Russian

. “ ”( ) “ ”( 7) 3D- . .( 7-112) . . . . . .( 7) 1 2009 .

3D- - . - - ( 3D- - ). - , - 3D- , - . : - , . , - . , : 1) - 3D- , ; 2) . - . ( . . 3D- ) . - 1.5-3 , - , CPU. 1

4 1. 6 1.1. 6 1.2. 7 1.3. 11 1.4. 14 1.5. 15 1.6. 18 1.7. CPU 19 2. 22 2.1. BVH 22 2.1.1. 22 2.1.2. BVH CPU 24 2.2. 27 2.2.1. SIMD- 29 2.2.2. 32 2.2.3. 34 2.2.4. SIMD- 34 2.2.5. CPU 36 2.3. BVH - 36 2.3.1. 37 2.3.2. 39 2.3.3. 42 2.3.4. BVH 44 2.3.5. 45 2.3.6. 47 2.4. 48 2.4.1. 51 2.4.2. 52 3. 55 3.1. - 55 3.2. 55 2

3.2.1. 55 3.2.2. 56 3.2.3. 56 3.2.4. 58 3.2.5. 59 3.2.6. 59 4. 60 4.1. 60 4.2. , 61 4.3. BVH 63 4.3.1. 63 4.3.2. , 67 4.3.3. CPU 68 4.3.4. 69 4.3.5. , 71 4.4. 72 4.4.1. 72 4.4.2. CPU 77 4.4.3. 78 4.4.4. , 79 81 83 3

3D- . 3D- - (GPU, graphics proc- essing unit) - . , - . - . ( . . , – ). , - . - 3D- , ( – 3D- ). - , . . 3D- - . , , , . , - , . . . - , . , . - 4

. - , - 3D- , . - - . , , , 3D- . 3D- . , , - . CPU. • - , , - 3D- . • - . , . - - ; , - . , , - . 5

1. 1.1. 3D- . , . : , , NURBS, - . 3D- , - - , ( - ). . - - 3D- , . . , ( , 3D- ). . - 3D- , ( . . 3D- ). , 3D- , 3D- . . - , . SAH- . SAH- (Surface Area Heuristic) , SAH , . . - 3D- ( . SAH- [GS87; Hav01]). AABB. - 3D- . AABB X = xa, X = xb, Y = ya, Y = yb, Z = za, Z = zb ( . . ) , 3D- [xa, xb], [ya, yb], [za, zb]. AABB 3D- min/max . BVH. Bounding Volume Hierarchy – - ( ) 3D- , - . SAH- , AABB . 6

. 3D- ( - ‘ ’, ). SIMD. Single Instruction Multiply Data. SIMD- - : , ( ) 4 ( - CPU). SIMD- – , - . 1.2. , , - . [Whi80; Shi00; CPC84]. . . ( . . 1.1) - – . . . . - - , , . , , , . ( - ), ( . . 1.1). . 1.1: . «1» - , «3» - , «2» - . 7

- . , . , . , , . , . ( -) , , . . – , - , – . , . . . ( . . 1.2) Int Ray ( – ): Pwri Pwri Int ( Ray ) = K C ∑ C i dot ( N , L ) + K ∑ C i dot ( R ,V ) P + K r Int ( RayR ) (1.1) d m 2 i s 2 i i Ti i Ti Int (Ray ) - , . Int ( Ray ) ∈ [0..1] dot ( a, b) - C - .C ∈ [0..1] m m K - . K ∈ [0, ∞) d d C - i- . C ∈ [0..1] i i Pwr - i- . Pwr ∈ [0, ∞) i i T - i- i N - L - , i- i K - . K ∈ [0, ∞) s s R - i V - , P - . P ∈ [1, ∞) K - . K ∈ [0,1] r r RayR - , Ray 8

, , . - . . - . , RGB. - : , - . (1.1) . . 1.2: ( ). Int Int: d Pwri Int =K C ∑ Ci dot ( N , Li ) (1.2) Ti2 d d m i - π : K ⋅ I l ⋅ cos α , α ∈ [0, ] - d 2 Pwri , Il = Ci - Ti 2 ( . . 1.2). L, N– . cos α = dot ( L, N ) . C Int Int : s Pwri Int = K ∑ C dot ( Ri ,V ) P (1.3) s s 2 i i Ti 9

, . - . R - - , V- , . - : K ⋅ I l ⋅ cos P y , s γ - R V. P - « » « » . R V- , : K ⋅ I l ⋅ dot ( R , V ) P . s V = − Ray.Dir , Ray.Dir - R = − L + 2 ⋅ dot ( L , N ) ⋅ N K , K , K - , . a d s . , , . - , , - . . 1.3 - . . 1.3: . - , . - 10

. - , 3D- [CPC84]. 1.3. . 3D- , - . - , . , - 3D- . , . - 3D- , . - . - SAH (Surface Area Heuristic [Hav01, GS87]). , - N, : SA( N L ) SA( N R ) SAHCost ( N ) = ⋅ Count ( N L ) + ⋅ Count ( N R ) (1.4) SA( N ) SA( N ) : SA(N) – AABB(N) N; Count(N) – N; NL NR – N. (1.4) [Hav01]. , - . - . (1.4). - . , - [Wal07; WBS07] [HMFS07; Gar08]. - (1.4), , . 11

3D- . 3D- , 3D- . , ( . . 1.4). . 1.4: 3D- . : 1. : (n), n– . 2. (3D- ). 3. 3D- - . : 1. ( ), 3D- . - ‘ ’ . . 3D- , . kd-tree. 3D- , 3D- , - X = divx, Y = divy, Z = divz ( . . 1.5). - divx, divy, divy , - . SAH- [GS87; Hav01]. . 1.5: kd-tree. 12

: 1. 3D- . 2. 3D- - . 3. SAH- . : 1. SAH- : O(n * log n), n– - . 2. - , . . kd-tree . 3. ‘ ’ ( kd-tree 1- ). . kd-tree 1 2 - BVH. 3 . 2 3 BVH. BVH (bounding volume hierarchy). ( ) 3D- , ( . . 1.6). BVH - AABB . - . BVH, SAH, AABB , - . . 1.6: BVH. : 1. . BVH - , kd-tree. 2. SAH- - ( ). 13

BVH - , , – BVH ‘ ’ ( . . ), kd-tree. : 1. SAH- : O(n * log n), n– - . 2. 3D- . 3. 3D- BVH. 4. AABB ( , . . 1.6). . kd-tree BVH 1. 3 4 BVH kd-tree ( 2), . . kd-tree. 3D- BVH, . . ( - ). 1.4. 3D- , - ( . . 1.7a). . 1.7: . - , . . ( BVH). , - 14

, - BVH, AABB . ( - 3D- ) - . , . - - . ‘ ’ ( . . 1.7b), . - , - ( . . 1.7c), . . , 3D- BVH . . , . . , . 1.5. [Whi80; CPC84; Shi00] - , , , [Dut03]. , - . , (BVH) [KK86], kd-tree [Hav01], 3D- 5D- [AK87], - 3D- , (log n), n– 3D- ( ). 3D- [Wal07; HM08]. - . . - 15

. - [RSH05; WBS07; HM08]. , , , - . , ( 3D- ) , . , . - SIMD- - [Wal04] [Res07]. , . - BVH SIMD- [DHK08; WBB08]. , SIMD- 100%, - . , SIMD- [SCS*08] ( 16- ). . [PKGH97] , . [GR08] , - . , - . [ORM08] , / - . [BWB08] - , / - , , SIMD- 16

, ( BVH). ( , - , ) - ( ) - SIMD. . - - . - [WMG*07]. BVH kd-tree , - , 2 - ( . . ). - [WBKP08]. [Wal07] BVH - AABB. BVH - , , 3D- AABB . [WK06] 3D- . 1D - AABB (3D- )( BIH – bounding interval hierarchy). , kd-tree. , [HMFS07], , 3D- . - , , , - . , - . , . [YCM07] BVH, . , - 17

, , - . [Gar08] BVH ( , 3D- ). - ( AABB - [WBS07]; BVH - BVH; BVH, - ). , BVH. - , BVH - ( . . ). [IWRP06; SSK07] ( 3D- kd-tree) CPU, AMD Opteron Intel Core 2. [WIP08] - BVH CPU. , - CPU , - , BVH . ( ), ( ) - . ( . . ), - . [ZHWG08; LGS*09] - kd-tree BVH - (GPU, ) [NVI]. , - . , - CPU. 1.6. [NBS06; SNB07] – z- , - 18

. [SSGH01]. - (level of detail, LOD). [GWH01] - (radiosity – ), - , . [GWH01] - 3D- . [GFW*06; GFSS06] - , , 3D- . - ; - kd-tree, . , , . - kd-tree, , ( ) kd-tree - . [LYTM08] 2- - . - ( – ), . (kd-tree BVH) , . - - , . 1.7. CPU , , - . 3D- , , - . . - . - / , , - 19

. . - . . 1.8 Intel Core 2 , Core 2 Duo, Core 2 Quad. - (SMP ). Pen- tium III CPU (Intel, AMD) SIMD- , . . 1.8: SMP CPU. - CPU . , - ( . . CPU), - . ( . . 1.8 6Gb/sec). ( ). 20

- ( . . , - ). - BVH ( . 2.3). - CPU, - ( . 2.2) - ( . 2.4) . SIMD- , . . - . , - SIMD- . , . . - , . CPU GPU ( ) [NVI] , - - . , GPU , . . GPU , CPU. CPU. - CPU [Ben06]. 21

