Texture Mapping with Vector Graphics: A Nested Mipmapping Solution

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1 Texture Maing with Vector Grahics: A Nested Mimaing Solution Wei Zhang Yonggao Yang Song Xing Det. of Comuter Science Det. of Comuter Science Det. of Information Systems Prairie View A&M University Prairie View A&M University California State University, LA Texas Texas CA 9003 ABSTRACT Texture maing with vector grahics, rather than raster grahics generates better rendering quality. This aer discusses a fully develoed aroach of texture maing 3D objects with vector grahics. First, the vector grahics is rendered to generate the corresonding raster grahics, which is temorarily stored in the back framebuffer. Then, using the newly generated raster grahics, a yramid of mima (LOD) images are dynamically generated and maintained. Finally, a nested dynamic mimaing mechanism is alied to ick the right image to achieve the best resolution during rendering. VTexturer, was develoed to test and evaluate the roosed aroach. The system runs on the regular PCs with the MS Windows oerating system, and is caable of using vector grahics in.wmf or.emf format to texture ma grid or TIN based 3D objects. The exerimental results show that our aroach maintains good rendering erformance and yields very satisfied results. KEYWORDS: Texture maing, vector grahics, raster grahics, mimaing, LOD. 1 Introduction Texture maing is a fundamental and must-have grahics rimitive in modern comuter grahics systems. It allows us to achieve realistic effects with relatively lower cost of comutation. However, the traditional raster grahics based texture maing has its limitation on rendering resolution because of its non-scalable feature. As vector grahics increases its oularity recently, it becomes necessary to investigate alying vector grahics to texture maing. This aer resents a fully develoed and efficient method of using scalable vector grahics to erform texture maing in 3D grahics. The aroach, nested dynamic mimaing, can be categorized as a LOD solution, where a textured object may have an inconstant number of textures at different LODs. Vector grahics based texture maing, or vector texture maing, has a distinct advantage, that is, the textured 3D objects suffer no texture blurry and deformation. Unfortunately, this toic has not been fully studied so far. Here we briefly summarize the existing work related to this toic. Lance Williams first coined the term mima in 1983 when he resented his novel idea to solve shimmering and flashing artifacts in regular texture maing [1]. Later Tanner etc. roosed a dynamic texture reresentation, named clima, to erform texture maing with texture images in huge size []. Recently, Ray introduced vector texture mas, where the discontinuity filtering algorithm relies on a manually designed texturing hierarchy [3]. Haddon and Stehenson reorted their vector texturing rendering method, which has certain similarity to our aroach [4]. However, their aroach does not allow the rasterized texture image in arbitrary size. Other related existing works include silhouette mas [5, 6], shar embedded boundaries [7], and discontinuity meshing related algorithms [8]. The solution resented in this aer extends the traditional raster image based mimaing to suort

2 vector texture maing. Our imlementation shows satisfactory rendering efficiency and quality. The remainder of this aer is organized as follows. Section elaborates on our aroach, including the nested dynamic mimaing mechanism and a set of related imlementation details. Section 3 describes the exerimental system, system erformance, and evaluation results. Finally, Section 4 concludes this work and oints out the future work directions. Nested Dynamic Mimaing In this section, we introduce the nested dynamic mimaing aroach to texture ma 3D objects with vector grahics in real time. A child level of mimas for geometric atches is generated from its arent level of mima, and they are nested, in this fashion, recursively to suort textures in arbitrary size..1 Overview With the geometric models and textures secified for 3D objects, texture maing takes as inuts a series of additional settings to roduce the final rendering result. These settings include texture reeating and claming, texture external and internal color formats, environment mode, and filtering settings. Among them, our nested dynamic mimaing aroach works on the filtering oerations that are executed to magnify or minify the texture. Our solution to vector texture maing is able to comletely eliminate the artifact of texture stretch and thus roduce the best resolution. In addition to the main aroach, a cache mechanism is devised to adjust texture memory allocation. Imlemented by aging algorithms, this mechanism ensures that 3D objects, maed with vector grahics, are rendered in real time. Table 1 shows the comarison of the filtering methods between raster texture maing and vector texture maing. Table 1: Comarison of filtering methods Raster textures Vector textures Nested dynamic Linear interolation mimaing Magnifying Prevents sudden Provides the best textures color changes on the screen resolution on maed surface; maed surface. Cannot avoid texture