Abstract:
A system that applies computer generated paint stamps to a target polygon and to neighboring texture polygons in such a way that each texture polygon affected by a stamp that is too big for the target polygon and that is not connected to the target polygon in texture space receives an appropriately positioned and oriented stamp. The system determines the relative position and orientation of the stamp with respect to a texture polygon adjacent to the target polygon and applies the stamp centered at that relative position and orientation, so that the stamp overlaps the adjacent polygon.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is related to U.S. application Ser. No. 09/024,122 entitled Computer Generated Paint Stamp Compensation having Silicon Graphics, Inc. by Reiter et al, filed concurrently herewith and incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention is directed to the compensation of the electronic paint that an artist can apply to a computer based model and, more particularly, to the compensation of a paint stamp when it exceeds or crosses the boundary of a texture triangle onto which it is applied. 
     2. Description of the Related Art 
     Computer generated three dimensional (3D) objects are typically comprised of polygons, typically triangles, of sufficiently small size that the surface of the model appears smooth. Surface detail (color, topology, reflectance, etc.) is applied to these smooth computer generated three-dimensional images by applying painted 2D images, known as textures, to the 3D models in a process called texture mapping. Much of the realism of the models is affected by these textures, and great care is therefore taken to produce the desired effects when painting the textures. 
     Digital paint is typically applied in brush strokes, with each stroke using a particular paint brush specified by the user. Various attributes of the brush must be specified before the brush can be used to produce a stroke. These attributes include, e.g., the color of paint; the radius, aspect ratio, and rotational angle of the brush; a detailed map specifying the amount of paint to be applied at each point in the brush. The collection of these attributes are called a brush stamp. Once the attributes are set, a digital image of the stamp is created: this is called the stamp image, or a stamp source image. Stamps can then be placed on a target image by copying the stamp image to various locations on the target. Paint brush strokes are typically applied by placing a sequence of consecutive stamps along the trajectory of a path as is indicated by the user with a stylus or mouse pointer. The spacing between the stamps on the path determine the appearance of the stroke. Stamp spacing is typically another attribute specified by the user. 
     Paint may be applied to 3D models by either painting directly onto the flat texture, or by painting on the model. Although both are useful, only the latter method provides direct visual feedback as to the final appearance of the painted model. 
     Two methods are conventionally provided for painting in 3D: projective and surface. In projective painting, the paint is applied to a flat surface which is shaded and masked by the model in such a way that the paint appears to be applied directly to the surface. A separate projection step is then necessary to move the paint from this paint plane onto the various textures of the object. 
     The second 3D painting method is known as painting on the surface. In this approach, paint is applied directly onto the texture assigned to each surface. In particular, brush stamps are applied to the texture in a manner which is consistent with the conventional triangulated surface tessellation of computer based models. Stamps are centered at the world space position designated by the mouse or stylus pointer. That is, given a world space point in the interior of a surface triangle, the corresponding texture space point is found in the interior of the texture triangle assigned to it. The point in texture space is then used as the center of the stamp where it is to be placed. This gives rise to the problem illustrated in FIG.  1 . Paint stamps a, b and c are identical in texture-space but quite dissimilar in world-space. When a stamp exceeds the boundary of the texture polygon on which it is applied, as occurs in triangle  12 , and the neighboring texture polygon has been assigned a different texture, the stamp will appear chopped off (disconnected) in world space after the texture triangle has been mapped to the corresponding world space triangle, as it appears in world space triangle  14 . 
     What is needed is a method of applying stamps to the texture polygons that eliminates the disconnection. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to apply paint to world space objects in such a way that disconnected or cutoff stamps do not occur. 
     The above objects can be attained by a system that applies stamps to neighboring texture polygons in such a way that each texture polygon affected by a stamp that is too big for the target polygon receives a proportional portion of a stamp. 
     These together with other objects and advantages, which will be subsequently apparent, reside in the details of construction and operation as more fully hereinafter described and claimed, reference being had to the accompanying drawings forming a part hereof, wherein like numerals refer to like parts throughout. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 depicts a paint stamp applied to a texture space polygon which is cutoff when the texture polygon is mapped onto the corresponding world space (3D) polygon. 