2. - BVH [Wal07] (bounding volume hierarchy, - ) [WBS07] SIMD- [Wal04; Ben06; Res07]. BVH - , . 2.1. BVH BVH [Wal07]. ‘ ’. - , . . ( - , ), SAH- BVH , . , - CPU. 2.1.1. 3D- 2 . - ( ) ( ) ( 4 32- ). BVH, - AABB. - SAH ( 1.3, (1.4)). - SAH - ( ) AABB N ( . . 2.1). AABB N , . N AABB . , i, i = int(0.999 K (x – a) / (b – a)), x – , int() – . - AABB . 22

AABB, , - ( . . 2.1). K-1 2 - ( , NL N R, . 2.1). - SAH (1.4) , . . - SA(NL), SA(NR) Count(NL), Count(NR). SA(NL) Count(NL) AABB , . SA(NR) Count(NR). K-1 SAH - , SAH. - , NL (NR), ( ) . . 2.1: ( ) N. AABB N K . - K-1 , . SAH , SAH. [Wal07] , K = 32, BVH , , . BVH , . . K, - , 2 . 23

SAH (1.4) . BVH - SAH (1.4) - ( SAH). 2.1.2. BVH CPU BVH, . - , . , BVH SMP , - ( . 1.7). – - BVH , / . BVH . , BVH , . . BVH - , . - 3D- BVH. - M , - 2M – 1 ( M – 1). - BVH . , . . . BVH , - 2 . [Wal07]. , , , BVH . 3D- . , - AABB , . , 1/6, [WK06]. . : AABB , . 24

. 2.2: 3D- . C 3D- , 3D- . T . T , /T 3D- ( . . 2.2). , , - : BMin, BMax – AABB 3D- . R = ( Rx , Ry , Rz ) – . X– . R ⋅ 0.999 F = ⋅ ( X − BMin ) – , , . BMax − BMin Id.x = int(F.x), Id.y = int(F.y), Id.z = int(F.z) – . : int() . AABB . , - . ( . 25

. 2.2). - . , . . . 3D- AABB. , - ‘ ’ BVH ( . 2.1). - . ‘ ’ BVH, 3D- ( . . ). ( - ). . - , . - - . : 1. BVH. BVH ( 3D- ) SAH, AABB , - . 2. 3D- - 3D- . . - BVH - . BVH . : 1. BVH - . - . BVH : , . . - . , - . 26

2. [Wal07] BVH 5.5- 8 Xeon. , - , CPU . [Wal07] BVH, BVH ( . 2.1) ‘ ’ . - BVH. , , - . - 1 , - BVH , - CPU. 2.2. 3D- , - ( . . 2.3). kd-tree BVH [RSH05; WBS07] . . 2.3: 3D- , . . , - (3D- ). ‘ ’. , , - 27

3D- . , , . , , BVH, - AABB . , ( . . 2.3), - , ( . . - ( ) ). [WBS07] ( . 2.1) - BVH. , 64, 256, 1024 . 2.1. BVH int BoxTest(int ActiveRayID, PACKET P, BVH_NODE * B) { // если пирамида пакета точно не пересекает охватывающий шестигранник if(AABBCulling(P.Frustum, B->AABB)) return P.N; // если пирамида пакета пересекает AABB, // то проверяются все отдельные лучи пакета до поиска первого пересечения for(int i = ActiveRayID; i < P.N; i++) { if(RayAABBTest(P.Ray[i], B->AABB)) // если луч пересекает AABB, см. 2.2.1 return i; } return P.N; } void PacketTraversal(BVH Bvh, PACKET P) { prepare(P.Frustum); // инициализация охватывающей пирамиды, см. в разделе 2.2.2 BVH_NODE * B = Bvh.Root; // текущий узел BVH int ActiveRayID = 0; // первый активный луч Init(Stack); while(true) { if((ActiveRayID = BoxTest(ActiveRayID, P, B)) < P.N) { // пакет пересекает AABB текущего узла B if(B.IsLeaf){ // если лист BVH // тест на пересечение с лучами для всех треугольников в листе for(all triangles in leaf) for(int i = ActiveRayID; i < P.N; i++){ // для всех лучей пакета RayTriangleTest(B->Tri[t], P.Ray[i]); // поиск ближайшего треугольника, см. 2.2.1 } else { // спуск глубже в BVH // отложить дальний узел их двух потомков узла B // (‘дальний узел’ - по отношению к основаниям пакета лучей) push(Stack, [ActiveRayID, FarChildNodePtr(B, P)]); // 2 значения в стек B = NearChildNodePtr(B, P); // а пока тестировать ближний узел continue; } } if(Stack.empty) break; [B, ActiveRayID] = pop(Stack); // извлечь 2 значения из стека } } ( - 3D- ) - 28

. CPU: BVH , . , CPU, . . BVH. 2.2.1. SIMD- [Wal04] SIMD [Intel-b] - ( 4 ) 4- . SIMD- - 4- ( float, 4 ). ( __m128, 16 ), , - 4- . - SoA ( ), . . 2.4. . 2.4: , SoA . 2.4, forg[0] (forg[1], forg[2]) x- (y-, z- ) . fdir . fT +1e+10, . ti orgi i- diri , . - trii. . 2.4, - 4 , SIMD- . 29

SIMD- AABB ( RayAABBTest, . 2.1). // ri – индекс SIMD-луча // P.Org4[0] = (__m128 *) forg[0]; и т.д. – см. рис. 2.4. P.T4 = (__m128 *) fT; // iDir4 = 1 / P.Dir4, т.е. обратное значение направления предварительно вычислено // sse_0 = [0, 0, 0, 0] // операторы *, -, + выполняют _mm_mul_ps, _mm_sub_ps, _mm_add_ps void RayAABBTest(unsigned int ri, PACKET P, AABB BV) { // см. Алгоритм 2.1 // эту репликацию можно вынести за скобки (за верхний цикл по лучам) const __m128 BV4[6] = {_mm_set_ps1(BV[0]),_mm_set_ps1(BV[1]),_mm_set_ps1(BV[2]), _mm_set_ps1(BV[3]), _mm_set_ps1(BV[4]), _mm_set_ps1(BV[5])}; const __m128 Org[3] = {P.Org4[0][ri], P.Org4[1][ri], P.Org4[2][ri]}; const __m128 iDir[3] = {P.iDir4[0][ri], P.iDir4[1][ri], P.iDir4[1][ri]}; const __m128 T[6] = {(BV4[0] - Org[0]) * iDir[0], (BV4[1] - Org[1]) * iDir[1], (BV4[2] - Org[2]) * iDir[2], (BV4[3] - Org[0]) * iDir[0], (BV4[4] - Org[1]) * iDir[1], (BV4[5] - Org[2]) * iDir[2]}; const __m128 taX = _mm_min_ps(T[0], T[3]), tbX = _mm_max_ps(T[0], T[3]); const __m128 taY = _mm_min_ps(T[1], T[4]), tbY = _mm_max_ps(T[1], T[4]); const __m128 taZ = _mm_min_ps(T[2], T[5]), tbZ = _mm_max_ps(T[2], T[5]); const __m128 ta = _mm_max_ps(_mm_max_ps(taX, taY), _mm_max_ps(taZ,sse_0)); const __m128 tb = _mm_min_ps(_mm_min_ps(tbX, tbY), _mm_min_ps(tbZ,P.T4[ri])); if(_mm_movemask_ps(_mm_cmple_ps(ta, tb))) // если какой-то луч пересекает AABB return true; // то считается, что SIMD-луч пересекает AABB return false; } SIMD- ( RayTriangleTest, . 2.1). [Wal04] ( . . 2.5). X B Y B` H A ab` C H` Z A` ac` dir C` org . 2.5: [org,dir] 2D- YZ. u, v t. , X YZ ( . . 2.5) 2D- . : , - . Cross( a, b) – , Dot(a, b) – . [A, B, ] – , [org, dir] – ( ). ab = B − A , ac = C − A , N = Cross( ab, ac) , N `= N / N . x = [1, N . y / N . x, N . z / N . y ] - 1 ( N`): 30

