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IE352 CAD/CAM 개론 Chap.3 Graphic programming - Using OpenGL, Part 2

IE352 CAD/CAM 개론 Chap.3 Graphic programming - Using OpenGL, Part 2. KAIST 산업공학과 신하용. Stock Price. World Coordinates. Stock Price. NDC. Stock Price. Date. Date. Date. Viewport Coordinates. 2D Case : Viewing transform is trivial. ModelView Matrix. Projection Matrix. Viewport.

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IE352 CAD/CAM 개론 Chap.3 Graphic programming - Using OpenGL, Part 2

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  1. IE352 CAD/CAM개론Chap.3 Graphic programming - Using OpenGL, Part 2 KAIST 산업공학과 신하용

  2. Stock Price World Coordinates Stock Price NDC Stock Price Date Date Date Viewport Coordinates 2D Case : Viewing transform is trivial

  3. ModelView Matrix Projection Matrix Viewport Local coord. Object coord. Modeling coord. (xo, yo , zo) Viewing coord. Eye coord. Camera coord. (xv, yv , zv) Normalized Device Coord. (NDC) VDC (xd, yd , zd) Projected Coord. (xd, yd) Viewport coord. Screen coord. (xs, ys) World coord. (xw, yw , zw) Graphic transformation pipeline

  4. Modeling transformation • glVertex ( …)에 넣을 좌표값을 World coord.에서 넣는 대신 • Local-to-World coord. transformation matrix를 주고 • Local coord. 상에서의 좌표값을 입력 Local coord. World coord.

  5. Modeling transformation in OpenGL • Translate object : Trans (x, y, z) glTranslate{fd}( x, y, z ) • Rotate object around arbitrary axis : Rot (k(x,y,z), angle) glRotate{fd}( angle, x, y, z ) • angle is in degrees • Dilate (stretch or shrink) or mirror object : Scale (x, y, z) glScale{fd}( x, y, z )

  6. Viewing coord. up World coord. at eye Viewing transformation • World coord.상의 좌표값을 Camera의 위치에서 보는 Viewing coord.로 변환 • Modeling transformation + Viewing transformation  ModelView matrix in OpenGL • Modeling transformation을 안하고, world coord.로 값을 주기로 하면  ModelView matrix represents viewing transformation glMatrixMode( GL_MODELVIEW ); glLoadIdentity(); gluLookAt( eyex, eyey, eyez, atx, aty, atz, upx, upy, upz )

  7. (1,1,1) (-1,-1, 0) Standard NDC cube in OpenGL Projection transformation • Define viewing volume • Transform viewing volume onto Standard NDC cube • (-1, -1, 0) ~ (1,1,1) • Perspective projection glMatrixMode( GL_PROJECTION ); glLoadIdentity(); // zNear에서의 left, right, bottom, top glFrustum( left, right, bottom, top, zNear, zFar ); // or gluPerspective(fovy, aspect, zNear, zFar ); • Orthographic(parallel) projection glMatrixMode( GL_PROJECTION ); glLoadIdentity(); glOrtho( left, right, bottom, top, zNear, zFar );

  8. Near plane Far plane Viewing volume right Near plane top Far plane bottom left Viewing volume Perspective vs Orthographic(parallel) projection

  9. aspect = w/h w  h View point fovy zNear zFar gluPerspective • gluPerspective(fovy, aspect, zNear, zFar ); • fovy : 상하 방향의 시각 (degree) • aspect = w/h == glFrustum( left, right, bottom, top, zNear, zFar ); w/ top = zNear * tan (fovy / 2); bottom = -top and right = top * aspect; left = -right

  10. Viewport mapping • gluViewport(int x, int y, int width, int height); • Map NDC cube to the view port • x, y • Specify the lower left corner of the viewport rectangle, in pixels. • Defines the origin of viewport • The initial value is (0, 0). • width, height • Specify the width and height of the viewport in pixels. • When a GL context is first attached to a window, width and height are set to the dimensions of that window. • Define the size of the viewport • Window resize시 주로 불리움