stretch artifacts. Linear convolution; Mimaing Nested dynamic mimaing with cache mechanism Minifying textures Prevents shimmering and flashing effects during real-time rendering. Inherits the merits of mimaing; dynamically allocates memory to hold textures for real-time rendering.. Polygon Tessellation and Division Polygon tessellation is to divide the olygons of an object surface into smaller ones. There are two main uroses of erforming tessellation: (a) roduce realistic lighting effects; and (b) rovide the base level of texture atches for dynamic texture division during rendering. The texture maing rocess is a set of er-fragment oerations. In our aroach, when vertex coordinates and texture coordinates are secified, a mesh of model atches is imlicitly set u and the texture is divided into corresonding texture atches. LOD modeling decomoses texture atches to more detailed levels in order to reresent objects better when they are closer to the viewing oint. A texture atch and its corresonding geometric atch are the base of the next level of the texture, as shown in Figure 1. Figure 1: Texture atch levels Grid based and triangulated irregular network (TIN) based models are the two most oular methods of reresenting 3D objects. Each geometric atch is a quadrangle or triangle in a grid based or TIN based geometric model. Since a texture image contains a rectangular array of data, grid based models can directly use the inut vertex and texture coordinates at any level of detail. However, when a triangular geometric atch is detached into a more detailed level, the texture atch needs to be recalculated and generated as a rectangular texture, which involves extra memory to hold unused data. To continue the division of texture atches to a further LOD, we simly draw virtual lines by connecting the midoints of the edges, thus obtain four quadrangles or four triangles.

3 .3 Dynamic Mimas Mima management is the core of our nested dynamic mimaing aroach. The objective is to rovide vector texture in certain sizes to revent texture stretch, that is, the to level mima image is large enough to be maed onto the model surface without being magnified. Rasterized images from the original vector grahics are obtained from the back framebuffer, which is more efficient than being loaded from the main memory since texture data is transferred directly from the framebuffer to texture memory. Here we resent an efficient aroach to manage mimas dynamically and rovide a set of criteria for nested mimas in our grahics alication. In a tyical rendering ieline of grahics systems, such as OenGL, a series of 4 4 matrices are used to generalize vertex calculations. A homogenous coordinate ( x, y, z, w) undergoes a series of calculations to obtain the screen coordinates ( x w, y w ). Let M reresent the model view matrix, P the rojection matrix, and the viewort size be w by h ixels. The rojected coordinate (x, y, z, w ) is: x y z w = P M We then calculate the normalized device coordinate (x nd, y nd ) as x nd = x / z, y nd = y / z. In the final ste, considering the window device context has its origin at the left bottom corner, we obtain the screen coordinate (x w, y w ) corresonding to the dimension of the viewort: w x w = (x nd + 1 )( ) + x h y w = (1 y nd )( ) + x With the above formulas, we calculate screen coordinates for any vertices in 3D sace. Figure illustrates the dynamic mimas. x y z w w 1 (x 1, y 1) w (x, y ) v 1 (x 1, y 1, z 1) v (x, y, z ) Texture 1 (s 1, t 1) (s, t ) Figure : Dynamic mimas Given a geometric atch G and its corresonding texture atch T, we examine first two adjacent sace vertices v 1 (x 1, y 1, z 1 ) and v (x, y, z ) along the border of G. The rojected screen coordinates w 1 and w can be comuted from sace coordinates v 1 and v, resectively. The length of the line segment w 1 w in D screen ixels is designated d W. Texture coordinates for v 1 and v corresond to 1 and in texture sace. Since vector textures have no fixed dimension, the distance between 1 and might vary according to The current size of the vector texture The ratio of texture width to texture height Each vector grahics is drawn on a blank attern, whose size is called the original size of the vector grahics. Another size can be calculated and defined as the initial size of the vector grahics in which each dimension is the ower of closest to the original dimension. Assuming the initial width of the vector grahics is w I and the initial height h I, we define a ratio of w I to h I as r. In a mima, either for the original texture or a texture atch, the base level in the texture mima always has the highest resolution, which we define as w T by h T. Since the mimas are dynamically generated, the mima images at the base level also changes. For texture atch T, we call the size of the base level mima image the current size of the texture (w T by h T ). Mima images should have a consistent look within a mima; the ratio of w T to h T should always be equal to r. The distance d between 1 and in texture coordinates is calculated. Usually texture coordinates are between 0.0 and 1.0, but we need to unify the s and t coordinates to one direction before calculating d, assuming we use the s coordinate to calculate d.