t = ( Dot( A, N `) − Dot(org , N `)) / Dot(dir, N `) = ( DAN − Dot(org , N `)) / Dot( dir, N `) H = org + t ⋅ dir – . YZ: H `= [0, H . y, H . z ] , A`= [0, A. y , A. z ] , ab`= [0, ab. y , ab. z ] , ac`= [0, ac. y , ac. z ] , ah`= H `− A` . H − A = u ⋅ ab + v ⋅ ac , u, v – H. ah`= u ⋅ ab`+ v ⋅ ac` , . . u v . ah`. y = u ⋅ ab`. y + v ⋅ ac`. y ah`. z = u ⋅ ab`. z + v ⋅ ac`. z , : ah`. y ⋅ ac`.z − ah`.z ⋅ ac`. y ah`. y ⋅ ac`.z − ah`.z ⋅ ac`. y u= = ab`. y ⋅ ac`.z − ab`.z ⋅ ac`. y N .x ab`. y ⋅ ah`.z − ab`.z ⋅ ah`. y ab`. y ⋅ ah`.z − ab`.z ⋅ ah`. y v= = , : ab`. y ⋅ ac`.z − ab`.z ⋅ ac`. y N .x ac`.z − ac`. y A`.z ⋅ ac`. y − A`. y ⋅ ac`.z u = H `. y ⋅ + H `.z ⋅ + = H `. y ⋅ KUY + H `.z ⋅ KUZ + KUD N .x N .x N .x − ab`.z ab`. y A`. y ⋅ ab`.z − A`.z ⋅ ab`. y v = H `. y ⋅ + H `.z ⋅ + = H `. y ⋅ KVY + H `.z ⋅ KVZ + KVD N .x N .x N .x 0≤t, , . 0 ≤ u , 0 ≤ v , u + v ≤1, H . // P.Org4[0] = (__m128 *) forg[0]; и т.д. - см. рис. 2.4 // P.T4 = (__m128 *) fT; P.Tri4 = (__m128i *) ftri; // sse_0 = [0, 0, 0, 0], sse_1 = [1, 1, 1, 1] // __m128i NewTri4 = [TriID, TriID, TriID, TriID], где TriID – индекс треугольника A,B,C // операторы *, -, + выполняют _mm_mul_ps, _mm_sub_ps, _mm_add_ps // _mm_inverse_ps(a) = 1 / a (быстрое вычисление обратного значения) void PacketTriangleTest(float3 A, float3 B, float3 C, PACKET P) { // SIMD-тест из [Wal04] // Определить (X,Y,Z) (проекция вдоль X на плоскость YZ), где тройка может принимать значения: // (0,1,2), (1,2,0) или (2,1,0), где 0..2 – индексы для выбора значений компонент 3D данных. // Предварительно здесь вычислить DAN, N`, KUY, KUZ, KUD, KVY, KVZ, KVD for(int ri = 0; ri < P.N; ri++) { const __m128 Org[3] = {P.Org4[0][ri], P.Org4[1][ri], P.Org4[2][ri]}; const __m128 Dir[3] = {P.Dir4[0][ri], P.Dir4[1][ri], P.Dir4[2][ri]}; const __m128 Nom = DAN4 - Org[X] – N`[Y] * Org[Y] - N`[Z] * Org[Z] const __m128 T = Nom * _mm_inverse_ps(Dir[X] + N`[Y] * Dir[Y] + N`[Z] * Dir[Z]); __m128 mask = _mm_and_ps(_mm_cmplt_ps(sse_0, T), _mm_cmple_ps(T, P.T4[ri])); if(!_mm_movemask_ps(mask4)) continue; // 0 < t < сохранённый t const __m128 HY = Org[Y] + T * Dir[Y], HZ = Org[Z] + T * Dir[Z]; const __m128 U = KUY4 * HY + KUZ4 * HZ + KUD4; mask = _mm_and_ps(mask, _mm_cmple_ps(sse_0, U)); if(!_mm_movemask_ps(mask)) continue; const __m128 V = KVY4 * HY + KVZ4 * HZ + KVD4; mask = _mm_and_ps(mask, _mm_and_ps(_mm_cmple_ps(sse_0, V), _mm_cmple_ps(U + V, sse_1))); if(!_mm_movemask_ps(mask)) continue; // если есть какое-то пересечение, то обновить t и ссылку на треуг-ник tri для SIMD-луча // на основе полученной маски const __m128i imask = _mm_castps_si128(mask); P.T4[ri] = _mm_or_ps(_mm_and_ps(mask,T),_mm_andnot_ps(mask,P.T4[ri])); P.Tri4[ri] = _mm_or_si128(_mm_and_si128(imask,NewTri4),_mm_andnot_si128(imask,P.Tri4[ri])); } } 31

2.2.2. ( . . 2.3) 2- , ( . 2.3 YZ) [Res07; ORM08]. . . , - ( , ) - . . 2.3 - X. : - , X- ( +, -). X- , 2, . X- - ab ( a < b), AABB 3D- ( . . 2.6). a b AABB 3D- X . 2.6: 1D- X. X=a X=b. X=a X=b - ( Y Z, . 2.3). 4- [a, y00, z00], [a, y01, z00], [a, y00, z01], [a, y01, z01], 4- [b, y10, z10], [b, y11, z10], [b, y10, z11], [b, y11, z11]. , . 2.3. - ( . . 2.7): N0 = [y00-y10, b-a, 0], N1 = [z00-z10, 0, b-a], N2 = [y11-y01, a-b, 0], N3 = [z11-z01, 0, a-b]. 32

BV[3+Y] BV[3+Z] 2D AABB BV[X] BV[3+X] BV[X] BV[3+X] Y Z BV[Y] BV[Z] y11 z11 y01 N2 z01 N3 2D AABB y00 N0 z00 N1 y10 z10 a b X a b X . 2.7: 2D- ( . . 2.3) AABB. . [Vx, Vy, Vz] - N0 , : Dot( N 0 , [Vx,Vy,Vz ] − [a, y 00 , z 00 ]) = Vx ⋅ ( y 00 − y10 ) + Vy ⋅ (b − a ) + a ⋅ y10 − b ⋅ y 00 Vx ⋅ ( y 00 − y10 ) /(b − a ) + (Vy + a ⋅ y10 − b ⋅ y 00 ) /(b − a ) < 0 . : q 0 = [b − a , b − a , b − a , b − a ] , q2 = [ y00 − y10 , z00 − z10 , y11 − y01 , z11 − z01 ] / q0 , q1 = [a ⋅ y10 − b ⋅ y00 , a ⋅ z10 − b ⋅ z00 , b ⋅ y01 − a ⋅ y11 , b ⋅ z01 − a ⋅ z11 ] / q0 , SIMD- ([Res07]): // операторы *, -, + выполняют _mm_mul_ps, _mm_sub_ps, _mm_add_ps // Тройка (X,Y,Z) (где X - базовая ось пакета лучей) может принимать значения: // (0,1,2), (1,2,0) или (2,1,0), где 0..2 – индексы для выбора значений компонент 3D данных int VertexCulling(FRUSTUM F, float3 V) { const int BitCull56 = (V[F.X] < F.a ? 0x10 : 0) | (V[F.X] > F.b ? 0x20 : 0); const __m128 ZYZY = _mm_set_ps(-V[F.Z], -V[F.Y], V[F.Z], V[F.Y]); const int BitCull4x = _mm_movemask_ps(F.q1 + _mm_set_ps1(V[F.X]) * F.q2 + ZYZY); // Если битовый код содержит 1 в некоторой позиции, то точка V лежит по внешнюю сторону // (т.е. отсечена) от соответственной плоскости пирамиды // Битовый код нужен для отсечения треугольников от пирамиды. return BitCull56 | BitCull4x; } AABB ( 6 ) AABB . AABB 1D- , - float BV[6] , . 2.7. - BV ( AABB) - : S0 x = y00 − y10 < 0 ? X : 3 + X S0 y = b − a < 0 ? Y : 3 + Y ; 33

S1x = z00 − z10 < 0 ? X : 3 + X S1z = b − a < 0 ? Z : 3 + Z ; S 2 x = y11 − y 01 < 0 ? X : 3 + X S2 z = a − b < 0 ? Y : 3 + Y ; S 3 x = z11 − z 01 < 0 ? X : 3 + X S3z = a − b < 0 ? Z : 3 + Z ; S5x = 3 + X ; S6 x = X . SIMD- - AABB ( VertexCulling): // операторы *, -, + выполняют _mm_mul_ps, _mm_sub_ps, _mm_add_ps // Тройка (X,Y,Z) (где X - базовая ось пакета лучей) может принимать значения: // (0,1,2), (1,2,0) или (2,1,0), где 0..2 – индексы для выбора значений компонент 3D данных bool AABBCulling(FRUSTUM F, float BV[6]) { if(BV[F.S5x] < F.a || BV[F.S6x] > F.b) return true; // отсечено const __m128 XXXX = _mm_set_ps(BV[F.S3x], BV[F.S2x], BV[F.S1x], BV[F.S0x]); const __m128 ZYZY = _mm_set_ps(-BV[F.S3z], -BV[F.S2y], BV[F.S1z], BV[F.S0y]); if(_mm_movemask_ps(XXXX * F.q2 + ZYZY + F.q1)) return true; } 2.2.3. ( ) - ( ) 2.1 AABB , ‘ ’ BVH. , AABB BVH PacketTraversal. - . [ORM08] - , SIMD- , BVH ( . - 2.2). SIMD- , : . BoxFilter. 2.2.4. SIMD- [Res07] ‘ ’ kd-tree ( BVH) , ( , ). . . - BVH . , - BVH, ‘ ’ - , , AABB ( . 2.2.2). AABB 34

, . . ( . . 2.6) - . 2.2. BVH int BoxFilter(int ActiveRaysCount, PACKET P, BVH_NODE * B) { // если пирамида пакета точно не пересекает охватывающий шестигранник if(AABBCulling(P.Frustum, B->AABB)) return 0; // если пирамида пакета пересекает AABB, то фильтруются лучи [ORM08] int N = 0; for(int i = 0; i < ActiveRaysCount; i++) { const int RayID = P.ActiveSIMDRaysIDs[i]; if(RayAABBTest(RayID, P, B->AABB)) // если луч пересекает AABB swap(P.ActiveSIMDRaysIDs[N++], P.ActiveSIMDRaysIDs[i]); } return N; // возвращает количество активных лучей, сдвинутых в начало ActiveSIMDRaysIDs } void PacketTraversal(BVH Bvh, PACKET P) { prepare(P.Frustum); // инициализация охватывающей пирамиды, см. в разделе 2.2.2 // Для всех SIMD-лучей, определённых как в разделе 2.2.1 for(int i = 0; i < P.SIMDRaysCount; i++) P.ActiveSIMDRaysIDs[i] = I; BVH_NODE * B = Bvh.Root; // текущий узел BVH int ac = P.SIMDRaysCount; // кол-во активных SIMD-лучей Init(Stack); while(true) { if((ac = BoxFilter(ac, P, B)) > 0) { // Пакет пересекает AABB текущего узла B и есть активные лучи if(B.IsLeaf){ // если лист BVH // Транзитная пирамида для активных лучей, пересекающих AABB этого листа BVH [Res07], // строится так же как в разделе 2.2.2, но базовый охватывающий // интервал (см. рис.2.6) ограничивается по AABB этого листа (B->AABB) P.LeafFrustum = TransientLeafFrustum(P, ac, B); // Тест на пересечение с пакетом для всех треугольников в листе for(all triangles in leaf) { // Треугольник отсечён, если все вершины лежат по одну сторону пирамиды if(VertexCulling(P.Frustum, B->Tri[t].A) & VertexCulling(P.Frustum, B->Tri[t].B) & VertexCulling(P.Frustum, B->Tri[t].C)) continue; // Внутри этой функции перебирать только активные лучи, // как это сделано в BoxFilter здесь PacketTriangleTest(B->Tri[t].A, B->Tri[t].B, B->Tri[t].C, P, ac); } } else { // спуск глубже в BVH // отложить дальний узел их двух потомков узла B (дальний по отношению к пакету) push(Stack, [ac, FarChildNodePtr(B, P)]); B = NearChildNodePtr(B, P); // а пока тестировать ближний узел continue; } } if(Stack.empty) break; [B, ac] = pop(Stack); } } , , , BVH. . [Res07] , ( - ) - AABB . , - 35