  11. A simple example int main(int argc, char **argv) { glutInit(&argc, argv); // initialize window glutInitDisplayMode( GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH); glutCreateWindow(“Simple"); init (); initMenu (); registerCallbacks (); glutMainLoop (); return 0; } void init() { setLight (); glEnable(GL_DEPTH_TEST); glMatrixMode(GL_PROJECTION); glOrtho (-3.0, 3.0, -3.0, 3.0, 1.0, 20.0); glMatrixMode(GL_MODELVIEW); gluLookAt(3.0, 4.0, 5.0, // eye position 0.0, 0.0, 0.0, // center (target) 0.0, 0.0, 1.0); // up vector } void setLight () { // Enable a single OpenGL light // Red diffuse light. GLfloat light_diffuse[] = {1.0, 0.0, 0.0, 1.0}; // Infinite light location. GLfloat light_position[] = {1.0,1.0,5.0,0.0}; glLightfv(GL_LIGHT0, GL_DIFFUSE,light_diffuse); glLightfv(GL_LIGHT0, GL_POSITION,light_position); glEnable(GL_LIGHT0); glEnable(GL_LIGHTING); }

  12. A simple example - cont void registerCallbacks () { // register call back func glutDisplayFunc(displayBox); glutReshapeFunc(resize); glutMouseFunc(mouseButton); glutMotionFunc(mouseMove); } void drawBox() { glutSolidCube (2.0); } void drawBox2 () { glMatrixMode (GL_MODELVIEW); glPushMatrix (); // draw 1st cube drawBox (); // draw 2nd cube glTranslatef (0.0, 0.0, 2.0); glScalef (0.5, 0.5, 1.0); drawBox (); glPopMatrix (); } void displayBox() { glClear (GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); drawBox2 (); glutSwapBuffers (); } void resize (int w, int h) { glViewport (0, 0, w, h); } void mouseButton (int button, int state, int x, int y) { } void mouseMove (int x, int y) { }

  13. A simple example - cont void menuFunc (int select) { switch (select) { case 1 : // box glutDisplayFunc (displayBox); break; case 2 : // sphere glutDisplayFunc (displaySphere); break; case 3: // flat glShadeModel (GL_FLAT); break; case 4: // smooth glShadeModel (GL_SMOOTH); break; case 0 : // quit menu exit(0); break; default : ; // do something } glutPostRedisplay(); } void initMenu () { glutCreateMenu(menuFunc); glutAddMenuEntry ("Box", 1); glutAddMenuEntry ("Sphere", 2); glutAddMenuEntry ("Flat", 3); glutAddMenuEntry ("Smooth", 4); glutAddMenuEntry("Quit", 0); glutAttachMenu(GLUT_RIGHT_BUTTON); } void displaySphere () { glClear (GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glutSolidSphere (2.0, 20, 20); glutSwapBuffers (); }

  14. Shading model : Flat & Smooth glShadeModel (GL_SMOOTH) glShadeModel (GL_FLAT)

  15. ModelView Matrix Viewing Matrix Eye coord. World coord. = ModelView Matrix Viewing Matrix Modeling Matrix Modeling Matrix Eye coord. Local coord. = … Local coord. World coord.

  16. Matrix Stack xyz’ World coord. • glPushMatrix (); • glPopMatrix (); Viewing Matrix V Modeling Matrix M1 Modeling Matrix M2 Eye coord. xyz = V V M1 V M1M2 V V M1 V

  17. frame buffer CPU pixels display list client Display lists • What’s for display processor? • CPU does everything. • Display processor(GPU) : a separate processor on a graphic card frame buffer GPU CPU primitives pixels server

  18. pixels objects CPU GPU Frame buffer objects display display command Display List re-display Immediate mode vs. Retained mode • Immediate mode pixels objects CPU GPU Frame buffer display GPU does not “remember” any of graphic objects. clear display • Retained mode • cons • requires memory on the server. • overhead of creating a display list. • pros • reduce traffic between client and server. • utilize any special hardware available on the server

  19. Display list in OpenGL • To define a new display list, glNewList (BOX, GL_COMPILE); // drawing commands, here glEndList (BOX); • To display the display list, glCallList (BOX); • Do not display now. • (c.f. GL_COMPILE_AND_EXECUTE)

  20. 은선 제거, 은면 제거 (Hidden-line/surface removal) • Back-face removal algorithm • Depth-sorting, or Painter’s algorithm • Hidden-line removal algorithm • Z-buffer method

  21. Face, Normal vector N Vertex Face Edge N Polyhedron

  22. Back-face removal algorithm (1) • A face of an object is visible if its normal vector in the direction of the outside of the object is pointing toward the viewer. MN > 0  Visible MN = 0  Line MN < 0  Invisible • 적용가능 경우 • planar face • Convex solid

  23. ? Back-face removal algorithm (2) • 적용이 어려운 경우 • 여러 개 물체, • 오목한 형상, • 곡면의 경우 • 곡면의 경우 • 실루엣 곡선 (Silhouette curve) 이용 • Curve along which M  N=0 • 계산이 복잡하고, 시점에 따라 다시 계산되어야 하므로 실용성?

