1. Viewing Korea Univ. Computer Graphics Lab. Hong, Jin Kyung

2. Korea Univ. Computer Graphics Lab.2 Chapter Objectives View a geometric model Control the location Clip Undesired portions of the model Manipulate the appropriate matrix stacks

3. Korea Univ. Computer Graphics Lab.3 Transformation Viewing transformation Modeling transformation Projection transformation Viewport transformation

4. Korea Univ. Computer Graphics Lab.4 Transformation Stages of Vertex Transformation v’ = Mv

5. Korea Univ. Computer Graphics Lab.5 Viewing Transformation(1/6) Eye position 의 위치와 방향을 결정 Default 위치 : 원점, negative z-axis, y-axis up void gluLookAt(GLdouble eyex, GLdouble eyey, GLdouble eyez, GLdouble centerx, GLdouble centery, Gldouble centerz, GLdouble upx, GLdouble upy, GLdouble upz); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); // 현재 행렬을 단위 행렬로 초기화

6. Korea Univ. Computer Graphics Lab.6 Viewing Transformation(2/6) Default camera position Using gluLookAt()

7. Korea Univ. Computer Graphics Lab.7 Viewing Transformation(3/6) Example 3-1. void display() { glClear(GL_COLOR_BUFFER_BIT); glColor3f(1.0, 1.0, 1.0); glLoadIdentity(); /* Viewing Transformation */ gluLookAt(0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); glScalef(1.0, 2.0, 1.0); /* Modeling Transformation */ glutWireCube(1.0); glFlush(); }

8. Korea Univ. Computer Graphics Lab.8 Viewing Transformation(4/6) void glTranslate{fd}(TYPE x, TYPE y, TYPE z); glLoadIdentity(); glColor3f(1.0, 1.0, 1.0); draw_triangle(); glEnable(GL_LINE_STIPPLE); glLineStipple(1, 0xF0F0); glTranslated(-1.0, 0.0, 0.0); glColor3f(1.0, 0.0, 0.0); draw_triangle(); glDisable(GL_LINE_STIPPLE);

9. Korea Univ. Computer Graphics Lab.9 Viewing Transformation(5/6) void glRotate{fd}(TYPE angle, TYPE x, TYPE y, TYPE z); glLoadIdentity(); glColor3f(1.0, 1.0, 1.0); draw_triangle(); glEnable(GL_LINE_STIPPLE); glLineStipple(1, 0x8888); glRotatef(90.0, 0.0, 0.0, 1.0); glColor3f(1.0, 1.0, 0.0); draw_triangle(); glDisable(GL_LINE_STIPPLE);

10. Korea Univ. Computer Graphics Lab.10 Viewing Transformation(6/6) Rotating First or Translating First

11. Korea Univ. Computer Graphics Lab.11 Coordinate System (1/2) Grand, fixed coordinate system glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glMultMatrixf(N); // N matrix transformation glMultMatrixf(M); glMultMatrixf(L); glBegin(GL_POINTS); glVertex3f(v);// draw transformed vertex v glEnd() // v’ = N(M(Lv)) - 변환되는 점의 좌표를 명령 순서와 반대로 계산해야 함

12. Korea Univ. Computer Graphics Lab.12 Coordinate System (2/2) Local coordinate system glMatrixMode(GL_MODELVIEW); glLoadIdentity(); glMultMatrixf(T);// Translation glMultMatrixf(R);// Rotation draw_the_object(); - 변환되는 점의 좌표가 명령 순서와 일치 예 ) 로봇의 운동

13. Korea Univ. Computer Graphics Lab.13 Modeling Transformation(1/4) 물체들의 위치와 방향을 결정 World 좌표에 대한 각 물체의 좌표 값이 결정 -> x, y, z 축에 따른 model 의 비율 결정 void glScale{fd}(TYPE x, TYPE y, TYPE z);

14. Korea Univ. Computer Graphics Lab.14 Modeling Transformation(2/4) void glScalef{fd}(TYPE x, TYPE y, TYPE z); glLoadIdentity(); glColor3f(1.0, 1.0, 1.0); draw_triangle(); glEnable(GL_LINE_STIPPLE); glLineStipple(1, 0xF00F); glScalef(1.5, 0.5, 1.0); glColor3f(0.0, 1.0, 0.0); draw_triangle(); glDisable(GL_LINE_STIPPLE);

15. Korea Univ. Computer Graphics Lab.15 Modeling Transformation(3/4) Example 3-1. void display() { glClear(GL_COLOR_BUFFER_BIT); glColor3f(1.0, 1.0, 1.0); glLoadIdentity(); /* Viewing Transformation */ gluLookAt(0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); glScalef(1.0, 2.0, 1.0); /* Modeling Transformation */ glutWireCube(1.0); glFlush(); }

16. Korea Univ. Computer Graphics Lab.16 Modeling Transformation(4/4) 프로그램 명령 순서 Viewing Transformation -> Modeling Transformation 실제 좌표 값 결정 Modeling Transformation -> Viewing Transformation