4 For texture coordinates 1 (s 1, t 1 ) and (s, t ), since s coordinates and t coordinates are roortional to the initial width w T and the initial height h T, we obtain d as follows: s1) + (( t t1) ) d = ( s r where r = w / T. T h When texture coordinates (s1, t 1 ) and (s, t ) are set to relate texture atch T with geometric atch G, d is calculated at that time. Since it remains the same as long as texture coordinates are not reassigned, we kee d in a structure for T or G. Based on d, in the next ste, we obtain the actual number of texels d T on the line between 1 and. Since we use the s coordinate in calculating d, d T is thus related to w T : d = d w T T In revious stes, we already know the distance between w 1 and w (d W ) in screen ixels. We comare d W with d T to determine whether we need to generate texture mima images with higher resolutions to revent them from being magnified. The two ossible situations are: (a) dw d T : The screen dislay of the texture is smaller than the largest mima image. Grahics systems will automatically select roer mima levels to texture ma the 3D object. (b) d W > d T : The base level mima image is not large enough to cover the whole maed model surface without being stretched. One or more detailed mima images need to be generated. The number of those new images is defined as nm, which can be calculated by n M = log ( d W / d T ) For examle, when the viewing oint is moving toward the texture maed object and at a certain oint, d W goes a little bigger than d T but still smaller than d T. However, in order to avoid stretching the texture, the mima for the texture needs an additional image (since n M = 1) to the to of it. This way, the system kees track of d W and d T for udating the mimas for all texture atches. The above calculation of n M is only for a single line segment in v 1 v and its corresonding line segment w 1 w is dislayed within the viewort. To consider a geometric atch and its texture atch, we need to know this n M value for the other sides that encomass the atch. The other three sides in a grid based model or the other two sides in a TIN based model are calculated. For each side of geometric atches on a model surface, d W / d T is only calculated once, since we save all of the ratios to avoid unnecessary calculations. Then we select the largest d W / d T and then get the largest n M. In ractice, we obtain the values of w 1, w from v 1, v. We check if the line segment is within the viewort; if not, this segment should not count as a criterion to comute how many more detailed images need to be added to the object s mima. Since we have checked all of the line segments for a geometric atch G, we know if G is within the viewing volume. If G is clied out of the viewing volume, we don t render it at all..4 Nested Patch Mimas In the receding subsection, we use the ratio of d W to d T to determine whether more detailed mima images need to be added to the object s mima. For a 3D object, we obtain the largest n M for all its texture atches. Considering texture size limit, for examle, 104 ixels, if a dimension of a visible texture atch reaches 104 and it still cannot satisfy the resolution requirement, we check to see if G already has a searate mima. If not, we detach G s texture atch T and create a new mima from T and bind it to G. Instead of using the original texture mima of the object, we select the detached mima for future rendering of G. The rocedures of building a nested atch mima, M G, are as follows: 1) Find the offsets and dimensions in s and t directions of T in the object s original texture. ) Use the largest mima image of the object to get the actual size of T, (w T, h T ). 3) Calculate the initial dimensions of M s to level mima image. 4) Generate the nested mima for G. 5) Kee the number of levels n PM in which mima images are larger than T. 6) Calculate a new set of texture coordinates for G s vertices using M G s texture mas. G s mima is udated when G is currently using a detached mima and the object demands more detailed mima images.

