WebGL Safari WebGL Kageyama (Kobe Univ.) Visualization / 55

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1 WebGL WebGL X Kageyama (Kobe Univ.) Visualization / 55

2 WebGL Safari WebGL Kageyama (Kobe Univ.) Visualization / 55

3 Kageyama (Kobe Univ.) Visualization / 55

4 WebGL WebBL = HTML5 canvas JavaScript 3D CG API Kageyama (Kobe Univ.) Visualization / 55

5 WebGL Web GPU OpenGL UI Kageyama (Kobe Univ.) Visualization / 55

6 Kageyama (Kobe Univ.) Visualization / 55

7 homogeneous coordinates 3 x v 4 3 x x y z (1) 1 v v x v y v z 0 (2) Kageyama (Kobe Univ.) Visualization / 55

8 3 x v x y F (x). (3) Kageyama (Kobe Univ.) Visualization / 55

9 n u u = u u v = u i v j = u v cos ϕ v u φ Kageyama (Kobe Univ.) Visualization / 55

10 e i e j = δ ij v {e 0, e 1,..., e n 1 } v i v i = v e i Kageyama (Kobe Univ.) Visualization / 55

11 3 w = u v w i = ϵ ijk u j v k w u v w = u v sin ϕ u v = v u u (v w) = (u w) v (u v) w Kageyama (Kobe Univ.) Visualization / 55

12 M N M M ij (i, j = 0, 1,..., n 1) N N ij (i, j = 0, 1,..., n 1) L = MN n 1 L ij = M ik N kj = M ik N kj k=0 Kageyama (Kobe Univ.) Visualization / 55

13 (LM) N = L (MN) (L + M) N = LN + MN MI = IM = M I MN NM Kageyama (Kobe Univ.) Visualization / 55

14 M N MN = NM = I M 1 glmatrix.js 4 4 Kageyama (Kobe Univ.) Visualization / 55

15 det (M) det (I) = 1 det (MN) = det (M) det (N) det ( M t) = det (M) Kageyama (Kobe Univ.) Visualization / 55

16 M M ij (i, j = 0, 1,..., n 1) M t a M N (am) t = am t (M + N) t = M t + N t ( M t ) t = M (MN) t = N t M t Kageyama (Kobe Univ.) Visualization / 55

17 n 1 tr(m) = i=0 M ii Kageyama (Kobe Univ.) Visualization / 55

18 MM t = M t M = I M M t = M 1 det (M) = ±1 M t Mu = u u v = 0 (Mu) (Mv) = 0 Kageyama (Kobe Univ.) Visualization / 55

19 3 p u v x = p + s u + t v n u v/ u v n x + d = 0 n f(x) = n x + d f(x 0 ) = 0 x 0 f(x 0 ) > 0 x 0 p + n f(x 0 ) < 0 x 0 p n Kageyama (Kobe Univ.) Visualization / 55

20 3 p, q, r 3 S = 1 (p r) (q r) 2 x-y n S = 1 n 1 (x i y i+1 y i x i+1 ) = 1 n 1 {x i (y i+1 y i 1 )} 2 2 i=0 i=0 mod (n) Kageyama (Kobe Univ.) Visualization / 55

21 3 u, v, w 6 V = u (v w) = v (w u) = w (u v) w v u Kageyama (Kobe Univ.) Visualization / 55

22 3 = x x y = y z z 1 v x v y = v z v x v y v z 0 Kageyama (Kobe Univ.) Visualization / 55

23 M = M 00 M 01 M 02 0 M 10 M 11 M 12 0 M 20 M 21 M Kageyama (Kobe Univ.) Visualization / 55

24 T (t x, t y, t z ) = t x t y t z (4) Kageyama (Kobe Univ.) Visualization / 55

25 z R z (θ) = cos θ sin θ 0 0 sin θ cos θ (5) Kageyama (Kobe Univ.) Visualization / 55

26 S(s x, s y, s z ) = s x s y s z (6) Kageyama (Kobe Univ.) Visualization / 55

27 H xy (β) = 1 β (7) Kageyama (Kobe Univ.) Visualization / 55

28 M 1 M 2 M 2 M 1 Kageyama (Kobe Univ.) Visualization / 55

29 RT T R Kageyama (Kobe Univ.) Visualization / 55

30 RT T R Kageyama (Kobe Univ.) Visualization / 55

31 WebGL Safari Kageyama (Kobe Univ.) Visualization / 55

32 WebGL WebGL Kageyama (Kobe Univ.) Visualization / 55

33 WebGL WebGL Web アプリ HTML + CSS + JavaScript + シェーダソースコード + オブジェクトデータ WebGL JavaScript API 頂点シェーダ プリミティブ組み立て ラスタ化 フラグメントシェーダ シザーテスト マルチサンプリング ステンシルテスト デプステスト アルファブレンディング ディザリング WebGL 用描画バッファ cavas の他の画像 スクリーン Kageyama (Kobe Univ.) Visualization / 55