  24. Edge와 face간의 위치 관계 Hidden-line removal algorithm • Back-face removal algorithm의 단점 보완 필요. • 그려질 부위만 미리 계산 • Algorithm 복잡하고, 계산시간 많이 필요

  25. Depth-sorting, or Painter’s algorithm • Hidden-surface removal • 물체의 면 (surface)을 관찰자와의 거리에 따라 정렬 (sorting)한 후, 가장 먼 거리에 있는 면부터 색깔을 채워 그린다. • 관찰자와 면간의 거리는 viewing 좌표계의 Z값 (Zv)을 기준으로 한다. 따라서 Z값이 더 크면 더 가깝다. • 여러 개의 면이 있을 경우 Zv값의 범위가 겹치는 경우가 발생함. • 면을 다시 작은 조각으로 쪼개어 Zv값의 범위가 겹치지 않도록 한다 (예: 삼각형 조각). • Triangulation (facet conversion)

  26. A D E Viewer C View Plane B Depth Sort Depth Sort • Painter’s Algorithm: • Sort surfaces in order of decreasing maximum depth • Draw surfaces in order starting with ones of greatest depth • Order : View point dependent

  27. Z-buffer method • 그리는 순서와 무관 • 스크린 상의 pixel은 관찰자와 가장 가까운 entity가 차지한다. • Z-buffer (depth buffer) : viewport pixel수만큼, 투영된 물체의 Zv값을 저장하는 HW memory • Color value for each pixel : color buffer z=3 • 각 polygon에 대해, 해당 pixel의 Zv 계산 • Zv가 저장된 Z값보다 작을 경우 • - color buffer의 해당 pixel update • (현재 polygon의 color값으로) • - z-buffer의 해당 pixel update w/ Zv z=1 z=2 z=4

  28. BSP(Binary Space Partition) Trees • BSP tree: organize all of space (hence partition)into a binary tree • Preprocess: overlay a binary tree on objects in the scene • Runtime: correctly traversing this tree enumerates objects from back to front • Idea: divide space recursively into half-spaces by choosing splitting planes • Splitting planes can be arbitrarily oriented • Notice: nodes are always convex • Ref. A Watt, F Policarpo, 3D Games : real-time rendering and software technology, Addison-Wesley, 2001, Chap.9

  29. BSP Trees: Objects

  30. BSP Trees: Objects

  31. BSP Trees: Objects

  32. BSP Trees: Objects

  33. BSP Trees: Objects

  34. Rendering BSP Trees renderBSP(BSPtree *T) BSPtree *near, *far; if (eye on left side of T->plane) near = T->left; far = T->right; else near = T->right; far = T->left; renderBSP(far); if (T is a leaf node) renderObject(T) renderBSP(near);

  35. Rendering BSP Trees renderBSP(BSPtree *T) BSPtree *near, *far; if (eye on left side of T->plane) near = T->left; far = T->right; else near = T->right; far = T->left; renderBSP(far); if (T is a leaf node) renderObject(T) renderBSP(near);

  36. Rendering BSP Trees

  37. Ouch Discussion: BSP Tree Cons • No bunnies were harmed in my example • But what if a splitting plane passes through an object? • Split the object; give half to each node: • Worst case: can create up to O(n3) objects!