     FIG. 2 shows a system according to the present invention. 
     FIG. 3 illustrates how the location for a stamp during seaming compensation is determined. 
     FIG. 4 shows the operations performed during seaming compensation. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     When two triangles, which are adjacent in world-space (such as triangles  14  and  18  in FIG.  1 ), and the corresponding texture space triangles are not adjacent in texture-space (such as triangles  12  and  16 ), the common (world-space) edge  24  is said to have a seam. As illustrated in FIG. 1, stamps that are applied across a seam will appear chopped off in world-space. This problem can be overcome by applying multiple stamps to the texture triangles in a consistent manner, one stamp per each disconnected component. 
     The present invention is implemented in a computer system  26  as depicted in FIG.  2 . An input device  28 , such as a stylus and tablet available from WACOM, capable of providing inputs for a paint program is coupled to a computer  30  and display  32 , such as an O2 available from Silicon Graphics, Inc. Of course the input device could be other types of devices such as a mouse and the computer could be a personal computer. As the input device  28  is moved, paint is applied to a model displayed on display  32  by computer  30 . This paint or the paint stamps are compensated for any lack of adjacency of the texture space triangles and world space triangles used by the system to apply the paint to the model. 
     To apply multiple stamps to the textures in a consistent manner, one stamp per each disconnected component, a simplified winged edge data structure is constructed using the polygonal mesh (vertices and edges). A winged edge data structure contains the information about all the vertices, edges, and polygons embodying a polygonal mesh, and provides methods of cross referencing the various data. That is, given an edge, the structure can return the two vertices and the two polygons incident on that edge; given a polygon, the structure can return all the edges and vertices incident on it, and; given a vertex, the structure can return all the polygons and all the edges incident on it. The advantage of this structure is that it is indexed by edges so that essentially each edge knows about the two polygons (“wings”) incident on it from which it finds the incident vertices. This data structure can take many forms but usually is implemented as a table which is indexed by the edges of the set of polygons. 
     For each polygon all the edges incident to it are determined and the distances from the polygon centroid to that of each of the polygon&#39;s neighbors is determined. For each edge is stored an indication of the two adjacent polygons, and the edge is flagged to indicate the existence of a seam. 
     A shadow of a stamp is the region of world space in which the stamp appears; a shadow list is a list of polygons lying in the shadow. Given the radius of a compensated stamp, the shadow list can be easily determined from the above winged-edge structure. 
     Given two neighboring world-space triangles W,W′ ( 32  and  34 ) as depicted in FIG. 3, their corresponding disconnected texture-space triangles T,T′ ( 36  and  38 ) with a seam existing between the two, and a point p ε T, we must find a new point p′ ε T′ that corresponds to p in such a way that the world-space position of p′ matches that of p. To find this new point, let (u,v,w) be the barycentric coordinates of p with respect to triangle T, and find {circumflex over (p)} ε W, the point with barycentric coordinates (u,v,w) with respect to triangle W. Since W and W′ are neighbors, rotate W′ around the common edge until the two are coplanar. This places the 3D world space triangles in the same plane which is already the case for the texture space triangles. Then compute (u′,v′,w′), the barycentric coordinates of p with respect to triangle W′. The desired point p′ is the one with barycentric coordinates (u′,v′,w′) with respect to triangle T′. 
     Seaming artifacts can now be avoided by recursing through the shadow list, applying stamps to selected regions using the following method which will be discussed in more detail with respect to FIG.  4 . Given the point p in texture triangle T and the shadow list L: 
     1. Draw the stamp centered at p and remove T from the shadow list L. 
     2. Remove from L all polygons adjacent to T whose common edge with T has no seam. 
     3. Select T as the next triangle in shadow list L, and compute p relative to this new T as described above. 
     4. Recurse until the shadow list L is exhausted 
     Because of the way in which stamps are placed across edges, the chopped off stamps will line up in world-space to create a full stamp. This method is fairly slow as numerous stamps are drawn for each visible one. The winged-edge structure can therefore be used to determine the distance between the position of a stamp and the nearest seam, and then cull all polygons that are sufficiently distant. Distant stamps would be placed once and avoid the seaming process; the others would be drawn as described. 
