The method 100 thus allows obtaining a second object from a first object as a result of a remeshing procedure, keeping the texture quality of the second object substantially unchanged from that of the first object.

In order to avoid incorrect interpretations and to simplify the understanding of the subsequent description of the computer- implemented method 100 according to the invention, definitions of terms used are given below.

3D object: a 3D object consists of a list of geometric coordinates, of type (x, y, z), which identify the vertices of the 3D grid, ordered according to global numbering; of a list of triplets of integers which tell, for each triangle (or a different type of convex geometric figure used), which vertices identify it, according to global numbering; a list of UV coordinates, of type (x, y), in the 2D plane of the texture; and a list of texture triangles, constructed according to the same standards as the geometric triangles.

UV coordinates: coordinates related to texture points on the two-dimensional plane.

Convex envelope: it should be understood in the sense of Euclidean graphs, that is, it must pass through the sides and nodes of the Euclidean graph, where, by Euclidean graph, is meant a graph wherein each node has coordinates in the Cartesian plane and the length of one side corresponds to the Euclidean distance between the points bounding it.

Raycasting techniques: techniques used in the rendering of three-dimensional graphic objects, which allow the path and interactions of a ray to be identified when this encounters such objects within a scene.

Octree: a tree-like data structure which allows rapid execution of geometric queries, such as, e.g., spatial location of a specific geometric quantity.

Patch: the patch of elements of a geometric entity is the set of elements directly connected to that entity. For example, the patch of vertices associated with a vertex is the set of vertices which are directly connected to that vertex via one side.

Barycentric coordinates: relative coordinates of a point within a triangle. They are equivalent to the areas of the sub-triangles formed by connecting such a point to the vertices of the triangle.

Remeshing: processes which modify the mesh of one object, such as e.g. by reducing its number of polygons or eliminating nodes.

Seams: the “seams” between the different areas in the texture.

Connected component: each area in the texture, or texture “island”;

Texture atlas: the name which is assigned to the image containing the texture “islands”.

Patch order: number of neighbor elements considered for each vertex or mesh element. In the first order only elements connected to the vertex are considered, in the second order also neighbors of neighbors and so on.

Breadth First Search (BFS) algorithm: algorithm for identifying connected components, in our case it is used to identify the islands in the two-dimensional plane of the texture.

LPCN (Least Polar-angle Connected Node) algorithm: algorithm for identifying the convex envelope for each connected component, in our case it is used to identify the edges of the islands in the two-dimensional plane of the texture.

The computer- implemented method 100 according to the invention comprises the main phases schematized in Figure 1.

Specifically, the computer- implemented method 100 for remapping a texture of a three-dimensional graphic object comprises the following phases: a receiving phase 110 at input of a first three-dimensional graphic object A provided with texture and of a second three-dimensional graphic object B without texture and obtained following at least one remeshing process of the first object A; a reading phase 120 of geometric characteristics of the first object A and of the second object B and of first UV texture coordinates UV _A of the first object A; a creation phase 130 of patches for the first object A and for the second object B; an identification phase 140 of first connected texture components C _A for the first object A; a projection phase 150 of information related to the first UV texture coordinates UV _A from the first object A to the second object B, by means of projection techniques; an identification phase 160 of points in the first connected texture components C _A for the second object B, for the definition of second connected components C _B ; a returning phase 170 at output of second UV texture coordinates UV _B for the second object B.

In detail, the reading phase 120 comprises at least the following steps:

- a reading step 121 of the geometric coordinates (vertex coordinates) of the first object A and of the second object B;

- a reading step 122 of the geometric elements (polygons in 3D space, usually triangles) making up the first object A and the second object B;

- a reading step 123 of the first UV texture coordinates UV _A (texture triangle coordinates) from the first object A;

- a reading step 124 of the texture elements (polygons in the 2D plane, usually triangles) of the first object A.

In addition, the reading phase 120 comprises a composition step 125 of the UV mapping (texture map) of the first object A, wherein each vertex in the two- dimensional texture plane corresponds to a vertex in the 3D grid of the geometry of the first object A.

By way of example and for a better appreciation of the method 100 according to the invention, a mapping of the first UV texture coordinates UV _A of the first object A is shown in Figure 7.

Also shown in Figure 7 the first connected texture components for the first object A are illustrated and denoted by C _A , while the texture seams connecting the first connected texture components CA are illustrated and denoted by SA. Similarly, again by way of example, Figure 8 shows a mapping of the second UV texture coordinates UV _B of the second object B, obtained by the method 100 according to the invention.

Also in Figure 8, the second connected texture components for the second object B are illustrated and denoted by C _B , while the texture seams connecting the second connected texture components C _B are illustrated and denoted by S _B . The creation phase 130 of the patches comprises at least the following steps:

- a construction step 131 of patches of elements and vertices for the first object A in the 3D grid of the geometry;

- a construction step 132 of patches of elements and vertices for the second object B in the 3D grid of the geometry; - a construction step 133 of patches of elements and vertices for the first object A in the two-dimensional texture plane.

The next identification phase 140 of the first connected texture components C _A comprises a first identification step 141 of the first connected texture components C _A in the two-dimensional texture plane, for the first object A. Specifically, such identification step 141 of the connected components is carried out by a graph search algorithm. According to a preferred embodiment, this identification step 141 of the connected components is carried out through the use of a Breadth First Search (BFS) algorithm.

The use of equivalent algorithms cannot however be ruled out.

The identification phase 140 of the first connected texture components C _A also comprises an identification step 142 of the convex envelope of each first connected texture component C _A identified in the previous step 141.

Such identification step 142 of the convex envelope is carried out by means of an algorithm for finding the convex envelope for Euclidean networks.