34 WebGL Web アプリ HTML + CSS + JavaScript + シェーダソースコード + オブジェクトデータ WebGL JavaScript API 頂点シェーダ プリミティブ組み立て ラスタ化 フラグメントシェーダ シザーテスト マルチサンプリング ステンシルテスト デプステスト アルファブレンディング ディザリング WebGL 用描画バッファ cavas の他の画像 スクリーン Kageyama (Kobe Univ.) Visualization / 55

35 WebGL Web アプリ HTML + CSS + JavaScript + シェーダソースコード + オブジェクトデータ WebGL JavaScript API 頂点シェーダ プリミティブ組み立て ラスタ化 フラグメントシェーダ Kageyama (Kobe Univ.) Visualization / 55

36 WebGL WebGL Web HTML + CSS + JavaScript WebGL HTML + CSS + JavaScript + OpenGL SL Kageyama (Kobe Univ.) Visualization / 55

37 WebGL n n Kageyama (Kobe Univ.) Visualization / 55

38 WebGL 頂点シェーダ用ソースコード (GLSL) 頂点 attribute 変数 ( 座標 色など ) 頂点シェーダ 組み込み変数 gl_position gl_frontfacing g_lpointsize ユーザ定義 uniform 変数 ( 変換行列 光源位置 ) ユーザ定義の varying 変数 Kageyama (Kobe Univ.) Visualization / 55

39 WebGL C OpenGL SL (Shading Language) 4 4 a t t r i b u t e vec3 avertexpos ; a t r r i b u t e vec4 a V e r t e x C o l o r ; u n i f o r m mat4 umvmatrix ; u n i f o r m mat4 upmatrix ; v a r y i n g vec4 v C o l o r ; void main ( ) { g l P o s i t i o n = upmatrix umvmatrix vec4 ( avertexpos, 1. 0 ) ; v C o l o r = a V e r t e x C o l o r ; } Kageyama (Kobe Univ.) Visualization / 55

40 WebGL a t t r i b u t e vec3 avertexpos ; a t r r i b u t e vec4 a V e r t e x C o l o r ; attribute RGBA 4 Kageyama (Kobe Univ.) Visualization / 55

41 WebGL u n i f o r m mat4 umvmatrix ; u n i f o r m mat4 upmatrix ; mat4 4 4 uniform Kageyama (Kobe Univ.) Visualization / 55

42 WebGL v a r y i n g vec4 v C o l o r ; varing (varying variable) varying gl Position gl FrontFacing gl PointSize Kageyama (Kobe Univ.) Visualization / 55

43 WebGL void main ( ) { g l P o s i t i o n = upmatrix umvmatrix vec4 ( avertexpos, 1. 0 ) ; v C o l o r = a V e r t e x C o l o r ; main varying gl Position varying vcolor Kageyama (Kobe Univ.) Visualization / 55

44 WebGL primitive assembly 3 OpenGL 1.x 3 Kageyama (Kobe Univ.) Visualization / 55

45 WebGL プリミティブ フラグメント Kageyama (Kobe Univ.) Visualization / 55

46 WebGL varying varying varying varyingvalue_1 varyingvalue_2 varyingvalue_3 Kageyama (Kobe Univ.) Visualization / 55

47 WebGL フラグメントシェーダ用 ソースコード (GLSL) 組み込み変数 gl_position gl_frontfacing g_lpointsize フラグメント シェーダ 組み込み変数 gl_fragcolor ユーザ定義 varying 変数 ユニフォーム変数 テクスチャ用サンプラ Kageyama (Kobe Univ.) Visualization / 55

48 WebGL p r e c i s i o n mediump f l o a t ; // p r e c i s i o n q u a l i f i e r v a r y i n g vec4 v C o l o r ; // void main ( ) { g l F r a g C o l o r = v C o l o r ; } Kageyama (Kobe Univ.) Visualization / 55

49 WebGL WebGL Web アプリ HTML + CSS + JavaScript + シェーダソースコード + オブジェクトデータ WebGL JavaScript API 頂点シェーダ プリミティブ組み立て ラスタ化 フラグメントシェーダ シザーテスト マルチサンプリング ステンシルテスト デプステスト アルファブレンディング ディザリング WebGL 用描画バッファ cavas の他の画像 スクリーン Kageyama (Kobe Univ.) Visualization / 55

50 WebGL scissors OpenGL Super Bible (2011, p.112) シザーテスト不合格 シザーテスト 合格 Kageyama (Kobe Univ.) Visualization / 55

51 WebGL OpenGL Super Bible (2011, p.382) Kageyama (Kobe Univ.) Visualization / 55

52 WebGL OpenGL Super Bible (2011, p.399) Kageyama (Kobe Univ.) Visualization / 55

53 WebGL Kageyama (Kobe Univ.) Visualization / 55

54 WebGL Kageyama (Kobe Univ.) Visualization / 55

55 WebGL Kageyama (Kobe Univ.) Visualization / 55

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1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3 1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A 2 1 2 1 2 3 α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3 4 P, Q R n = {(x 1, x 2,, x n ) ; x 1, x 2,, x n R}

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