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1 RUF * (A Simple and Efficient Antialiasing Method with the RUF buffer) (, Byung-Uck Kim) (Yonsei Univ. Depth of Computer Science) (, Woo-Chan Park) (Yonsei Univ. Depth of Computer Science) (, Sung-Bong Yang) (Yonsei Univ. Depth of Computer Science) (, Tack-Don Han) (Yonsei Univ. Depth of Computer Science) : ( ) : ( ), (Fax) gstring@yonsei.ac.kr(or kimbu@mythos.yonsei.ac.kr)

2 RUF,. RUF (Recently Used Fragment) RUF.. 8 (sparse), 1.3%, 31%, 3 11%. :,,,, RUF(Recently Used Fragment) A Simple and Efficient Antialiasing Method with the RUF buffer ABSTRACT In this paper, we propose a simple and efficient hardware-supported antialiasing algorithm and its rendering scheme. The proposed method can efficiently reduce the required memory bandwidth as well as memory size compared to a conventional supersampling when rendering 3D models. In addition, it can provide almost the same high quality scenes as supersampling does. In this paper, we have introduced the RUF (Recently Used Fragment) buffer that stores some or whole parts of a fragment or two more the merged results of fragments that recently used in color calculation. We have also proposed a color calculation algorithm to deteriorate the image quality as referencing the RUF buffer. Because of the efficiency presented in the proposed algorithm, the more number of sampling points increases the more memory saving ratio we can gain relative to the conventional supersampling. In our simulation, the proposed method can reduce the amount of memory size by 31% and the memory bandwidth by 11% with a moderate pixel color difference of 1.3% compared to supersampling for 8 sparse sampling points. Keywords: Antialiasing, supersampling, memory size, memory bandwidth, RUF buffer

3 (object), - (average-down filtering) [1].. n- 1- n. (accumulation buffer), [2]. (multi-pass). (hidden surface removal) Z., (blending) A-buffer [3]. A-buffer (coverage mask) (subpixel),.,., (intersection).. A-buffer,,. A-buffer,. n- n,,.,, A-buffer.

4 , RUF(Recently Used Fragment), RUF., RUF.,.,,., 3, 8, 1.3%, 31% 11%.., 2, RUF,. 3,., (polygon based), 3D (geometry),. (sca n conversion),.,.,, RUF. 2.1 A-buffer. (m), (C), (Z 1 Z m), RUF (ObjTag).

5 3, [4].,. 1 8., m-bit, 8 8. C Z 32. [4] RUF.. RUF,,,,, RUF. ( 1) Struct framebuffer[x][y] { Struct RUF buffer[x][y] Struct color buffer { { Color C; ObjectTag Objtag; CoverageMask m; } CoverageMask m; Struct depth buffer { Color R,G,B,A; Depth Z1,,Zm;} } } (a) (b) RUF ( 2) [X][Y] RUF

6 ( 3) 2.2 3,,, RUF 3..,, RUF if, ff, RUF., M if, C ff, C RUF,, RUF. : Z. Z Z buffer. (survived fragment, sur), M sur (1). M sur = M if if and only if Z if(i) < Z ff(i) (1), (i),.

7 :.,,. (M ff) (M sur) OR,.,, (a) (b), 4 (c) (d). ( 4) : F a, F b, F c.) RUF,,. 4 (a), (b), (c), RUF F a, F b., (2)., F b, RUF F a.

8 C new ff = C ff + C if N( M sur ) N( M sur M CRUF T T m m RUF ) (2), N( ) 1., T m.,., 4 (d), F c, F ca, RUF., RUF F b., (3)., F ca. C new ff = C ff + C if N( M sur ) N( M sur M CRUF T T m m RUF ) C ff N( M sur M T m ff ) (3), 5. A, B, C, A B C,., A B, C AB (4). (4) C ø CA = C + CA; CAB = CA + CB CA (4), RUF B,,. C, 3 (a) (b). 3 (a), RUF B (2). 4 1 CABC = CAB + CC CB 8 8 (5), 3 (b), A (3) (5)., ⅛ (C AB -C A ).

9 ( 5) RUF :, (coplanar space), [3,4]. (exclusive),. (2) (3), RUF,., (6) (7) RUF. M new RUF = M RUF M sur (6) new N( M RUF ) N( M C RUF = CRUF + C new sur N( M ) N( M RUF sur new RUF ) ) (7), RUF,., (6) (M) OR, (7)., RUF,, RUF.

10 3. 1 3,,. 3, OpenGL Mesa [5]. < 1> 3 Al Castle Dolphins Pig Rose+vase Teapot Venus Mesa.. 1- (1p), 8 (8ss), 4 4 (4 4s), 8 8 (8 8s). 8, 8 '.,,. 3.1 [6]. Color error = i, j c= R, G, B ( r ijc t ijc ) 2 (8) r ij t ij (i,j), r ijc, t ijc. (8)

11 , ,, 8., , [4]. ( 6) 2 8., 1.3% 31%.,.

12 < 2> 8 8ss % 64Bytes 44Bytes +31.3% ( 8 8.) (m + C) + m Z + objtag. m (C + Z). 3.,. < 3> (Bytes) % % % % < 4> 8ss 8 ( ) Al % 2.9 Castle % 2.8 Dolphins % 3.2 Pig % 2.7 Rose+vase % 2.6 Teapot % 2.7 Venus % 3.9

13 3.3 7.,. (9), RMB i i (Required Memory Bandwidth). (RMB i Occurence i) i {access pattern} (9) 4 (9)., 11.0%.,.,.,,. 4.,.,., Z buffer,.,. [1] Alan Watt. 3D Computer Graphics, Third Edition, Addison-Wesley, [2] Paul E. Haeberli and Kurt Akeley. The Accumulation Buffer. Hardware Support for High-Quality Re ndering, In Computer Graphics Annual Conference Series (Proceedings of SIGGRAPH 90), volume 24, pages , August [3] Loren Carpenter, The A-buffer, an Antialiased Hidden Surface Method, In Computer Graphics Ann ual Conference Series (Proceedings of SIGGRAPH 84), volume 18, pages , July 1984.

14 [4] Jin-Aeon Lee and Lee-Sup Kim, Single-Pass Full-Screen Hardware Accelerated Antialiasing, Proce edings 2000 SIGGRAPH/EUROGRPHICS Workshop on Graphics Hardware, pages 67-75, August [5] The Mesa 3D Graphics Library, [6] Norman P. Jouppi and Chung-Fa Chang, Z3: an economical hardware technique for high-quality anti aliasing and transparency, Proceedings 1999 SIGGRAPH/EUROGRPHICS workshop on Graphics h ardware, pages 85-93, 1998 ( 7). RMB RMB C 4 Bytes O 2 Bytes Z 4 Bytes M m bits ( ) *1 *4 *2 *5 RUF *3 *6 RUF

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