  38. Plates (1-1) Wire-frame Ref : Foley et al, Computer Graphics Principles and Practice, 2nd edition, 1990, Addison-Wesley

  39. Plates (1-2) 은선 제거

  40. Plates (1-3) 은면 제거

  41. Rendering • 현실적인 느낌을 주기 위해서는 물체에 대한 빛의 효과를 나타냄. • Rendering: 색깔 + 빛의 세기 (intensity) 고려. • Rendering 기법 • Shading: 은면 제거와 유사, 단일 물체 • Ray tracing: 여러 개 물체

  42. Light modeling • Light source: 광원 • Direct illumination: 광원에 의한 직접조명 • Ambient illumination: 주변의 간접조명 • Reflected light: 반사광 • ambient + direct illumination

  43. Phong light intensity model • I = Ra + Rd + Rs • I : 눈에 들어오는 빛의 세기 • Ra : 주변광(Ambient illumination)이 반사된 빛의 세기 • Rd : 직접조명이 난반사된 반사된 빛의 세기 • Rd : 직접조명이 정반사된 반사된 빛의 세기

  44. 간접조명에 의해 반사된 빛의 세기 • Ambient illumination으로 반사된 빛의 세기 • Ra = KdIa • Ia: intensity of the ambient light • Kd: 물체 표면의 난반사율 (Diffuse reflectance coefficient) • 빛의 세기는 관찰자 위치와 무관. • 모든 위치에서 동일한 강도를 느낀다고 봄.

  45. 빛이 사방으로 방사됨.(거친 면) - 빛의 세기는 관찰자 위치와 무관함. 면에서 바로 반사됨. - 빛의 세기는 관찰자 위치에 따라 달라지게 됨. 직접조명 (광원)에 의한 반사 • 광원은 점 광원 (point light source)만을 고려. • 난반사 (diffuse reflection), 정반사 (specular reflection) • 반사광 세기 = 난반사 된 빛의 세기 + 정반사 된 빛의 세기 • Ip (반사광의 세기) = Ep(광원의 세기) / (D + D0) • D : 물체와 눈의 거리 • Do : constant added to prevent dividing by 0

  46. N L 난반사 된 빛의 세기 (Rd) • 입사각 (angle of incidence)의 cosine에 비례 • Lambert’s cosine 법칙 • Rd = Ip Kd (N•L) • Ip : 직접조명의 세기 • Kd : 물체 표면의 난반사율 (Diffuse reflectance coefficient) • N : 물체의 Normal vector • L : 입사광 방향

  47. L V H N 정반사 된 빛의 세기 • 입사 하는 빛의 방향은 L, 반사 된 빛의 방향은 R. • 관찰자가 느끼는 반사광의 세기는, R과 벗어 날수록 약해짐. • V: 관찰자가 보는 방향벡터. • Rs = Ip Ks (V•R)n • (V•R)n = (cos)n • 면이 밝을수록 n값은 커짐. 즉, 에 민감해짐. (예: 금속 n = 150, 종이 n = 1) • V•R = H•N, H=(L+V)/2 • H•N : 계산이 쉽다.

  48. Putting it together • 반사된 빛의 색깔 (color)을 고려한다면, Red, Green, Blue에 대해 식 (3.22)를 별도로 적용함 - Ir, Ig, Ib: 식 (3.23). • 이때 Ks (specular reflectance)는 일반적으로 색에 따라 달라지는 효과가 거의 없기에 분리하지 않음. • 일반적인 자유곡면에 대해서는 삼각형 등으로 잘게 쪼개어 각각의 삼각형 면의 법선 벡터 (N)을 구하여 상기 식을 적용하는 것이 일반적임. 식 (3.22)

  49. Approximations for Speed • The viewer direction, V, and the light direction, L, depend on the surface position being considered, x • Distant light approximation: • Assume L is constant for all x • Good approximation if light is distant, such as sun • Distant viewer approximation • Assume V is constant for all x • Rarely good, but only affects specularities

  50. Phong shading, Gouraud shading • 곡면을 삼각형으로 잘게 쪼개어 반사광 세기를 계산할 때, 삼각형 경계에서 법선벡터 (N)의 변화가 심하기 때문에 꺽인듯이 보임. • 법선벡터를 부드럽게 변화 시킴으로써 해결하고자 하는 노력 • Phong, Gouraud shading. • Phong shading • 삼각형 꼭지점의 법선벡터는 이웃한 삼각형의 평균법선벡터. • 삼각형 내부에서 법선벡터는 3 꼭지점 법선벡터를 조합하여 부드럽게 변화되도록 계산함. • Gouraud shading • 삼각형 꼭지점의 빛의 세기를 보간 (interpolating)하여 투영된 삼각형 내부에 들어오는 pixel에서 빛의 세기를 계산함.

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