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Viewing

Viewing. 고려대학교 컴퓨터 그래픽스 연구실. Fundamental Types of Viewing. Perspective views finite COP (center of projection) Parallel views COP at infinity DOP (direction of projection). parallel view. perspective view. Parallel View. Perspective View. Classical Viewing.

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Viewing

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  1. Viewing 고려대학교 컴퓨터 그래픽스 연구실 kucg.korea.ac.kr

  2. Fundamental Types of Viewing • Perspective views • finite COP (center of projection) • Parallel views • COP at infinity • DOP (direction of projection) parallel view perspective view kucg.korea.ac.kr

  3. Parallel View kucg.korea.ac.kr

  4. Perspective View kucg.korea.ac.kr

  5. Classical Viewing • Specific relationship between the objects and the viewers kucg.korea.ac.kr

  6. Orthographic Projections • Projectors are perpendicular to the projection plane • preserve both distances and angles temple and three multiview orthographic projections orthographic projections kucg.korea.ac.kr

  7. Axonometric Projections (1/2) • Projection plane can have any orientation with respect to the object • projectors are still orthogonal to the projection planes construction top view side view kucg.korea.ac.kr

  8. Axonometric Projections (2/2) • Preserve parallel lines but not angles • isometric – projection plane is placed symmetrically with respect to the three principal faces • dimetric – two of principal faces • trimetric – general case kucg.korea.ac.kr

  9. Axonometric Projections (2/2) • Preserve parallel lines but not angles • isometric – projection plane is placed symmetrically with respect to the three principal faces • dimetric – two of principal faces • trimetric – general case kucg.korea.ac.kr

  10. Oblique Projections • Projectors can make an arbitrary angle with the projection plane • preserve angels in planes parallel to the projection plane construction top view side view kucg.korea.ac.kr

  11. Perspective Projections (1/2) • Diminution of size • when objects are moved father from the viewer, their images become smaller kucg.korea.ac.kr

  12. Perspective Projections (2/2) • One-, two-, and three-point perspectives • how many of the three principal directions in the object are parallel to the projection plane • vanishing points three-point perspective two-point perspective one-point perspective kucg.korea.ac.kr

  13. Perspective Projections (2/2) • One-, two-, and three-point perspectives • how many of the three principal directions in the object are parallel to the projection plane • vanishing points three-point perspective two-point perspective one-point perspective kucg.korea.ac.kr

  14. Perspective Projections (2/2) • One-, two-, and three-point perspectives • how many of the three principal directions in the object are parallel to the projection plane • vanishing points three-point perspective two-point perspective one-point perspective kucg.korea.ac.kr

  15. Perspective Projections (2/2) • One-, two-, and three-point perspectives • how many of the three principal directions in the object are parallel to the projection plane • vanishing points three-point perspective two-point perspective one-point perspective kucg.korea.ac.kr

  16. Positioning of the Camera (1/3) • OpenGL places a camera at the origin of the world frame pointing in the negative z direction • move the camera away from the objects glTranslatef(0.0, 0.0, -d); initial configuration after change in the model-view matrix kucg.korea.ac.kr

  17. Positioning of the Camera (2/3) • Look at the same object from the positive x axis • translation after rotation by 90 degrees about the y axis glMatrixMode(GL_MODELVIEW); glLoadIdentity( ); glTranslatef(0.0, 0.0, -d); glRotatef(-90.0, 0.0, 1.0, 0.0); kucg.korea.ac.kr

  18. Positioning of the Camera (3/3) • Create an isometric view of the cube y y y z x x view from positive z axis view from positive z axis view from positive x axis kucg.korea.ac.kr

  19. Positioning of the Camera (3/3) • Create an isometric view of the cube glMatrixMode(GL_MODELVIEW); glLoadIdentity( ); glTranslatef(0.0, 0.0, -d); glRotatef(35.26, 1.0, 0.0, 0.0); glRotatef(45.0, 0.0, 1.0, 0.0); y y y x x x view from positive z axis view from positive z axis kucg.korea.ac.kr

  20. U-V-N System (1/2) • VRP (view-reference point), VPN (view-plane normal), and VUP (view-up vector) • u, v (up-direction vector), n (normal vector)  x, y, z axes respectively determination of the view-up vector camera frame kucg.korea.ac.kr

  21. U-V-N System (2/2) • Translation after rotation • VRP – (x, y, z)  T(-x, -y, -z) • VNP – (nx, ny, nz)  n • VUP – vup v = vup – (vup• n) n  u = v  n (※ our assumption – all vectors must be normalized ) kucg.korea.ac.kr

