Efficient Rendering of Glossy Reflection Using Graphics Hardware

Transcription

1 Efficient Rendering of Glossy Reflection Using Graphics Hardware Yoshinori Dobashi Yuki Yamada Tsuyoshi Yamamoto Hokkaido University Kita-ku Kita 14, Nishi 9, Sapporo , Japan Phone: , Fax: {doba, yamada, Abstract Recently, techniques for realistic image synthesis using computer graphics have been widely used in many applications. The reality of the computer-generated images can be greatly improved by taking into account the reflections observed in mirrors, cars, glass walls of a building, etc. Therefore, there has been extensive research into rendering these reflections. However, the computational cost associated with reflections is generally very high because of the complexity. On the other hand, recent advancements in graphics hardware have encouraged researchers to develop hardware-accelerated methods for realistic image synthesis. This paper proposes such a fast method for rendering reflections using graphics hardware. The proposed method can render not only the ideal specular reflection such as from a mirror but also the glossy reflections such as those from a metal surface. Keywords: Glossy Reflection, Efficient Rendering, Graphics Hardware. 1. Introduction The real-time rendering of realistic images has become one of the most important research fields in computer graphics. The intensities of virtual objects have to be calculated accurately by taking into account the reflectance property of the object in order to create realistic images. Rendering of specular reflections observed in surfaces of objects is important in order to enhance the reality of the image. Thus, there has been much research into the rendering of reflections. However, one of the problems is the high cost of computing the reflections, especially with glossy reflections. To address this problem, recent researchers have developed methods for rendering reflections using graphics hardware. The performance and the functionality of graphics hardware have been greatly improved in recent years. This has made it possible to create realistic images very quickly, including the specular reflections [11] [4] [7] [10] [15]. However, most of the previous methods have been limited to the reflections of objects far away from the specular object or the reflections of static objects. Therefore, these earlier methods are not suitable for the accurate rendering of reflections of dynamic objects close to the specular objects. Iwasaki et al. proposed a method to address this problem [8]. However, the method is limited to ideal specular reflections such as those from water surfaces. This paper addresses these problems and proposes a fast method for rendering both ideal specular and glossy reflections. The method realizes the efficient rendering of the reflections of dynamic objects that are close to the specular objects. In this method, the objects reflected in the specular objects are represented by a set of virtual planes. The part of the object between adjacent virtual planes is projected onto another virtual plane and the resulting image is stored as a slice texture. To display the reflected image from a specular object, the intersections between the virtual planes and the ray reflected from the specular object are calculated, instead of computing the intersections between the object and the reflected rays. The slice textures are then mapped onto the specular object using the intersection points as texture coordinates. The creation and the mapping of the slice textures are accelerated by graphics hardware. This realizes an efficient rendering of the reflections. The above idea has then been extended to the rendering of glossy reflections. The proposed method has the following advantages. - Efficient rendering of reflections of objects close to the specular object. - Efficient rendering of reflections of dynamic objects. - Efficient rendering of glossy reflections. The paper is organized as follows. In Section 2, the relationship between previous methods and the proposed method are discussed. In Section 3, the basic idea of the method is described. The details of the method are then explained in Sections 4 through 6. In Section 7, several examples are demonstrated and the usefulness of the method is discussed. Finally, Section 8 offers conclusions. 2. Related Work There are two representative approaches to rendering images of objects reflected in specular objects: a ray-tracing method [16] and an environmental texture mapping method [1]. The ray-tracing method is known to be one of the computationally expensive methods although it is able to calculate the reflections precisely by simulating the optical phenomena. Several researchers accelerate the ray-tracing method by making use of graphics hardware [12] [3]. However, these methods are not suitable for rendering complex scenes, due to the limitations in the current graphics hardware. Moreover, glossy reflections are not taken into account. On the other hand, the environmental texture mapping method can render reflections in real-time. However, the