5 .5 Cache Mechanism Without a cache mechanism, vector textures might consume all the texture memory, and even the main memory. On the other hand, unnecessary mimas waste a huge amount of comutation time. We roose a set of aging algorithm to cache texture mima among texture memory, main memory, and hard disk. At any moment, there are three tyes of mima memories that the aging algorithms work on: An object s mima images which are not currently in use; A atch s mima images which are not currently in use; A atch s mima which is no longer in need to revent texture stretch. For an object s mima, this base mima structure should always be ket in order to render geometric atches that do not have detached mimas and to rovide the basis for dividing texture atches and generating detached mimas. We set u a bottom level of image size in an object s mima, if a mima image is above that level and not in need, we can consider assigning ages for that image. If an image exceeds a certain age, it will be released from the object s mima. Similar rules aly to a atch s mima images. Note the bottom level image size for a atch mima is equal to the size of the largest corresonding texture atch. For the third tye, if the object is not using the largest texture image or the atch does not even need to use the largest texture atch from the object s texture, the atch s mima structure will be aged. If its age goes beyond a certain threshold, the whole mima will be destroyed. A comlete execution flow of the aging algorithm first increases ages for the objects that are not visible in the viewort, and then ages are added to those objects mimas and their atch s mimas, if alicable. Every time a mima or a mima image is aged, we check if it is old enough to be released from memory. During every cycle we look for the largest ratio of d W to d T (suose this ratio is r), the aging algorithm undergoes the following stes: (1) Case 1: r 0.5 : In this situation, the next or even a lower level of mima image can satisfy the resolution demand. Counting down from the to of the mima, the actual number of levels nal that needs adding ages is calculated as: nal = min( log r, nl ) The mimas of object s atches also need aging if the atch has a nested mima and either it is not currently in sight or its largest ratio of d W to d T is smaller than 1. () Case : 0.5 r 1 : We reset the ages of the object s mima images to 0 because all of these images are being used during rendering in order to revent texture stretch. (3) Case 3: r > 1 : First, we use the same method as stated in Case 1 to check and add age for every atch s mima. For each atch, we calculate n M as described using the formula n M = log ( dw / dt ) to udate the atch s mima. Again, n M is the number of mima images whose resolutions are higher than the object s texture atch. If n M is less than n PM, the number of levels already added, we calculate n AL based on n L, n M, and n PM by nal = min( npm nm, nl ). Then we aly the aging algorithm to the n AL images, that is, the number of mima images from the to of the atch s mima. With the aging algorithm, we kee track of the amount of memory that has been allocated to hold mimas and mima images. If this value reaches the uer limit, for examle, 18MB, mimas or mima images with the largest age are released. Besides the main execution flow of the cache mechanism, we may consider some other factors to design the aging algorithm: If a mima or a mima image has not been used for a certain eriod of time, its age increases. We set u a limit for the amount of memory that can be allocated to hold mimas. If mimas grow beyond that limit, the least recently used mima image is released. 3 An Exerimental System An exerimental system, VTexturer, has been develoed on Windows latform, using OenGL and VC++.Net. Besides the nested dynamic mimaing and aging algorithms, VTexturer has the following features: Suorts various vector grahics formats: wmf, emf, and raster grahics formats: bm, gif, jg.