VertexCulling ( 2.2) 90% - ( ) - SIMD- . [Res07], ‘ ’ kd-tree - , , ( ). BVH , 2.2. 2.2.5. CPU M ( – ), . 2.8. , - CPU, ( , - . .), . - , , , . . … … … M … … i … 0 1 … … . 2.8: . . - - . , . 2.3. BVH BVH, 3D- . - 3D- . - 3D- , ( . . ). 36

[WMG*07]. , - . 3D- - / - < 3, - . - – . - 3D- . BVH, . . - 3D- , . . - . - . - - BVH . , - , 3D- . , - . , . . , - . - , . 2.3.1. . X Y– 3D- X Y, . . X ∩ Y = Y ( . . 2.9a). - [Hav01] P(Y | X) = SA(Y) / SA(X) – , , - X, Y. SA(X) – X. BVH - 3D- BVH, P(Y | X), 3D- , (X AABB , - Y). - , BVH. 37

. 2.10: b ( / ), a. . . . , - , . . . 2.10: 14 , (b) (13 - ), (a) (16 ). , (a) , : (a) - , , . - (b), ( / ). (b) - 3D- . 2.3.2. / . , . k - S(k) R(k), ( . . 2.11). . 2.11: , . S(k): AreaC(k ) = π ⋅ R(k ) 2 (2.1) 39

P S(k) 1: k N AVG ( k ) = Normalized ( ∑ ni ) (2.2) i =1 ni – 1 i- . (2.2) - , NAVG(k) = NaN ( NaN=0/0) ( , , ). NAVG(k) ( , ni - ). ‘ ’ k P: k AreaP ( k ) = ∑ TriAreai ⋅ abs ( dot ( N AVG ( k ), ni )) (2.3) i =1 TriAreai – i- , dot(a, b) – . k , : AreaP ( k ) reg (k ) = (2.4) AreaC ( k ) / 3D- reg (k ) ∈ [0..1) ( i dot(NAVG(k),ni) > 0). , reg(k) 1. 3D- reg(k) 1( - , ). : reg(k) - , . . AreaC(k) - S(k), k . reg(k) - . . - ( ) k - : CountDistinctVertices( k ) regBound ( k ) = (2.5) MaxCount MaxCount – , - . regBound(k) - k - ( . . 2.10). regBound(k) ( / - ). k , : reg ( k ) − regBound ( k ) > 0 (2.6) 40

(2.6) reg(k) - . . 2.12: : (a) AABB AABB , ; (b) - , - AABB , - (a). (2.6). 3D- , ( , ). . 2.12a - , , . AABB AABB . - AABB. - - - , , ( . . 2.12b). ‘ ’ : SA( S ( k )) sizeBound ( k ) = max(1, ) (2.7) MaxSize ⋅ AvgSA AvgSA – 3D- . MaxSize – (MaxSize – ). sizeBound(k) 1 k , . sizeBound(k) (2.6) : reg ( k ) − sizeBound ( k ) ⋅ regBound ( k ) > 0 (2.8) 41

‘ ’ sizeBound(k), - k ‘ ’ . (2.8) , k - , , 2.3.1. 2.3.3. (2.8) : Acc ( k ) = reg ( k ) − sizeBound ( k ) ⋅ reg Bound ( k ) (2.9) Acc(k) ‘ ’ ( - , . 2.3.1). Acc(k) > 0, k - . Acc(k) ‘ ’ ‘ - ’ , (2.4), (2.5) (2.7), ‘ ’ . Acc(k) - , / ( . . 2.15). Acc(k) , - : ‘ ’ ‘ ’ . . , . k-1 Acc(k) , - ( , . . 2.13). , - Acc(k), . ‘ - ’ , Acc(k) < 0 . . 2.13: Acc(k) : t1, t2, t3, t4. , Acc(k), - . : t1 t4 . 42

. 2.14: : 2 (a), - , (b). ( [GWH01]). - , 3D- ( . . 2.14a). - , 2- , - . 2 1 ( . . 2.14b). 2- . Acc(k). - ( - , [-2..2] – Acc(k) - 3D- ). Acc(k). 2 Acc , . , Acc 0. ( . . - ). . 2.15: : 3D- ( ), , ( ) ( ). 43

‘ ’ . ‘ ’ , ‘ - ’ ( . . 2.15, ). ‘ ’ , - . Acc ‘ ’ - . ( . . 2.15, ). 3D- [SSGH01]. - . 2.3.4. BVH BVH. , , - , . - AABB , 3D- . . 2.16: BVH . BVH - AABB, BVH , - [Wal07] ( . BVH 2.1). ( ) , AABB. - AABB ( . . 2.16). BVH ( BVH - AABB), . 44

. AABB 2 - . 2- : 1) - , , , , - L( L = 32); 2) AABB 2 - . , . 2 , AABB 3D- BVH, - ( . . 2.17b). , 3D- , - AABB - ( . . 2.17a). . 2.17: AABB , 3D- (a). , 3D- - , BVH (b). 2.3.5. . . - , , , . 3D- , . ( . . 2.18, VertexIndices). - , , . . . 3 - 3D- , 4 ( . . 2.18a). 45

, , - 255 ( , - ). 3D- , ( . . 2.18, VCache), ( . . 2.18b). - , , ( 1 ). . - BVH , - 3D- ( . . 2.18, VCache). 3D- . . 2.18: , - , . 46

, - , ( . . 2.18, VCullCodes). SIMD- ( . 2.2.4 [Res07]) , - . =1 , - ( . . ), =0 , - . 3 , - . [Res07] 3- - , . . 2.18 (6 ) 6* 3 = 18 . , 7 , VCullCodes ( . 2.3). 2.3. void PacketClusterTest(TRIANGLE_CLUSTER C, PACKET P) { // загрузка вершин в кэш for(int i = 0; i < C.VerticesCount; i++) P.VertexCache[i] = GlobalVertices3DCoords[C.VertexIndices[i]]; // отсечение вершин (см. подраздел 2.2.2, [Res07]) for(int i = 0; i < C.VerticesCount; i++) P.VCullCodes[i] = VertexCulling(P.LeafFrustum, P.VCache[i]); // тест треугольников for(int i = 0; i < C.TrianglesCount * 3; i += 3) { unsigned char a = C.TrianglesCompressed[i]; unsigned char b = C.TrianglesCompressed[i+1]; unsigned char c = C.TrianglesCompressed[i+2]; if(P.VCullCodes[a] & P.VCullCodes[b] & P.VCullCodes[c]) continue; // треугольник отсечён // тест треугольника и пакета лучей (см. раздел 2.2.1, [Wal04]) PacketTriangleTest(P.VCache[a], P.VCache[b], P.VCache[c], P); } } 2.3.6. - , [GWH01] . [GWH01] - ‘ ’. ‘ ’: Error(k) = Efit + a1Edir + a2Eshape, Efit ‘ ’ ( . . ); Edir ‘ ’ - ; Eshape ‘ 47

’ (‘ ’ ‘ ’ ; a1 a2 – - ( ). - . Acc(k), , . , , BVH ( ). Acc(k) ‘ - ’ , - . Acc(k) ‘ ’ - , - BVH AABB ( , - ). Error(k) Acc(k) , Error(k) = 0 – ‘ ’ , - . , Acc(k) = 0 – : Acc(k) > 0, . - MaxSize MaxCount, . ( . 4.3.4) Acc(k) Error(k) . - Acc(k) Error(k) BVH. 2.4. , - 3D- . - , - ( 1.4). . - 48

, « - » ( . . )( ‘ ’ [Wal04; WBS07; RSH05; Res07], 2.2). - , . , ( . . 2.19). , , . . - , - ( ). - - . - - , - [Dut03]. . 2.19: . , - . - . [NM08] . , - 3D- , CPU , . . - . . . 2.20 . , 4- , 4 . - 4- ( . . 2.20a). , 49

‘ ’ ( , . 2.20a). - - 3D- 4- . , 4 4- .4 - 4- 4- ( . . 2.20b). - . 4×4 ( . . 2.20c), - . - AABB, . . AABB - - , . . 2.20: . , - , . , - ( ) . 3D- ( . . 2.20d). 3D- , . , - 50

, , . 2.20a 2.20b. - , . . - - - , - . BVH AABB ( ). 2.4.1. . 2.21 . , - - , ( . . 2.21a). - 3D- ( . . 2.21b). ( ) 3D- , - . . 2.21: - . i P0P1P2P3 ( , ) - 1 i - P'0P'1P'2P'3 ( . . 2.21c). , i ( . . 2.21d). , 64- - . , 16 . ( - 51

) 64/16 . ( ) . - ( ), , - ( . 0 . 2.21d 2.21c). ( ) - ( , 3D- ). [Dut03]. 3D- ( . . 2.21b) : Re s i = min(max(1, Alpha ⋅ PBoxSizei / LBoxSizei ), 8) i ∈ {x, y , z} , PBoxSize (LBoxSize) – AABB - ( AABB ); Alpha – ( Alpha = 256). , , , , . 2.4.2. , - 3D , SIMD- SIMD- ( . . 2.22). SIMD- (0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF). - , - - , . SIMD- 4 - SIMD- . 2 - . ( . . 2.22a) 1 - , - - , SIMD- , - . - , SIMD- . - - - , SIMD- - 10% ( - ). - , - - . 52