2 resulting image is valid only when the object is at a sufficient distance from the reflective specular object. In addition, the environmental texture mapping method is basically applicable only to ideal specular reflection. Thus, many methods have been developed to address these problems. Heidrich et al. proposed a method using the idea of the light field for rendering reflections from both the ideal specular and the glossy surfaces [6]. However, this method requires a large amount of memory to store the light field. Hakura et al. proposed an extended version of the environment mapping techniques and succeeded in displaying local reflections [4] [5]. This method requires a sequence of environment maps that are pre-recorded over a selection of viewpoints by ray tracing. The method is efficient for static scenes but is not appropriate for scenes including dynamic objects. Iwasaki et al. addressed this problem and proposed a fast method for rendering ideal specular reflections [8]. However, their method is tailored to the rendering of water surfaces but the glossy reflections are not taken into account. In order to take the glossy reflections into account, several methods use pre-filtered environment maps based on the surface reflectance properties [9] [10] [7] [2]. Sloan et al. proposed precomputed radiance transfer functions for the efficient rendering of glossy surfaces [14] [15]. These methods can render the glossy surfaces in real-time, even if the viewpoint and the lighting environment are changed. However, since these methods extend the environmental texture mapping, the reflected objects must be sufficiently far from the reflective objects. Ofek et al. proposed a different approach for rendering reflections at interactive frame rates by using an explosion map [11]. However, the method is limited to ideal specular reflections. The method proposed in this paper is based on the method developed by Iwasaki et al [8]. The proposed method extends their method, not only to water surfaces but also to arbitrary objects, including glossy reflections. 3. Basic Idea Fig. 1 shows the basic concept of the proposed method. For simplicity, in the following, objects reflected in the specular objects are denoted as target objects. First, as shown in Fig. 1(a), multiple virtual planes (sample planes) are generated around the target object. The number of sample planes is determined adaptively by using the idea of LOD. When the distance between the specular object and the target object is long, the size of the reflected image in the specular object is expected to be small. In this case, the errors caused by using a small number of sample planes would not be perceived visually. If the target object is sufficiently far from the specular object, only a single sample plane is sufficient. This is equivalent to using the environmental texture mapping technique. Therefore the rendering time can be reduced by choosing an appropriate number of sample planes according to the distance from the specular object. Next, a virtual camera is placed in front of the sample planes. The part of the target object between adjacent sample planes is projected onto the screen of the virtual camera. Parallel projection is used for this process. The resulting image is stored as a texture. This texture is denoted as a slice texture. As shown in Fig. 1(b), the target object is represented by a set of slice textures. Next, the reflected rays of the viewing ray are calculated for each vertex of the specular object. As shown in Fig. 1(c), multiple reflection rays are generated according to the reflectance distribution at each vertex. We assume that each reflection ray represents a subtle

3 solid angle and the reflectance within the solid angle is constant. The intersections between the reflection rays and the sample planes are then calculated as shown in Fig. 1(c). The slice textures are mapped onto the specular object using the intersections as texture coordinates. Then, an intermediate image is generated by rendering the texture-mapped specular objects, viewed from the actual viewpoint. We call the intermediate image a reflection image. The reflection images are generated for all the reflected rays as shown in Fig. 1(c). The final image is created by accumulating all reflection images using the additive color blending functions of graphics hardware. In summary, the proposed method consists of the following three steps. 1. Generation of the sample planes using the idea of LOD. 2. Creation of the slice textures. 