     In an implementation of the invention method described above, the steps are preferably divided into preprocessing steps which occur before paint is applied and while the 3D model is loaded and steps that are performed during painting. 
     The preprocessing steps, as depicted in FIG. 4, start with a list of the triangles of the model and determines  42  all the joining edges of the model in world space by checking the model triangles for two shared vertices. Next, the system determines  44  whether each edge is also a shared edge between corresponding triangles in texture space by checking for the same shared vertices. All shared edges of the model in world space which are not shared in texture space are flagged  46  as seams. Next, a circle is computed  48  for each of the triangles. The circle is the largest circle that will fit within the corresponding triangle. To do this the centroid of each triangle is found; the distance from the centroid to the nearest edge is the radius of the circle. This ends the preprocessing stage. 
     During painting, the location of the stamp on the model, that is the world space triangle (and the corresponding texture space triangle) where the cursor is located along with the location within the world space triangle (and within the texture space triangle), is found  50 . The radius of the stamp at this location is compared  52  to the boundary of the computed circle: if the radius extends beyond the boundary, the stamp extends outside the circle and therefore possibly extends outside the triangle. In this case seaming compensation is performed. If the stamp is completely within the circle, then no seaming compensation need be performed  54  and the stamp is drawn  56  on the texture polygon at the location of the cursor obtained from the input device. 
     If seaming compensation is necessary the system finds  58  an adjacent triangle by examining the edges of the triangle in which the center of the stamp resides. Next, the stamp is placed  60  on the same plane as the adjacent triangle by rotating the center of the stamp in world space about the adjoining edge. Then, the barycentric coordinates of the center of the stamp with respect to the adjacent triangle in world space are found  62 . These coordinates are used in texture space to locate  64  the center of the stamp in texture space relative to the texture space triangle that corresponds to the adjacent world space one by weighting the vertices of the texture space triangle by the factors of the barycentric coordinates. The stamp is then drawn  66  at that location. This location is outside the adjacent texture triangle so only part of the stamp is drawn within the adjacent texture triangle (see the right side of FIG.  3 ). If another adjacent triangle exists  68  the system returns for another cycle. 
     The culling of polygons is performed in concert with the seaming process in the following manner. Given a point and a target polygon, the initial stamp is placed at the point and the polygon is marked as having been stamped. Then, the radius of a circle circumscribing the image of the stamp just placed is computed, as described above. The distance between the given point and each edge of the target polygon is now compared to the circumscribing radius. If the distance is no greater than the radius and the edge is flagged as a seam, then the neighboring polygon is in the stamp shadow; otherwise the neighboring polygon is culled. When a polygon is resolved as lying in the shadow and has not yet been stamped, the process is recursed with the neighbor as the target polygon. The process is completed when all the edges of the target polygon have been considered. 
     The process described above includes finding the polygon that lies under the mouse pointer in order to compute its distortion compensation. This follows the assumption that all polygons along the path of the cursor will be hit. Unfortunately, this may not always be the case as sliver triangles and those with sub-pixel extent may be overlooked by the process and ignored. Fortunately this is not a grave problem, as the process of painting is incremental in nature. The workflow typically consists of painting several strokes, then rotating the object, and painting several more. Textures are often touched up and painted directly regardless of the paint mode. In this way, all the required triangles will eventually get painted. An assumption is also made that all neighboring polygons share common edges, regardless of whether they belong to different surface patches. The algorithm will thus work properly only when the surface contains no cracks. This is an unfortunate limitation considering that not all surface tesselators can maintain a global view of the 3D scene. With global tesselators, however, seaming is handled properly and, therefore, it is preferred that the invention be used with a global tesselator. 
     The present invention has been described with respect to the texture space and world space tessellations being triangles, however, it is possible for the tessellations to be any shape polygon. The present invention has been described with respect to polygons of three sides, however, the invention will work equally well with polygons of any degree. 
     The many features and advantages of the invention are apparent from the detailed specification and, thus, it is intended by the appended claims to cover all such features and advantages of the invention which fall within the true spirit and scope of the invention. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the invention to the exact construction and operation illustrated and described, and accordingly all suitable modifications and equivalents may be resorted to, falling within the scope of the invention.