. 2.22: - , : (a) . - - ; (b) - . : SIMD- __m128, . . 128- , 4- float. , Orgi.X, Orgi.Y, Orgi.Z – __m128, 4 4- , - ; Dirj,i.X, Dirj,i.Y, Dirj,i.Z – __m128 ; maskj,i – __m128 SIMD- . SIMD- [Orgi, Dirj,i, maskj,i] SIMD- , 4- j- - i- ( . 2.21b). - - 2- , ( . . 2.21e, 2.2.2, [ORM08] [Res07], - SIMD- ). - AABB . 2.4 AABB AABB ( BVH, 2.2, . 2.1). - - . - - ( . . 2.22b). - - , SIMD- - 10%. - 53

- ( . 2.22b) / SIMD- ( - 2.2.3 [ORM08]). 2.4. - BVH int BoxTest(int ActiveSubFrustum, MULTIPACKET MP, BVH_NODE * B) { // если пирамида мульти-пакета точно не пересекает охватывающий шестигранник if(AABBCulling(MP.Frustum, B->AABB)) return MP.N; // см. раздел 2.2.2 // если пирамида мульти-пакета пересекает AABB, // то проверяются динамически уменьшающиеся суб-пирамиды for(int i = ActiveSubFrustum; i < MP.N; i++) { if(AABBCulling(MP.SubFrustum[i], B->AABB)) continue; // см. раздел 2.2.2 return i; } return MP.N; } void MultiPacketTraversal(BVH Bvh, MULTIPACKET MP) { // инициализация охватывающей пирамиды и суб-пирамид for(int i = 0; i < MP.N; i++) prepare(MP.SubPacket[i].Frustum); prepare(MP.Frustum); // инициализация общей пирамиды на основе суб-пирамид BVH_NODE * B = Bvh.Root; // текущий узел BVH int ActiveSubFrustum = 0; // первый активный суб-пакет Init(Stack); while(true) { // обновление суб-пирамид, если счётчик активных лучей уменьшен // пирамиды вычисляются как в разделе 2.2.2 for(int i = ActiveSubFrustum; i < MP.N; i++) if(MP.SubPacket[i].ActiveSIMDRaysCounter уменьшен на 10%) recompute(MP.SubPacket[i].Frustum); // на основе SIMD-масок лучей if((ActiveSubFrustum = BoxTest(ActiveSubFrustum, MP, B)) < MP.N) { // какая-то суб-пирамида пересекает AABB текущего узла B if(B.IsLeaf){ // если лист BVH for(int i = ActiveSubFrustum; i < MP.N; i++) { // транзитная пирамида для активных лучей, пересекающих этот лист BVH, // для эффективного SIMD-отсечения треугольников, // см. подраздел 2.2.4 и [Res07] MP.SubPacket[i].LeafFrustum = TransientLeafFrustum(MP.SubPacket[i], B); // проверить все кластеры листа на пересечение // см. подраздел 2.3.5 Алгоритм 2.3 for(int c = 0; c < B->ClustersCount; c++) PacketClusterTest(B->Cluster[c], MP.SubPacket[i]); } } else { // спуск глубже в BVH // отложить дальний узел их двух потомков узла B (дальний по отношению к пакету) push(Stack, [ActiveSubFrustum, FarChildNodePtr(B, MP)]); B = NearChildNodePtr(B, MP); // а пока тестировать ближний узел continue; } } if(Stack.empty) break; [B, ActiveSubFrustum] = pop(Stack); } } 54

3. - , ( 2.3 2.4). 3.1. - Microsoft Visual Studio 2005 [Microsoft], , Intel C++ Compiler 10.1 [Intel-a], . Intel C++ Compiler, . . - . - - Intel Core 2 Duo, Quad, Nehalem. Visual Studio - , MSDN IntelliSence. CPU - OpenMP ++ [OMP]. 3.2. - , : 1) 3D- ; 2) 3D- ( . 2.3.3) 3) BVH ( . 2.1) - ( . 2.3). 4) ( . 2.2). 5) - ( . 2.4). 3.2.1. 3D- ply [PLY]. [UNC], [Stanford]. , - , . 55

3.2.2. (a) 3D- CPU (b) (c) , - BVH (d) - 3D- (e) 3D- (f) BVH - , (g) GPU GPU ( ) CPU . 3.1: . 3.2.3. . 3.2 BVH . 3D- ( . 3.1, a) 3D- Vertices Triangles. Triangles - 4- Vertices. - ( . 3.1 b) Vertices Triangles. Clusters, ClustersVerticesIDs, ClustersTri- 56

anglesIDs. Clusters 1 : ClustersVerticesIDs ClustersTrianglesIDs. , ( . 2.3.5). Triangles - 1- ( , . . 2.18). M– . - ( . 3.1 c) 2M – 1 BVH, BvhNodes. BVH 3D- BVH_NODE * BvhNodes → node0 … nodei … leafj … unsigned int * SortedClustersIDs → … … TRIANGLE_CLUSTER * Clusters → cluster0 … clusteri … clusterj … unsigned int * ClustersVerticesIDs→ … … unsigned int * ClustersTrianglesIDs→ … … VERTEX * Vertices → vertex0 … vertexi … TRIANGLE * Triangles → 3D- triangle0 … trianglei … : struct BVH_NODE { //32 байта struct TRIANGLE_CLUSTER {//12 байт float AABB[6]; int TriOffset, VertexOffset; int Info1, Info2; unsigned short TriCount; }; unsigned short VerticesCount; }; if(Info1 & 0x80000000 == 0) { // внутренний узел struct float3 { //12 байт // Info1 = cсылка на 1-ый потомок этого узла float F[3]; // x, y, z // Info2 = cсылка на 2-ой потомок }; } else { // листовой узел // Info1 & 0x7FFFFFFF = ссылка на первый элемент блока struct TRIANGLE { //12 байт // индексов кластеров, относящихся к этому листу, unsigned char V[3]; // Info2 = ссылка на последний элемент блока кластеров. }; } . 3.2: . 57

( . 3.1 d) 3D- Vertices ( . 3.1 e). BVH - 3D- ( . 3.1 f) 3D- . , Sort- edClustersIDs. BVH ( BvhNodes) 2 AABB. SortedClustersIDs, . , 2.2 2.4, ( . 3.1 g). - 3D- . 4.5. 3.2.4. . , - CPU . 4- - SIMD- [Intel-b] ( - SIMD- ). , - SIMD- , (SoA, structure of array), . SIMD- 2.2.1., . 2.4. - . , - , - . , : template <typename T> struct UNROLLED_LIST_NODE { UNROLLED_LIST_NODE<T> * NextNode; T UserData[8]; // небольшой развёрнутый массив unsigned int RealDataCount; // количество занятых ячеек UserData }; , , , . , - 58

. , . . ( malloc), . 3.2.5. - , SIMD- SSE SSE2 (Pentium III ). - ( , Intel Core, Nehalem AMD Opteron, Phenom). CPU Core 2 Duo T5550 (32-bit Vista) CPU Core 2 Quad Q6600 (32-bit Windows XP). 3.2.6. 3D- . 3.1 - , . Home / End / A/D / W/S / Delete Page Down / / / / Q/E / V BVH B F 3D- 2 10% 2 + Shift 10% 4 5 4 5 + Shift 4 9 1 9 + Shift 1 ESC 3.1: 59

4. , : 1) BVH ( 2.3); 2) ( 2.4). ( 2.1, 2.2) , . . , , , . 4.1. , , - , ASUS G1S - Intel Core 2 Duo T5550 (2 1.83GHz, FSB 667MHz, L2 cache 2Mb, RAM 2Gb DDR2, 32-bit Windows Vista). 1024×1024. , 2.2 ( , SIMD- , , SIMD- [Res07]), SIMD- ( . 2.2.3 [ORM08]). 32×32, 1024 , 256 SIMD- ( . 2.2.1 2.2.5). ( . 2.2.4 [Res07]) ‘ ’ ( . . kd- tree BVH , 3D- ( )). [Res07] - , , . , ( . 2.3.5). - - BVH ( . 2.3). 60

BVH ( . 2.1.2) ( . - 2.2.5) CPU. , , BVH, ( - ), - BVH , , 32 ( . 2.3.4). 3D- 1 3D- 1- . , - . 4.2. , - Acc(k) - ( . 2.3.3) 3D- . 4.1. - , . . 32- 10.000.000 . - ‘ ’ , , . . ‘ ’ Acc(k) – - , , . 3D- ‘ ’ , . . . - ‘ ’ ( . . 4.1 ). - . ‘ ’. - , . . ( . . 4.1 , ). ‘ ’ ‘ ’ , - . , - ‘ ’ ‘ ’ . 4.3 BVH, . 61

. 4.1: : (92K ), : (10M - )– . : (282K - ): , ‘ ’ ( ). : , - Acc(k) MaxSize = MaxCount = 100 - . 62

4.3. BVH 6 3D- ( . . 4.2), - : [UNC], [UNC], [UNC], , , . . 4.2: 3D- . (92K ), (252K), (146K), (174K), (282K), (10M). 4 . - Acc(k) BVH , ( ). , MaxSize = MaxCount = 50 Acc(k). - BVH . 4.1. 4.3.1. Acc(k). BVH Acc(k) . 4.3 , 4.1 - . BVH - . , - . 4.1 - 63

( ) 2- - ( 6- , 2 ). - BVH, - . 4.1 MaxCount = MaxSize = 0 BVH, - , . . - ( . 2.1 [Wal07]). - BVH . MaxCount > 0, MaxSize > 0 BVH , ‘ ’. ‘ ’, ( ). BVH - 3D- , (10.000.000 - ). BVH - Acc(k) : a) : 70 60 50 40 30 20 10 0 0 10 50 100 200 b) : BVH, + , / 10 , FPS . × 10 90 FPS . 80 70 60 50 40 30 20 10 0 0 10 50 100 200 MaxSize = MaxCount = X . 4.3: BVH - Acc(k) (a) (b) . - 4.1. FPS = 1000 / ( BVH + ). 64