3. Rendering of reflections of the target object. In the following sections, the details of these processes are described. 4. Generation of Sample Planes The quality of the final image depends on the size, orientation, the number of sample planes. However, the rendering time is proportional to the number of sample planes. In this section, a method for determining the size and the orientation of the sample planes is proposed. An adaptive method for determining the number of sample planes is also proposed. The number of sample planes is chosen so that the quality of the resulting image is maintained. In the following, these methods are described with reference to Fig. 2. This figure shows a two-dimensional case for simplicity. 4.1 Size and Orientation of Sample Planes To determine the size and the orientation of the sample planes, a reference plane is generated as shown in Fig. 2. The reference plane is a square whose side is equal to the length of the diagonal line of the bounding box of the target object. The center of the reference plane is placed at the center of the bounding box. The orientation of the reference plane is perpendicular to a line connecting the center of the bounding box of the target object and the center of the bounding box of the specular object. We use the size of the reference plane as the size of the sample planes. The orientation of the sample planes is determined as follows. First, polygons, visible from the viewpoint, are extracted from the polygons consisting of the specular object. Next, an ideal specular reflection ray is calculated for each vertex of the visible polygons. Next, the vertices at which the reflection rays intersect the reference plane are extracted from the vertices of the visible polygons. Then, an average position, O, of the vertices and an average reflection ray, R, at the vertices are calculated. The orientation of the sample plane is set to be perpendicular to the average reflection ray, R, (see Fig. sample plane target object reference plane l 1 d 2 O d 1 specular object Figure 2:Generation of sample planes. 2). Using this method, the sample planes are almost perpendicular to as many reflected rays as possible. 4.2 Position and Number of Sample Planes Amongst the vertices of the bounding box of the target object, the nearest and the farthest vertices from the average position, O, are extracted to determine the positions of the sample planes. The sample planes are generated between these vertices. The center of each sample plane is placed on a line that is parallel to R and passes through the center of the bounding box of the target object. Intervals between the sample planes are determined adaptively according to the distance from the specular object. In our method, the reflection of the target object is computed approximately by using the sample planes. When the distance between the target object and the specular object is short, the approximation error becomes large, unless many sample planes are used. On the contrary, when the distance is long, the error is small even if the number of sample planes is small. Moreover, when the distance from the viewpoint to the specular object is long, the error is less perceptible since the reflected image of the target object occupies a small region on the screen. Based on this fact, we determine the intervals between sample planes so that the following equation is satisfied. di ε (i = 1,, n), (1) l v + l i where, as shown in Fig. 2, l v is the distance between the viewpoint and O, l i is the distance between ith sample plane and O, and d i is the interval between sample planes i and i+1. n is the number of the sample planes. As shown in Fig. 2, using the distance between the nearest vertex of the bounding box and O as l 1, l i and d i for i = 2,, n are determined by using the following equations. li = li 1 + di 1 di 1 = ε ( lv + li 1 ) (i = 2,, n), (2) where the number of the sample planes n is chosen so that l n exceeds the distance between the farthest vertex of the bounding box and O. R l v viewpoint

4 target object parallel projection α =1 Q j h sample plane j normal of sample plane j θ Δφ viewpoint virtual camera sample plane RGB components (a) Rendering part of target object. Figure 3:Creation of slice texture. 5. Creation of Slice Texture The slice texture for each sample plane is created by generating images of part of the target object between adjacent sample planes. To do this, a virtual camera is placed in front of the sample plane as shown in Fig. 3(a). The reference point is at the center of the sample plane. The viewing direction is the normal of the sample plane and the parallel projection is specified. The adjacent sample planes are used as a near and a far clipping planes. Then, a part of the target object is rendered. As shown in Fig. 3(b), the alpha component of the pixels corresponding to the part of the target object is set to zero. The alpha component of the other pixels is set to one. The resulting image forms the slice texture. The alpha component is used for determining the visible part of the target object when viewed from the specular object (see Section 6). Finally, the slice texture is stored after constructing a Mip-Map structure [17]. 