17. Korea Univ. Computer Graphics Lab.17 Vertex Transformation TranslateRotate Scale

18. Korea Univ. Computer Graphics Lab.18 Duality of Modelview(1/2) Viewing Transformation – 관측자를 이동 Modeling Transformation – 좌표계를 이동  결과적으로 같은 효과

19. Korea Univ. Computer Graphics Lab.19 Duality of Modelview(2/2) Creating a Custom Utility Routine void pilotView(double planex, double planey, double planez, double roll, double pitch, double heading) { glRotated(roll, 0.0, 0.0, 1.0); glRotated(pitch, 0.0, 1.0, 0.0); glRotated(heading, 1.0, 0.0, 0.0); glTranslated(-planex, -planey, -planez); } void polarView(double distance, double twist, double elevation, double azimuth) { glTranslated(0.0, 0.0, -distance); glRotated(-twist, 0.0, 0.0, 1.0); glRotated(-elevation, 1.0, 0.0, 0.0); glRotated(azimuth, 0.0, 0.0, 1.0); }

20. Korea Univ. Computer Graphics Lab.20 Projection Transformation(1/6) Projection Define a viewing volume glMatrixMode(GL_PROJECTION); glLoadIdentity();

21. Korea Univ. Computer Graphics Lab.21 Projection Transformation(2/6) 1) Perspective Projection –foreshortening void glFrustum(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far);

22. Korea Univ. Computer Graphics Lab.22 Projection Transformation(3/6) void glPerspective(GLdouble fovy, GLdouble aspect, GLdouble near, GLdouble far); aspect = width / height Symmetric perspective-view frustum

23. Korea Univ. Computer Graphics Lab.23 Projection Transformation(4/6) Calculating field of view – Example 3-3. #define PI 3.1415926535 double calculatingAngle(double size, double distance) { doubleradtheta, degtheta; redtheta = 2.0 * atan2(size/2.0, distance); // radian degtheta = (180.0 * redtheta) /PI; // degree return degtheta; }

24. Korea Univ. Computer Graphics Lab.24 Projection Transformation(5/6) Example 3-1. void reshape(int w, int h) { glViewport(0, 0, (GLsizei) w, (GLsizei) h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); //glFrustum(-1.0, 1.0, -1.0, 1.0, 1.5, 20.0); gluPerspective(80.0, 1.0, 1.5, 20.0); glMatrixMode(GL_MODELVIEW); }

25. Korea Univ. Computer Graphics Lab.25 Projection Transformation(6/6) 2) Orthographic Projection – 물체의 실제 사이즈와 각도를 유지 void glOrtho(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far);

26. Korea Univ. Computer Graphics Lab.26 Manipulating the Matrix Stacks(1/3) A stack of matrices –Useful for constructing hierarchical models glLoadIdentity() glMatrixMode() glMultMatrix() glLoadMatrix() void glPushMatrix(void); void glPopMatrix(void);

27. Korea Univ. Computer Graphics Lab.27 Manipulating the Matrix Stacks(2/3) void draw_wheel_and_bolts() { long i; draw_wheel(); for(i=0; i<5; i++) { glPushMatrix(); glRotatef(70.0*i, 0.0, 0.0, 1.0); glTranslatef(3.0, 0.0, 0.0); draw_bolt(); glPopMatrix(); } Example 3-4. Pushing and Pop Matrix

28. Korea Univ. Computer Graphics Lab.28 Manipulating the Matrix Stacks(3/3) The Modelview Matrix Stack The Projection Matrix Stack

29. Korea Univ. Computer Graphics Lab.29 Viewport Transformation(1/3) Viewport 3D 모델 좌표 -> 스크린 좌표로 변환

30. Korea Univ. Computer Graphics Lab.30 Viewport Transformation(2/3) –Viewport 의 aspect ratio –Viewing volume 의 aspect ratio void glViewport(GLint x, GLint y, GLsizei width, GLsizei height); => 일치해야 함

31. Korea Univ. Computer Graphics Lab.31 Viewport Transformation(3/3) The Transformed Depth Coordinate –Range : [0.0, 1.0] –near clipping plane 에서 멀어질수록 정밀도 떨어짐 void glDepthRange(GLclampd near, GLclampd far);

32. Korea Univ. Computer Graphics Lab.32 Homogeneous Coordinates System Homogeneous Vertex (x, y, z, w) – 위치나 벡터를 나타냄 –W≠0 일 경우 –W ＝ 0 일 경우 point at infinity –Use only non-negative w-values

33. Korea Univ. Computer Graphics Lab.33 Additional Clipping Planes Example 3-5. Wireframe Sphere with two Clipping Planes GLdouble eqn[4] = {0.0, 1.0, 0.0, 0.0}; // y=0 GLdouble eqn2[4] = {1.0, 0.0, 0.0, 0.0}; // x=0 glClipPlane(GL_CLIP_PLANE0, eqn); glEnable(GL_CLIP_PLANE0);

34. Korea Univ. Computer Graphics Lab.34 Examples of Composing Several Transformation Example 3-6. Planetary System

35. Korea Univ. Computer Graphics Lab.35 Examples of Composing Several Transformation Example 3-7. Robot Arm

36. Korea Univ. Computer Graphics Lab.36 Reverse and Mimicking Transformation Example 3-8. Take and reverse