  22. Look-At Function • OpenGL utility function • VRP: eyePoint • VPN: – ( atPoint – eyePoint ) • VUP: upPoint – eyePoint gluLookAt(eyex, eyey, eyez, atx, aty, atz, upx, upy, upz); look-at positioning kucg.korea.ac.kr

  23. Others • Roll, pitch, and yaw • ex. flight simulation • Elevation and azimuth • ex. star in the sky kucg.korea.ac.kr

  24. Simple Perspective Projections (1/2) • Simple camera • projection plane is orthogonal to z axis • projection plane in front of COP three-dimensional view top view side view kucg.korea.ac.kr

  25. Model-view Projection Perspective division projection pipeline Simple Perspective Projections (2/2) • Homogeneous coordinates • Perspective projection matrix kucg.korea.ac.kr

  26. Simple Orthogonal Projections • Projectors are perpendicular to the view plane • Orthographic projection matrix kucg.korea.ac.kr

  27. Projections in OpenGL • Angle of view • only objects that fit within the angle of view of the camera appear in the image • View volume • be clipped out of scene • frustum – truncated pyramid kucg.korea.ac.kr

  28. Perspective in OpenGL (1/2) • Specification of a frustum • near, far: positive number !!  zmax = – far  zmin = – near glMatrixMode(GL_PROJECTION); glLoadIdentity( ); glFrustum(xmin, xmax, ymin, ymax, near, far); kucg.korea.ac.kr

  29. Perspective in OpenGL (2/2) • Specification using the field of view • fov: angle between top and bottom planes • fovy: the angle of view in the up (y) direction • aspect ratio: width divided by height glMatrixMode(GL_PROJECTION); glLoadIdentity( ); gluPerspective(fovy, aspect, near, far); kucg.korea.ac.kr

  30. Parallel in OpenGL • Orthographic viewing function • OpenGL provides only this parallel-viewing function • near < far !!  no restriction on the sign  zmax = – far  zmin = – near glMatrixMode(GL_PROJECTION); glLoadIdentity( ); glOrtho(xmin, xmax, ymin, ymax, near, far); kucg.korea.ac.kr

  31. Walking Though a Scene (1/2) void keys(unsigned char key, int x, int y) { if(key == ‘x’) viewer[0] -= 1.0; if(key == ‘X’) viewer[0] += 1.0; if(key == ‘y’) viewer[1] -= 1.0; if(key == ‘Y’) viewer[1] += 1.0; if(key == ‘z’) viewer[2] -= 1.0; if(key == ‘Z’) viewer[2] += 1.0; } void display(void) { glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); glLoadIdentity(); gluLookAt(viewer[0], viewer[1], viewer[2], 0,0,0, 0,1,0); glRotatef(theta[0], 1.0, 0.0, 0.0); glRotatef(theta[1], 0.0, 1.0, 0.0); glRotatef(theta[2], 0.0, 0.0, 1.0); colorcube( ); glFlush( ); glutSwapBuffers( ); } kucg.korea.ac.kr

  32. Walking Though a Scene (2/2) void myReshape(int w, int h) { glViewport(0, 0, w, h); glMatrixMode(GL_PROJECTION); glLoadIdentity( ); if( w <= h ) glFrustum(-2.0, 2.0, -2.0*(GLfloat)h/(GLfloat)w, 2.0*(GLfloat)h/(GLfloat)w, 2.0, 20.0); else glFrustum(-2.0 *(GLfloat)w/(GLfloat)h, 2.0 *(GLfloat)w/(GLfloat)h, -2.0, 2.0, 2.0, 20.0); glMatrixMode(GL_MODELVIEW); } kucg.korea.ac.kr

  33. Projections & Shadows (1/2) • Shadow polygon • Steps • light source at (xl, yl, zl) • translation (-xl, -yl, -zl) • perspective projection through the origin • translation (xl, yl, zl) kucg.korea.ac.kr

  34. Projections & Shadows (2/2) GLfloat m[16]; /* shadow projection matrix */ for(i=0; i<16; i++) m[i] = 0.0; m[0] = m[5] = m[10] = 1.0; m[7] = -1.0/yl; glColor3fv(polygon_color); glBegin(GL_POLYGON); . . /* draw the polygon normally */ . glEnd( ); glMatrixMode(GL_MODELVIEW); glPushMatrix( ); /* save state */ glTranslatef(xl, yl, zl); /* translate back */ glMultMatrixf(m); /* project */ glTranslatef(-xl, -yl, -zl); /* move light to origin */ glColorfv(shadow_color); glBegin(GL_POLYGON); . . /* draw the polygon again */ . glEnd( ); glPopMatrix( ); /* restore state */ kucg.korea.ac.kr

  35. Shadows from a Cube onto Ground kucg.korea.ac.kr

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