. - 92K 252K 146K 174K 282K 10M - 46.5K 192K 73.9K 97K 166K 5M MaxCount = 0, MaxSize = 0. ( BVH ‘ ’ ) , 0 0 0 0 0 0 - 92K 252K 146K 174K 282K 10M BVH, 23 62.8 37.2 52 82.4 4.9K 44.5 32.1 50.2 68 109 250 , + 2- 163 213 533 718 1940 1270 , MaxCount = 10, MaxSize = 10 , 1.9K 2.9K 7.4K 1.2K 3K 165K - 49K 139K 69K 83K 148K 5.1M BVH, 14.4 39.2 23.6 27.2 43 2.6K 42.1 28.2 44.4 63.6 108 240 , + 2- 152 188 448 688 1880 1255 , MaxCount = 50, MaxSize = 50 , 1.5K 1.9K 8.4K 2.8K 5.5K 143K - 5.2K 24.6K 8.2K 17.9K 32K 469K BVH, 6.7 12.1 5.2 7.8 12.6 311 36.6 24.4 42 57.5 110 174 , + 2- 154 157 409 702 1990 980 , MaxCount = 100, MaxSize = 100 , 3.7K 2.3K 9.3K 5.8K 10K 139K - 3.7K 16.4K 4.3K 10.7K 20.4K 194K BVH, 5.6 7.1 4.1 4.5 9.2 167 34.9 25.7 41.9 57.5 109 166 , + 2- 167 161 452 781 2326 1070 , MaxCount = 200, MaxSize = 200 , 11K 3.7K 14K 14K 25K 146K - 2.4K 12.3K 2.5K 6.9K 11.3K 88K BVH, 4.2 5.1 1.8 3.5 5.9 106 37 28.6 41.6 59 104 177 , + 2- 201 164 569 878 2755 1560 , 4.1: BVH - Acc(k) . 6 . 4.2. 2- - 6 ( BVH ). 65

Acc(k) MaxCount = Max- Size = 50 3D- : 1) BVH , - ( MaxCount = MaxSize = 0); 2) ‘ ’ . (MaxCount = MaxSize >= 100). ‘ ’. - ( ), . . - 3D- . , BVH - . BVH . ( - 2.2.4 [Res07]) BVH, - . 4.1 MaxCount > 0, MaxSize > 0 , ‘ ’ ( . . BVH ). 3D- ( 255), - ( . 2.3.5). , CPU - , . . . - ( . . - ). , - BVH ( ) - . BVH 3D- . . 4.4 BVH, Acc(k)50,50 (Max- Count=MaxSize=50), ‘ ’ BVH Acc(k)0,0 (Max- Count= MaxSize = 0). , , Acc(k)50,50, 1 3D- 1- ( - ), BVH - . 66

, , , , . - , AABB - AABB , . - , BVH. , ( . 2.3.5). 1,20 . . . . 1,15 1,10 1,05 1,00 0 10 20 30 40 50 60 70 80 90 100 . 4.4: BVH, Acc(k)50,50 (MaxSize=MaxCount=50), BVH Acc(k)0,0. , , BVH. 3D- - . = (RT Acc(k)0,0) / (RT Acc(k)50,50), RT – 3D- c 2- . BVH Acc(k)50,50 BVH . .>1 BVH Acc(k)50,50. 4.3.2. , 3D- , , 0,84 0,69 3,07 2,21 1,33 1,07 1,68 1,46 . 2,75 2,47 90 65 0,0% 10,0% 20,0% 30,0% 40,0% 50,0% 60,0% 70,0% 80,0% 90,0% 100,0% . 4.5: BVH, Acc(k)50,50, , 3D- ( . . 4.2). : , , - . 67

. 4.5 BVH ( , , . - . 3.2), Acc(k)50,50. , 3D- , : . . 3D- ( 2.3.5). 4.3.3. CPU . 4.6 - BVH 3D- : . BVH , - Acc(k)50,50 (MaxCount=MaxSize=50) Acc(k)0,0 ( . . ). Intel Core 2 Quad Q6600 (4 2.4GHz, FSB 1066MHz, L2 cache 2×4Mb, RAM 3Gb DDR2, 32-bit Windows XP). CPU, - ( 100%- , . . 4.6). . ( . 2.1) - ( . . 1.7). BVH : BVH : Acc(k)0,0 Acc(k)50,50 Acc(k)0,0 Acc(k)50,50 2- CPU Core 2 Duo 1.83GHz 500,0 100,0 20,0 7000,0 6000,0 400,0 80,0 15,0 5000,0 60,0 300,0 4000,0 10,0 3000,0 200,0 40,0 5,0 2000,0 20,0 100,0 1000,0 0,0 0,0 0,0 0,0 1 2 1 2 1 2 1 2 4- CPU Core 2 Quad 2.4GHz 70,0 12,0 350,0 5000,0 60,0 10,0 300,0 50,0 4000,0 250,0 8,0 40,0 3000,0 200,0 6,0 30,0 2000,0 150,0 20,0 4,0 100,0 10,0 2,0 1000,0 50,0 0,0 0,0 0,0 0,0 1 2 4 1 2 4 1 2 4 1 2 4 . 4.6: BVH. : - , . : BVH . 68

4.3.4. a) SAH- Naïve(k): 2,8 2,6 2,4 2,2 2,0 1,8 1,6 1,4 1,2 1,0 0 10 20 30 40 50 60 70 80 90 100 b) Error(k) – [GWH01]: 1,8 . . 1,7 . . 1,6 1,5 1,4 1,3 1,2 1,1 1,0 0 10 20 30 40 50 60 70 80 90 100 . 4.7: BVH, Acc(k)50,50 (MaxSize=MaxCount=50), BVH (a) SAH- Naïve(k) (b) Error(k) – [GWH01]. - , , BVH. 3D- . = (RT (a) (b)) / (RT Acc(k)50,50), RT – - 3D- c 2- . .>1 - BVH Acc(k)50,50. BVH, Acc(k)50,50 (MaxCount= MaxSize=50), - BVH, SAH- , - [GWH01] ( . Error(k) 2.3.6). SAH- k : k Naive( k ) = ∑ SA( i ) / SA( AABB k ) i =1 SA() – . Naïve(k) k - , 3D- . Error(k) a1 = 0.2 a2 = 2 ( - , . . ‘ ’ ). Acc(k)50,50, Naïve(k) Error(k) 3D- . - 69

( . 2.3.3) 3D- 1- . Naïve(k) Error(k) - , , - Acc(k)50,50. . . 3D- BVH , Acc(k)50,50, Naïve(k) Error(k). . 4.7a, 4.7b Acc(k)50,50 . BVH, - Acc(k)50,50, - 3D- . , Naïve(k), BVH ( . . - SAH). , - , - P(Y | X) BVH, ( . 2.3.1). - Naïve(k) . - 3D- . Error(k) , . Error(k) . 4.7 , Naïve(k) 3D- , . . ( . . ). - BVH . Acc(k)50,50, 1.83GHz Core 2 Duo, 2 5.2 7.8 12.1 311 [Wal07], 2.6GHz Xeon X5355, 8 n/a 21 20 1100 [WIP08], 3GHz Opteron, 8 n/a 53 14 n/a [LGS*09] GeForce 280GTX 10 / 17 / n/a n/a / 124 66 [ZHWG08], kd-tree, GeForce 8800 Ultra n/a 77 93 n/a [GAR08], 2.4GHz Core 2 Quad, 86 25 n/a n/a (1 ) 4.2: BVH (Acc(k)50,50) BVH/kd-tree. 4.2 BVH . [Gar08] BVH 70

, . - [HMFS07], - ( ) - . , 3D- , ( 3D- ) . , ( . .), , - , . 4.3.5. , . BVH, , - . 3D- ( - / - = 3). . 4.8: BVH: BVH - « » - / , . , - ( . . 4.8), - . : ‘ - ’ ( . . , . . 4.8). BVH, AABB ( 6 3D). ‘ ’ BVH ( . . - , ) 71

3D- BVH ( . 2.3.4). . , - OBB (oriented bounding box), 3D- , AABB. OBB kd-tree, 3D- ( BVH- kd-tree ). . . BVH - BVH ( [Wal07], . 2.1). - / 3D- , - ( 3D- ). BVH, - BVH ( . . ) . - 3D- : , , , . 4.4. ( . 2.4). 3D- BVH , , Acc(k)50,50 (MaxCount= MaxSize=50) ( . 2.3 4.3). 4.4.1. 3D- . 4.9, 4.10, 4.11 : 2- Alg1 Alg2 ( . 2.20a 2.20b) Multi1 Multi2 ( . 2.22a 2.22b). Alg1 Alg2 , . 2.2. 4.3 - BVH. 72

8,0 250 7,5 238 Alg1 Alg2 = 20002 225 Multi1 Multi2 7,0 213 6,5 200 6,0 188 5,5 175 163 5,0 150 4,5 138 4,0 125 3,5 113 - 100 3,0 88 2,5 75 2,0 63 1,5 50 38 1,0 25 0,5 13 0,0 0 1 4 16 64 256 1024 8,0 300 7,5 285 = 80002 270 7,0 255 6,5 240 6,0 225 5,5 210 195 5,0 180 4,5 165 4,0 150 3,5 135 - 120 3,0 105 2,5 90 2,0 75 1,5 60 45 1,0 30 0,5 15 0,0 0 1 4 16 64 256 1024 20,0 500 19,0 475 = 320002 18,0 450 17,0 425 16,0 400 15,0 375 14,0 350 13,0 325 12,0 300 11,0 275 10,0 250 9,0 225 - 8,0 200 7,0 175 6,0 150 5,0 125 4,0 100 3,0 75 2,0 50 1,0 25 0,0 0 1 4 16 64 256 1024 . 4.9: 3D- - (67K ) 1024×1024. Alg1 (Alg2) ( ) , . 2.4, . 2.20a (2.20b). : , . 2.20c, Alg1 Alg2. Multi 1 (Multi 2) . 2.22a (2.22b). : - ( ) . : 1 . 256 . . 73