6 Suorts both grid-based (quadrangular atch) and TIN-based (triangular atch) object models. Allows creating, loading, editing, and saving 3D object models in VTexturer scene file format. Allows navigating freely in the virtual scene. Allows tracking internal data structures and keeing record of their dynamic changes. We conducted the erformance evaluation on lato with a Pentium4.GHz rocessor, ATI Radeon 7500 grahics card, and 56MB main memory. The testing result may vary on different hardware latform and software settings. We used a 34KB wmf vector grahics to texture-ma 100 to 1089 quadrangles. We tested them from a distance that we can view all objects clearly. (a) Original vector grahics image Frames er second Raster texture average frame rate Vector texture average frame rate Number of quadrangles (b) Raster grahics based texture maing Figure 3: Rendering erformance comarison Figure 3 shows the erformance comarison between raster texture maing and vector texture maing. The raster image and the vector grahics are in the same size and they look the same. The test result shows that the vector texture maing is slightly slower that the traditional raster texture maing. The frame rate of the vector texture maing remains above 0 fs when more than 1000 quadrangles of object models are visible. Figure 4 shows the examle discussed in the receding section. The object surfaces, texture-maed with the same grahics but one in raster format and the other in vector format, look the same as Figure 4(a) if viewed from a far distance. When the viewing oint is moved closer to the object, the surface maed with the raster texture aears blurred, as shown in Figure 4(b), while the surface maed with the vector texture always has the best screen resolution, as shown in Figure 4(c). (c) Vector grahics based texture maing Figure 4: Texture maing comarison Figure 5 illustrates a TIN object model texture-maed with a vector grahics. There are two strings of text on the vector texture, which are not clearly visible due to the far distance. When the viewing oint is moved closer to the object model, the text is getting clearer.

7 shows satisfactory results of real-time rendering and memory usage. When objects are textured with vector grahics and rendered on the screen, they exhibit high rendering quality as they are maed with dynamically generated raster textures that are large enough to meet the screen resolution demand. The nested dynamic mimaing solution is currently imlemented at software level. The mima udating takes most of comutation time. It involves a large amount of comutation, such as matrix transformation, rasterized texture generation, and mima image settings. All these tasks can be imlemented and accelerated at hardware level, and thus imroving the general erformance. Figure 5: Texture ma a TIN model with vector grahics In the last examle, we set a two-level tessellation for an object surface that has u to 100 quadrangular atches. If the maximum texture size for the OenGL system is selected for the largest size of a mima image, the entire texture ma will be in the size of 00k by 00k ixels in the rasterized format. 4 Conclusion This aer resents a novel mima based solution to extend the traditional raster grahics image based texture maing to vector texture maing. The nested dynamic mimaing aroach, comosed of two level-of-detail hases, is devised to realize vector grahics based texture maing in real time. Vector textures are first rasterized in the back framebuffer and tessellated or further divided when building nested mimas. Besides the texture atches visible in the viewort, the nested mima structure also kees texture data of lower or higher levels of mima images and, if alicable, texture data of neighboring detached texture atches, which are generated during mima udating in every rendering cycle. A cache mechanism, imlemented with a set of aging algorithms, accelerates the real-time rendering and also limits the amount of texture memory and main memory allocated for the dynamic mimas. The exerimental system, VTexturer, References [1] L. Williams Pyramidal Parametrics. ACM SIGGRAPH '83. vol.17, Issue 3, [] C. Tanner, C. Migdal, and M. Jones The Clima: a Virtual Mima. Proc of the 5th Annual Conference on Comuter Grahics and Interactive Techniques [3] N. Ray, X. Cavin, and Bruno Levy Vector Texture Mas on the GPU. ublications/aers/005/vtm/vtm.df [4] J. Haddon and I. Stehenson Imlementing Vector-based Texturing in RenderMan. DCT Systems. uk/text/haddon.df [5] P. Sen, M. Cammarano, and P. Hanrahan Shadow Silhouette Mas. ACM Transactions on Grahics. vol., Issue [6] P. Sen Silhouette Mas for Imroved Texture Magnification. EUROGRAPHICS Worksho on Grahics Hardware [7] J. Tumblin and P. Choudury Bixels: Picture Samles with Shar Embedded Boundaries. Proc of the Eurograhics Symosium on Rendering. [8] P. Heckbert Discontinuity Meshing for Radiosity. Eurograhics Worksho on Rendering