According to a preferred embodiment, such identification step 142 of the convex envelope is carried out by a Least Polar-angle Connected Node (LPCN) algorithm.

The use of equivalent algorithms (Graham scanning, Preparata & Hong’s recursive approach) cannot however be ruled out.

The points constituting the convex envelopes are named texture seams. Referring to the example in Figure 7, they are denoted by reference SA.

Finally, the identification phase 140 of the first connected texture components C _A comprises an extension step 143 of the convex envelopes calculated in the two-dimensional texture plane to the corresponding 3D geometric grid, using the UV texture mapping of the first object A.

The points belonging to the extension of the convex envelopes to the 3D geometric grid are named geometric seams.

In addition, each first connected texture component CA is marked with a unique identification number.

The projection phase 150 comprises at least the steps described below and is schematically shown in Figure 9.

Specifically, the projection phase 150 comprises a first identification step 151, for each point PB of the second object B, of the nearest point PA of the first object A in the 3D grid of the geometry.

Such an identification step 151 of the nearest point PA is carried out through a spatial localization algorithm. For example, such a spatial localization algorithm may consist of an Octree algorithm.

The use of equivalent algorithms (Depth First Search algorithm, Connected- component labeling algorithm) cannot however be ruled out.

Next, the projection phase 150 comprises a projection step 152 of the point PB of the second object B considered in step 151 above, onto the patch of elements associated with the nearest point PA of the first object A identified in step 151 above.

Specifically, such projection step 152 is carried out by means of raycasting techniques.

In addition, the projection phase 150 comprises an identification step 153 of the patch element of the first object A which contains the projection of each point of the second object B.

Also, if the projection is not contained in any of the patch elements of the first object A identified in step 152 above, such identification step 153 uses the vertex of the mesh composing the first object A nearest to the projection.

Next, the projection phase 150 comprises an assignment step 154 to each projected vertex of the second object B of a flag corresponding to the unique identification number associated with the first connected component CA of the first object A to which such projection belongs.

In addition, the projection phase 150 comprises the following steps: a calculation step 155 of the barycentric coordinates of the point P _B of the second object B projected onto the first object A in the triangle of the first object A containing such projection; a using step 156 of the calculated barycentric coordinates to find the texture coordinates associated with the texture triangle of the first object A (following the UV mapping of the object A) to which the projection of the point of the second object B belongs; an assignment step 157 of the texture coordinates of the first object A, found at the point PB of the second object B whose projection onto the first object A is being considered. Next, the projection phase 150 comprises a projection step 158 of each vertex belonging to the convex envelope of each component of the first object A onto the 3D mesh of the second object B.

Specifically, this projection step is carried out by means of a raycasting technique.

In addition, if there is more than one projection per vertex, such projection step 158 comprises the choice of the projection that minimizes the distortion of the second object B, i.e., the point which minimizes the area of the triangle which is formed.

The newly identified points are named new geometric seams.

The new geometric seams on the second object B correspond to the geometric seams on the first object A.

Finally, the projection phase 150 comprises, for each point in the new geometric seams of the second object B, a transfer step 159 for transferring the texture coordinates related to the geometric seams of the first object A onto the new geometric seams of the second object B, using the texture mapping indicated in the first object A.

The points so found are named new texture seams SB and correspond to the texture seams SA of the first object A.

The identification phase 160 of points in the first connected texture components C _A for the second object B comprises, for each triangle of the second object B, the analysis of the flags, assigned during the projection phase 150, of the vertices of such triangle, related to the connected component in the texture plane to which each vertex of the second object B, projected onto the first object A, belongs.

Specifically, such analysis of the flags comprises:

- if all three vertices have the same flag, then the triangle is completely contained within one of the “islands” of texture, so no action is carried out;

- if two vertices have the same flag and the third vertex has a different flag, an identification step, among all the points belonging to a new texture seam (i.e., to the convex envelope of the texture island to which the two points with the same flag belong), the point that minimizes the distance from these two points;

- if all three vertices have a flag related to a different connected component, a construction step of three different texture triangles and a selection step, among such three texture triangles, of the one having the smaller area (to minimize the distortion of the applied texture). Such triangles preserve one of the three original vertices, while replacing the other two with the vertices belonging to the convex envelope of the texture island to which the preserved original point (i.e., to a new texture seam) belongs and found to be the nearest thereto.

Finally, the returning phase 170 of the second UV texture coordinates UV _B for the second object B specifically comprises the following steps:

- a returning step 171 of the texture coordinates assigned to the geometric vertices of the second object B; and

- a returning step 172 of the texture triangles assigned to the geometric triangles of the second object B.

It has in practice been ascertained that the described invention achieves the intended objects. In particular, the fact is emphasized that the method according to the invention allows texture remapping to be carried out effectively after remeshing operations on an object, particularly in the case where such remeshing operations result in a reduction in the number of polygons constituting the object, while maintaining substantially the same quality of the final modified object.

In particular, the method according to the invention allows automating the reconstruction process of texture map (i.e., the generation of the function that associates the two-dimensional texture with the mesh 3D grid).

In addition, the method according to the invention allows significantly decreasing the computational time to have simplified graphic objects directly usable in practice, avoiding any user intervention in a potential pre- or post- processing phase.

In addition, the method according to the invention avoids texture modification during the re-mapping process, thus greatly reducing the space allocated in memory for the graphic object of interest. In fact, the texture atlas remains unique, that is, only one two-dimensional image is obtained for different meshes representing the same graphic object. Therefore, by having to store only one texture instead of one for each simplified mesh, the space allocated in memory for the graphic object of interest is reduced.