2,6 100 = 20002 95 Alg1 Alg2 2,4 90 Multi1 Multi2 2,2 85 80 2,0 75 1,8 70 65 1,6 60 1,4 55 50 1,2 45 1,0 40 35 0,8 30 0,6 25 20 0,4 15 0,2 10 5 0,0 0 1 4 16 64 256 1024 3,0 100 = 80002 2,8 95 90 2,6 85 2,4 80 2,2 75 70 2,0 65 1,8 60 1,6 55 50 1,4 45 1,2 40 1,0 35 30 0,8 25 0,6 20 0,4 15 10 0,2 5 0,0 0 1 4 16 64 256 1024 8,0 190 = 320002 7,5 180 7,0 170 160 6,5 150 6,0 140 5,5 130 5,0 120 4,5 110 100 4,0 90 3,5 80 3,0 70 2,5 60 2,0 50 40 1,5 30 1,0 20 0,5 10 0,0 0 1 4 16 64 256 1024 . 4.10: 3D- - (174K ) 1024×1024. Alg1 (Alg2) ( ) , . 2.4, . 2.20a (2.20b). : - , . 2.20c, Alg1 Alg2. Multi 1 (Multi 2) - . 2.22a (2.22b). : - ( ) . : 1 . - 256 . . 74

5,7 350 Alg1 Alg2 = 20002 5,4 325 5,1 Multi1 Multi2 4,8 300 4,5 275 4,2 250 3,9 3,6 225 3,3 200 3,0 175 2,7 2,4 150 2,1 125 1,8 1,5 100 1,2 75 0,9 50 0,6 0,3 25 0,0 0 1 4 16 64 256 1024 10,0 500 = 80002 9,5 475 9,0 450 8,5 425 8,0 400 7,5 375 7,0 350 6,5 325 6,0 300 5,5 275 5,0 250 4,5 225 4,0 200 3,5 175 3,0 150 2,5 125 2,0 100 1,5 75 1,0 50 0,5 25 0,0 0 1 4 16 64 256 1024 11,0 660 = 320002 10,5 630 10,0 600 9,5 570 9,0 540 8,5 510 8,0 480 7,5 450 7,0 420 6,5 390 6,0 360 5,5 330 5,0 300 4,5 270 4,0 240 3,5 210 3,0 180 2,5 150 2,0 120 1,5 90 1,0 60 0,5 30 0,0 0 1 4 16 64 256 1024 . 4.11: 3D- (10M ) 1024×1024. Alg1 (Alg2) ( ) - , . 2.4, . 2.20a (2.20b). : - , . 2.20c, Alg1 Alg2. - Multi 1 (Multi 2) - . 2.22a (2.22b). : ( ) . : 1 . 256 . . 75

- - 6% 6% 8% 9% 86% 87% - =4 - = 64 . 4.12: 3D- . Multi1 ( = 20002, . . 4.10, ). , . 2.21, - . - . Alg1 Alg2 Multi1 Multi2 - BVH 766.3M 319.8M 30.9M 31.2M - 10870M 2465M 2786M 3087M AABB - 1134M 2670M 1442M 3429M / 1113 157 92 121 4.3: BVH - 3D- ( = 320002, - = 256, . . 4.11 ). ‘ ’ BVH 194K 10M . , Multi1 Multi2 1.5-3 , - ( . . 4.9-4.11). - 3D- ( , = 320002 ( ) , ). Multi 1 2 , Alg 1 2, . . BVH Multi 1 2 AABB BVH ( . 2.4) ( - ) AABB ( . 2.2). , Multi 1 2 , . Multi 1 2 BVH ( . 4.3), - 76

CPU. - Multi 1 , Multi 2, . . - - ( . . 2.22a). , 8-9% ( . . 4.12), 1.5-3 . 4.4.2. CPU . 4.13 - Multi 1 ( . 2.4 . 2.22a) - 3D- : ( . . 4.10) ( . . 4.11). , . Intel Core 2 Quad Q6600 (4 2.4GHz, FSB 1066MHz, L2 cache 2×4Mb, RAM 3Gb DDR2, 32-bit Windows XP). . 4.13 , . . ( , - , 4.3). ( 4 ) ( 64 ). - . - . CPU - ( . . ~1.95-2 2 ). , - , 3D- ( . . 2.20d 2.21). - - , 1 . . - CPU: BVH , . , CPU, . . 77

. - , , . 4 64 4 64 2- CPU Core 2 Duo 1.83GHz 12 5 60 1,2 10 4 50 0,9 8 40 3 6 30 0,6 2 4 20 0,3 2 1 10 0,0 0 0 0 1 2 1 2 1 2 1 2 4- CPU Core 2 Quad 2.4GHz 4 50 1,0 8 3 40 0,8 6 0,6 30 4 2 0,4 20 2 1 0,2 10 0,0 0 0 0 1 2 4 1 2 4 1 2 4 1 2 4 . 4.13: 2- 3D- - Multi1 ( = 320002, . . 4.10, 4.11, ). : , . : 1 . 4.4.3. , , , - . - ( ). , . [ORM07] ( , ). - ( 3D- - ). [ORM07], 512×512 9 3GHz Pentium 4. , - , 1024×1024 ( 78

256 ) 13 1.83GHz Core 2 Duo ( . . 4.9 ). [HM08] 3D- , 3D- . - - . - . [HM08], 1920×1280 (8 - ) 2 8 2.6GHz Xeon. , , 1024×1024 ( 16 - ) 0.68 1.83GHz Core 2 Duo ( . . 4.10 ). - , [SEA08], - - , 3D- . - 3D- . - . , , 3D- - , BVH. 4.4.4. , . - - , - , . - - . . , - ( -) , - ( - ) 1.5-3 - . - 79

3D- - ( . . ). , - CPU. - - . 80

2 - , . - , BVH 3D- . BVH. , BVH - . BVH 3D- - , 3D- . - / 3D- , - ( . . 3D- ). BVH, BVH ( . . ) . - 3D- : - , , , . - 3D- . - , - - ( - ). 3D- - ( . . ). , - 1.5-3 , . : • 3- IRT 2008 (Interactive Ray Tracing Symposium 2008), “Efficient Clustered BVH Update Algo- rithm for Highly-Dynamic Models” (“ - 81

BVH - ”), , - , 2008 [Gar08]. • 20- EGSR 2009 (Eurographics Symposium on Rendering 2009), “The Use of Precomputed Triangle Clusters for Ac- celerated Ray Tracing in Dynamic Scenes” (“ - - ”), , , 2009 [Gar09]. • . . ( - , ), 2009. - , - - . - SIMD- . Intel Nehalem, - Larrabee [SCS*08], GPU - MIMD- . Larrabee - - , - . 82

[AK87] ARVO J., KIRK D.: Fast Ray Tracing by Ray Classification. Computer Graphics (SIG- GRAPH’87 Proceedings), 21(4):55-64 (July 1987). [Ben06] BENTHIN C.: Realtime Ray Tracing on current CPU Architectures. PhD thesis, Com- puter Graphics Group, Saarland University, 2006. [Bik07] BIKKER J.: Real-time Ray Tracing through the Eyes of a Game Developer. In Proceed- ings of the 2007 IEEE/EG Symposium on Interactive Ray Tracing (2007). [BWB08] BOULOS S., WALD I., BENTHIN C.: Adaptive Ray Packet Reordering. In Proceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [CPC84] COOK R., PORTER T., CARPENTER L.: Distributed Ray Tracing. Computer Graphics (Proceeding of SIGGRAPH 84) 18, 3 (1984), 137–144. [DHK08] DAMMERTZ H., HANIKA J., KELLER A.: Shallow Bounding Volume Hierarchies for Fast SIMD Ray Tracing of Incoherent Rays. In Proceedings of the Eurographics Symposium on Rendering (2008). [DK08] DAMMERTZ H., KELLER A.: The Edge Volume Heuristic – Robust Triangle Subdivision for Improved BVH Performance. In Proceedings of the 2008 IEEE/EG Symposium on Interac- tive Ray Tracing (2008). [Dut03] DUTRÉ P.: Global Illumination Compendium (2003). http://www.cs.kuleuven.ac.be/~phil/GI/ [Eri03] ERICSON C.: Memory Optimization. In Game Developers Conference, Sony Computer Entertainment, Santa Monica (March 2003). [Gar08] GARANZHA K.: Efficient Clustered BVH Update Algorithm for Highly-Dynamic Mod- els. In Proceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [Gar09] GARANZHA K.: The Use of Precomputed Triangle Clusters for Accelerated Ray Tracing in Dynamic Scenes. Accepted to Computer Graphics Forum 28, 4. (Proceedings of Eurograph- ics Symposium on Rendering 2009). [GR08] GRIBBLE C.-P., RAMANI K: Coherent Ray Tracing via Stream Filtering. In Proceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [GS87] GOLDSMITH J., SALMON J.: Automatic Creation of Object Hierarchies for Ray Tracing. IEEE Computer Graphics and Applications 7, 5 (1987), 14–20. [GFW*06] GÜNTHER J., FRIEDRICH H., WALD I., SEIDEL H.-P., SLUSALLEK P.: Ray tracing animated scenes using motion decomposition. Computer Graphics Forum 25, 3 (Sept. 2006), 517– 525. (Proceedings of Eurographics 2006). [GFSS06] GÜNTHER J., FRIEDRICH H., SEIDEL H.-P., SLUSALLEK P.: Interactive Ray Tracing of Skinned Animations. The Visual Computer (Proceedings of Pacific Graphics 2006). 83

