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Viewing and Transformation

Viewing and Transformation. The Camera Analogy 1/2. Set up tripod and pointing the camera at the scene (viewing transformation). Arrange the scene to be photographed into the desired composition (modeling transformation). The Camera Analogy 2/2. Choose a camera lens or adjust the zoom

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Viewing and Transformation

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  1. Viewing and Transformation Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  2. The Camera Analogy1/2 • Set up tripod and pointing the camera at the scene(viewing transformation). • Arrange the scene to be photographed into the desired composition (modeling transformation). Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  3. The Camera Analogy2/2 • Choose a camera lens or adjust the zoom (projection transformation). • Determine how large you want the final photograph to be (viewport transformation). Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  4. Overview Modelview Matrix Projection Matrix Viewport Transformation Perspective Division Vertex X Y Z W X Y eye coordinates clip coordinates normalized device coordinates window coordinates Object coordinates TODO: 1. Switch matrix mode to GL_PROJECTION and call glLoadIdentity(). 2. Call gluPerspective() if you want perspective projection. 3. Call gluOrtho2D() if you want orthogonal projection. TODO: 1. Call glViewport(). TODO: 1. Switch matrix mode to GL_MODELVIEW and call glLoadIdentity(). 2. Call gluLookAt(). 3. Your own modeling transformations. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  5. //Rotate then translate: glTranslatef( 1,0,0 ); glRotatef(45.0, 0,0,1 ); drawObject(); Matrices in OpenGL X Y Z W • Consider a transformation: (T1T2…Tn)。 (multiply object coordinate by Tn first, then Tn-1 …until T1 ), To build the transformation matrix: (T1T2…Tn) we shall multiply identity matrix by T1 then T2…until Tn, as: I。T1。T2。…。T3. • Thus, the order of issuing commands shall be inversed. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  6. Viewing Transformations1/2 • To positioning and aiming the camera. • Use gluLookAt() to indicate where the camera is placed and aimed. • If gluLookAt() was not called, the camera has a default position at the origin, points down the negative Z-axis, and an up-vector of positive Y-axis. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  7. Viewing Transformations2/2 • gluLookAt( GLdouble eyex, GLdouble eyey, GLdouble eyez, GLdouble centerx, GLdouble centery, GLdouble centerz, GLdouble upx, GLdouble upy, GLdoubpe upz ); • eyex, eyey, eyez is where the camera is positioned. • centerx, centery, centerz is where the camera looks at. • Upx, upy, upz is the up-vector of the camera. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  8. Modeling Transformations1/5 • To position and orient the models. • Perform rotate, translate, scale and combinations of these transformations. • In OpenGL, modeling and viewing transformation are combined into the modelview matrix before the transformation are applied. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  9. Modeling Transformations2/5 • glTranslate{fd}( TYPE x,TYPE y,TYPE z ); • Multiplies current matrix by a matrix that moves an object by x,y,z glTranslatef( 0, 0, -1 ); Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  10. Modeling Transformations3/5 • glRotate{fd}( TYPR angle,TYPE x,TYPR y,TYPE z ); • Multiplies current matrix by a matrix that rotates an object in a counterclockwise direction about the ray from origin to (x,y,z) with angle as the degrees. glRotatef( 45.0, 0, 0, 1); Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  11. Modeling Transformations4/5 • glScale{fd}( TYPE x,TYPE y,TYPE z ); • Multiplies current matrix by a matrix that scales an object along axes. glScalef( 2.0, -0.5, 1.0 ); Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  12. Modeling Transformations5/5 • The order of transformations is critical. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  13. Projection Transformations1/5 • Determine what the field of view(or viewing volume) is and how objects are projected onto the screen. • Two types of projections are provided: • Perspective projection • Orthographic projection Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  14. Projection Transformations2/5 • Perspective Projection • glFrustum( GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far ); Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  15. Projection Transformations3/5 • gluPerspective( GLdouble fovy, GLdouble aspect, GLdouble near, GLdouble far ); Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  16. Projection Transformations4/5 • Orthographic Projection • glOrtho( GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far ); • gluOrtho2D( GLdouble left, GLdouble right, GLdouble bottom, GLdouble top); • For 2D projection matrix • The Z coordinates for objects are assumed to lie between –1.0 and 1.0. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  17. Projection Transformations5/5 Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  18. Viewport Transformations • Transform the final image into some region of the window. • The viewport is measured in window coordinates. • glViewport( GLint x, GLint y, GLsizei width, GLsizei height ); • Initial values are (0, 0, winWidth, winHeight). Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  19. Matrix Manipulation1/3 • glMatrixMode( GLenum mode ); • Switch between modelview, projection, texture matrix mode.(GL_MODELVIEW, GL_PROJECTION, GL_TEXTURE) • Each matrix mode has its own matrix stack. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  20. Matrix Manipulation2/3 • glLoadIdentity(); • Set current matrix to the 4x4 identity matrix. • glLoadMatrix{f,d}( const TYPE* m ); • Replaces current matrix by a user defined matrix. • The user defined matrix m is a 4x4 array. • glMultMatrix{f,d}( const TYPE* m ); • Multiplies current matrix by a user defined matrix. • The user defined matrix m is a 4x4 array. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  21. Matrix Manipulation3/3 • glPushMatrix(); • Push current matrix into matrix stack. • glPopMatrix(); • Pop matrix from matrix stack. • These stack operations of matrix is very useful for constructing a hierarchical structure. Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  22. Transformation Program1/6 #include <GL/glut.h> static GLfloat year=0.0f, day=0.0f; void init() { glClearColor(0.0, 0.0, 0.0, 0.0); } void GL_display() { // clear the buffer glClear(GL_COLOR_BUFFER_BIT); glColor3f(1.0, 1.0, 1.0); glPushMatrix(); glutWireSphere(1.0, 20, 16); // the Sun glRotatef(year, 0.0, 1.0, 0.0); Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  23. Transformation Program2/6 glTranslatef(3.0, 0.0, 0.0); glRotatef(day, 0.0, 1.0, 0.0); glutWireSphere(0.5, 10, 8); // the Planet glPopMatrix(); // swap the front and back buffers glutSwapBuffers(); } void GL_reshape(GLsizei w, GLsizei h) { // viewport transformation glViewport(0, 0, w, h); // projection transformation glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluPerspective(60.0, (GLfloat)w/(GLfloat)h, 1.0, 20.0); Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  24. Transformation Program3/6 // viewing and modeling transformation glMatrixMode(GL_MODELVIEW); glLoadIdentity(); gluLookAt(0.0, 3.0, 5.0, // eye 0.0, 0.0, 0.0, // center 0.0, 1.0, 0.0); // up } // GLUT idle function void GL_idle() { day += 10.0; if(day > 360.0) day -= 360.0; year += 1.0; if(year > 360.0) year -= 360.0; // recall GL_display() function glutPostRedisplay(); } Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  25. Transformation Program4/6 // GLUT keyboard function void GL_keyboard(unsigned char key, int x, int y) { switch(key) { case 'd': day += 10.0; if(day > 360.0) day -= 360.0; glutPostRedisplay(); break; case 'y': year += 1.0; if(year > 360.0) year -= 360.0; glutPostRedisplay(); break; case 'a': // assign idle function glutIdleFunc(GL_idle); break; case 'A': glutIdleFunc(0); break; case 27: exit(0); } } Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  26. Transformation Program5/6 int main(int argc, char** argv) { glutInit(&argc, argv); glutInitWindowSize(500, 500); glutInitWindowPosition(0, 0); glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB); glutCreateWindow("Planet"); init(); glutDisplayFunc(GL_display); glutReshapeFunc(GL_reshape); glutKeyboardFunc(GL_keyboard); glutMainLoop(); } Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  27. Transformation Program6/6 Tan-Chi Ho, CGGM Lab., CSIE of NCTU

  28. Any Question? ? Tan-Chi Ho, CGGM Lab., CSIE of NCTU

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