6. Rendering Reflection A viewing ray is generated for each vertex of the specular object. Next, multiple reflection rays are generated at each vertex (see Fig. 1(c)). The number of the reflection rays, m, is determined according to the reflectance distribution at the vertex. We assume that each reflection ray represents subtle solid angle, Δφ, specified by the user. Within this solid angle, the reflectance is assumed to be constant. Next, the intersection between the reflection ray and the sample plane is calculated. Using this intersection as the texture coordinate, the slice texture is mapped onto the specular object. In this mapping process, an appropriate level in the Mip-Map structure is selected according to the distance from the intersection to the vertex of the specular object. Then, the specular object is rendered and the resulting image is stored as a reflection image. m reflection images are created, corresponding to m reflection rays. The final image is created by blending all these reflection images. In the following, the Mip-Map level selection and the creation of the reflection image are described in detail. 6.1 Mip-Map Level Selection Consider reflection ray, r i (i = 1,, m), at vertex P as shown in Fig. 4. The intersection point between ray, r i, and sample plane, j, is Q j and the distance from P to Q j is s j. As mentioned previously, ray r i represents a beam α =0 α component (b) RGB and α components of slice texture. Figure 4: Mip-Map level selection. with solid angle Δφ (see Fig. 4). The Mip-Map level is selected, based on the intersection area ΔA of the beam with the sample plane. ΔA is approximately calculated by the following equation. 2 2 πh π ( s j tan( Δφ / 2)) ΔA =, (3) cosθ cosθ where h is the radius of an intersection circle between the beam and a plane perpendicular to ray r i, and θ is the angle between ray r i and the normal vector of sample plane j (see Fig. 4). We choose the Mip-Map level so that an area corresponding to a single pixel is nearly the same as ΔA. This makes it possible to approximately compute the average color of the target object within the beam. 6.2 Creation of Reflection Image Let us assume the distances of the sample planes from the center of the specular object increase in the order i = 1, 2,, n. First, the intersection, Q n, between ray r i and the farthest sample plane n is calculated. The slice texture of sample plane n is mapped onto the specular object so that Q n maps to P. Then the texture-mapped specular object is rendered. Similarly, the slice texture of sample plane n-1 is mapped onto the specular object. Again, the specular object is rendered. But in this case, the colors in the frame buffer are multiplied by the alpha components of the slice texture. This process removes the invisible part of the target object from the specular object, since the alpha components of the texels corresponding to the target object are set to 0. These processes are repeated for all sample planes. The resulting image is then the reflection image for r i. 7. Results s j P specular object This section shows several examples to demonstrate the usefulness of our method. We use a desktop PC with Pentium GHz and ATI RADEON X800. In the following examples, the size of images is 512x512 and the size of the slice textures is 256x256. The solid angle, Δφ, represented by each reflection ray is set to 0.1 degrees. Table 1 shows the rendering time and the number of sample planes. Fig. 5 shows examples of the glossy reflections. The car is the glossy reflective object. We use the Phong reflection model [13]. Figs. 5(a) and 5(b) shows the images from different viewpoints. As shown in these figures, the occlusions in the reflected image in the car are computed accurately. The average numbers of r i

5 reflection rays for these images are 18. The numbers of the samples planes ranged from 2 to 7. To verify our method, we calculated a difference image between Fig. 5(b) and an image generated by using a sufficient number of sample planes. The sufficient number of sample planes is determined experimentally and in this case 20 sample planes are used. Fig. 5(c) shows the resulting difference image. In this image, the 100 % indicates the difference in intensity is 255. As shown in this image, our method can render the glossy reflection accurately. The rendering time for Figs. 5(a) and 5(b) are 0.9 and 2.5, respectively. Next, Fig. 6 shows glossy reflections in various situations. In Fig. 6(a), multiple target objects are reflected in the side