[GWH01] GARLAND M., WILLMOTT A., HECKBERT P.: Hierarchical Face Clustering on Polygo- nal Surfaces. In Proceedings of the Symposium on Interactive 3D Graphics and Games (2001). [Hai08] HAINES E.: Ray Tracing: Strengths and Opportunities. In Proceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [Hav01] HAVRAN V.: Heuristic Ray Shooting Algorithms. PhD thesis, Faculty of Electrical Engi- neering, Czech Technical University in Prague, 2001. [HMFS07] HUNT W., MARK W., FUSSELL D., STOLL G.: Fast and Lazy Build of Acceleration Structures from Scene Hierarchies. In Proceedings of the 2007 IEEE/EG Symposium on Inter- active Ray Tracing (2007). [HM08] HUNT W., MARK W.-R.: Ray-Specialized Acceleration Structures for Ray Tracing. In Proceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [HM08] HUNT W., MARK W.-R.: Adaptive Acceleration Structures in Perspective Space. In Pro- ceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [Intel-a] Intel Corporation: Intel C/C++ Compilers. http://www.intel.com/software/products/compilers [Intel-b] Intel Corporation: Intel Pentium III Streaming SIMD Extensions. http://developer.intel.com/vtune/cbts/simd.htm [IWRP06] IZE T., WALD I., ROBERTSON C., PARKER S.: An Evaluation of Parallel Grid Construc- tion for Ray Tracing Dynamic Scenes. In Proceedings of the 2006 IEEE Symposium on Inter- active Ray Tracing (2006). [KK86] KAY T., KAJIYA J.: Ray tracing complex scenes. In Proceedings of SIGGRAPH (1986). [LBBS08] LACEWELL D., BURLEY B., BOULOS S., SHIRLEY P.: Raytracing Prefiltered Occlusion for Aggregate Geometry. In Proceedings of the 2008 IEEE Symposium on Interactive Ray Tracing (2008). [LGS*09] LAUTERBACH C., GARLAND M., SENGUPTA S., LUEBKE D., MANOCHA D.: Fast BVH Construction on GPUs. Computer Graphics Forum (In Proceedings of Eurographics 2009) (2009). [LYM07] LAUTERBACH C., YOON S.-E., MANOCHA D.: Ray-strips: A compact mesh representa- tion for interactive ray tracing. In Proceedings of the 2007 IEEE Symposium on Interactive Ray Tracing (2007). [LYTM06] LAUTERBACH C., YOON S.-E., TUFT D., MANOCHA D.: RT-DEFORM: Interactive Ray Tracing of Dynamic Scenes using BVHs. In Proceedings of the 2006 IEEE Symposium on Interactive Ray Tracing, 39–45 (2006). [LYTM08] LAUTERBACH C., YOON S.-E., TANG M., MANOCHA D.: ReduceM: Interactive and Memory Efficient Ray Tracing of Large Models. In Proceedings of the Eurographics Sympo- sium on Rendering (2008). [Microsoft] Microsoft Corporation: Microsoft Visual Studio. http://www.microsoft.com/visualstudio/en-us/default.mspx 84

[NM08] NAVRATIL P.A., MARK W.-R.: An Analysis of Ray Tracing Bandwidth Consumption. In Tech Report TR-06-40, The University of Texas at Austin, Department of Computer Science (2008). [NBS06] NEHAB D., BARCZAK J., SANDER P.: Triangle Order Optimization for Efficient Graphics Hardware Computation Culling. In Proceedings of the Symposium on Interactive 3D Graphics and Games (2006). [NVI] NVIDIA: The CUDA Homepage. http://developer.nvidia.com/cuda [OMP] OpenMP C++/Fortran API. http://openmp.org/wp/ [ORM07] OVERBECK R., RAMAMOORTHI R., MARK W.-R.: A Real-time Beam Tracer with Ap- plication to Exact Soft Shadows. In Proceedings of the 18th Eurographics Symposium on Ren- dering (2007). [ORM08] OVERBECK R., RAMAMOORTHI R., MARK W.-R.: Large Ray Packets for Real-time Whitted Ray Tracing. In Proceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [PLY] PLY: Polygon File Format. http://local.wasp.uwa.edu.au/~pbourke/dataformats/ply/ [PKGH97] PHARR M., KOLB C., GERSHBEIN R., HANRAHAN P.: Rendering complex scenes with memory-coherent ray tracing. In Proceedings of SIGGRAPH, pages 101-108 (1997). [RAH07] ROGER D., ASSARSSON U., HOLZSCHUCH N.: Whitted Ray-Tracing for Dynamic Scenes using a Ray-Space Hierarchy on the GPU. In Proceedings of the Eurographics Symposium on Rendering (2007). [Res07] RESHETOV A.: Faster ray packets - triangle intersection through vertex culling. In Pro- ceedings of the 2007 IEEE/EG Symposium on Interactive Ray Tracing, 105–112 (2007). [RSH05] RESHETOV A., SOUPIKOV A., HURLEY J.: Multi-level ray tracing algorithm. ACM Transactions on Graphics (Proc. SIGGRAPH 2005), 1176-1185 (2005). [SCS*08] SEILER L., CARMEAN D., SPRANGLE E., FORSYTH T., ABRASH M., DUBEY P., JUNKINS S., LAKE A. SUGERMAN J, CAVIN R., ESPASA R., GROCHOWSKI E., JUAN T., HANRAHAN P.: Lar- rabee: A Many-Core x86 Architecture for Visual Computing. ACM Transactions on Graphics (Proc. SIGGRAPH 2008) (2008). [SEA08] SINTORN E., EISEMANN E., ASSARSSON U.: Sample Based Visibility for Soft Shadows using Alias-free Shadow Maps. In Proceedings of Eurographics (2008). [SNB07] SANDER P., NEHAB D., BARCZAK J.: Fast Triangle Reordering for Vertex Locality and Reduced Overdraw. ACM Transactions on Graphics (Proc. SIGGRAPH 2007) (2007). [Shi00] SHIRLEY P.: Realistic Ray Tracing. AK Peters, Ltd., 2000. [SSGH01] SANDER P., SNYDER J., GORTLER S., HOOPE H.: Texture Mapping Progressive Meshes. ACM Transactions on Graphics (Proc. SIGGRAPH 2001) (2001). 85

[SSK07] SHEVTSOV M., SOUPIKOV A., KAPUSTIN A.: Highly parallel fast kd-tree construction for interactive ray tracing of dynamic scenes. Computer Graphics Forum 26, 3, 395-404 (2007). [Stanford] The Stanford 3D Scanning Repository. http://graphics.stanford.edu/data/3Dscanrep/ [UNC] University of North Carolina: Dynamic Scenes Benchmarks. http://gamma.cs.unc.edu/DynamicB [Wäc07] WÄCHTER C.: Quasi-Monte Carlo Light Transport Simulation by Efficient Ray Tracing. PhD thesis, Ulm University, 2007. [Wal04] WALD I.: Realtime Ray Tracing and Interactive Global Illumination. PhD thesis, Com- puter Graphics Group, Saarland University, 2004. [Wal07] WALD I.: On fast construction of SAH-based bounding volume hierarchies. In Proceed- ings of the 2007 IEEE/EG Symposium on Interactive Ray Tracing (2007). [WBB08] WALD I., BENTHIN C., BOULOS S: Getting Rid of Packets – Efficient SIMD Single-Ray Traversal using Multi-branching BVHs. In Proceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [WBKP08] WALTER B., BALA K., KULKARNI M., PINGALI K.: Fast Agglomerative Clustering for Rendering. In Proceedings of the 2008 IEEE/EG Symposium on Interactive Ray Tracing (2008). [WBS07] WALD I., BOULOS S., SHIRLEY P.: Ray Tracing Deformable Scenes using Dynamic Bounding Volume Hierarchies. ACM Transactions on Graphics 26, 1, 1–18 (2007). [Whi80] WHITTED T.: An Improved Illumination Model for Shaded Display. Communications of the ACM 23, 6, 343–349 (1980). [WIK*06] WALD I., IZE T., KENSLER A., KNOLL A., PARKER S.-G.: Ray Tracing Animated Scnes using Coherent Grid Traversal. ACM Transactions on Graphics (Proc. SIGGRAPH 2006) (2006). [WIP08] WALD I., IZE T., PARKER S.: Fast, Parallel, and Asynchronous Construction of BVHs for Ray Tracing Animated Scenes. Tech. Rep. SCI Institute, University of Utah (Feb. 2008). [WK06] WÄCHTER C., KELLER A.: Instant Ray Tracing: The Bounding Interval Hierarchy. In Rendering Techniques 2006 – Proceedings of the 17th Eurographics Symposium on Rendering, 139–149 (2006). [WMG*07] WALD I., MARK W., GÜNTHER J., BOULOS S., IZE T., HUNT W., PARKER S., SHIRLEY P.: State of the Art in Ray Tracing Animated Scenes. In State of the Art Reports, Eurographics 2007 (2007). [YCM07] YOON S.-E., CURTIS S., MANOCHA D.: Ray Tracing Dynamic Scenes using Selective Restructuring. In Proceedings of the Eurographics Symposium on Rendering (2007). [ZHWG08] ZHOU K., HOU Q., WANG R., GUO B.: Real-Time KD-Tree Construction on Grpa- hics Hardware. ACM Transactions on Graphics (Proc. SIGGRAPH Asia 2008) (2008). 86

Russian

by guest0e111f3 on Sep 09, 2009

Accessibility

Upload Details

Usage Rights

Statistics

Russian Document Transcript