face of the toaster. Fig. 6(c) shows the reflection of a soccer ball on the glossy reflective box. In Figs. 6(b) and (c), not only the reflection of surrounding objects but also the reflection of the reflective object itself are rendered. Fig. 6(d) shows reflections of dynamic objects. The airplane and the buggy on the desk move. Even when the objects move, the glossy reflections are rendered accurately and efficiently. The rendering times for these images are less than 0.2seconds. This implies that our method can create realistic glossy reflections almost in real-time. 8. Conclusion We have proposed an efficient method for rendering reflections using graphics hardware. In the method, an object is represented approximately by using sample planes and slice textures. The number of sample planes is determined adaptively to speed up the computation. The idea of the Mip-Map texture is utilized to increase the accuracy of the intensity calculation. The image of the reflection of the object is created by mapping the slice textures onto specular objects. There are several outstanding items to be addressed in the future. First, in our current implementation, the reflection rays are calculated at only the vertices of the specular object. Therefore, the accuracy of the final image depends on the number of polygons in the specular objects. The solution to this problem is to use a pixel shader to compute the reflections on a pixel by pixel basis. Next, when there are multiple specular objects, we must take multiple reflections into account. Our method can be extended to multiple reflections by considering the reflections in the creation of the slice textures. However, this will increase the computation time. Therefore, a further acceleration method must be developed to take multiple reflections into account. References [1] J. Blinn, M. Newell, Texture and Reflection in Computer Generated Images, Communications of the ACM, Vol. 19, No. 10, pp (1976). [2] B. Cabral, M. Olano, P. Memec, Reflection Space Image Based Rendering, Proc. SIGGRAPH 99, pp (1999). [3] N. A. Carr, J. D. Hall, J. C. Hart, The Ray Engine, Proc. Graphics Hardware 2002, pp (2002). [4] Z. S. Hakura, J. M. Snyder, Realistic Reflections and Refractions on Graphics Hardware with Hybrid Rendering and Layered Environment Maps, Proc. Eurographics Workshop on Rendering 2000, pp (2000). [5] Z. S. Hakura, J. M. Snyder, J. E. Lengyel, Parameterized Environment Maps, Proc. Symposium on Interactive 3D Graphics 2001, pp (2001). [6] W. Heidrich, H. Lensch, M. F. Cohen, H. P. Seidel, Light Field Techniques for Reflections and Refractions, Proc. Eurographics Workshop on Rendering 1999, pp (1999). [7] W. Heidrich, H. Lensch, M. F. Cohen, H. P. Seidel, Realistic, Hardware-accelerated Shading and Lighting, Proc. SIGGRAPH 99, pp (1999). [8] K. Iwasaki, Y. Dobashi, T. Nishita, A Fast Rendering Method for Refractive and Reflective Caustics due to Water Surfaces, Computer Graphics Forum (Proc. EUROGRAPHICS 2002), Vol. 23, No. 3, pp (2003). [9] J. Kautz, M. D. McCook, Approximation of Glossy Reflection with Prefiltered Environment Maps, Proc. Graphics Interface 2000, pp (2000). [10] J. Kautz, P. P. Vazquez, W. Heidrich, H. P. Seidel, A Unified Approach to Prefiltered Environment Maps, Proc. Eurographics Workshop on Rendering 2000, pp (2000). [11] E. Ofek, A. Rappoport, Interactive Reflections on Curved Objects, Proc. SIGGRAPH 98, pp (1998). [12] T. J. Percell, I. Buck, W. R. Mark, P. Hanrahan, Ray Tracing on Programmable Graphics Hardware, ACM Trans. on Graphics (Proc. SIGGRAPH 2002), Vol. 21, No. 3, pp (2002). [13] B. T. Phong, Illumination for Computer Generated Images, Communications of the ACM, Vol. 18, No. 6, pp (1975). [14] P. P. Sloan, J. Kautz, J. Snyder, Precomputed Radiance Transfer for Real-time Rendering in Dynamic, Low-frequency Lighting Environments, ACM Trans. on Graphics (Proc. SIGGRAPH 2002), Vol. 21, No. 3, pp (2002). [15] P. P. Sloan, J. Hart, J. Snyder, Clustered Principal Components for Precomputed Radiance Transfer, ACM Trans. on Graphics (Proc. SIGGRAPH 2003), Vol. 22, No. 3, pp (2003). [16] T. Whitted, An Improved Illumination Model for Shaded Display, Communications of the ACM, Vol. 23, No. 6, pp (1980). [17] L. Williams, Pyramidal Parametrics, Computer Graphics, Vol. 17, No. 3, pp (1983).

6 10 [%] 5 0 (a) (b) (c) Figure 5: Rendering of glossy specular reflections. There are three objects and the car is glossy reflective object. In (a) and (b), the number of sample planes are determined adaptively depending on the distance from the car center and the viewpoint. (c) shows a difference image between Fig. (b) and an image generated by using 20 sample planes. (a) Reflections in a toaster (b) Reflections in a pot (c) Reflection in a toy box (d) Reflections in a dynamic scene. Figure6:Glossy specular reflections in various situations.