Computer Graphics Through OpenGL: From Theory to

Experiments, Second Edition

Chapter 4

Figure 4.1: Screenshot ofbox.cpp.

Figure 4.2: Translation: glTranslatef(p, q, r).

Figure 4.3: Translating into the viewing frustum.

Figure 4.4: Screenshot ofExperiment 4.3.

Figure 4.5: Scaling:glScalef(u, v, w).

Figure 4.6: Screenshot ofinitial configuration ofExperiment 4.4.

Figure 4.7: Reflection inthe yz-plane.

Figure 4.8: Screenshots of Experiment 4.5: (a) before scaling (b) after.

Figure 4.9: Screenshotfor Experiment 4.6.

Figure 4.10: Turningalong a cylinder.

Figure 4.11: Rotation: glRotatef(A, p, q, r). The point P is rotated according tothe 4-step process in the text. The rotation of a box is also shown.

Figure 4.12: glRotatef(A, 0.0, 0.0, 1.0).

Figure 4.13: Screenshots from Experiment 4.9.

Figure 4.14: Rotating a square about its own center.

Figure 4.15: Screenshots: (a) Experiments 4.10 and (b) 4.11.

Figure 4.16: Local system (bold) coincides with the global initially. The global systemis fixed.

Figure 4.17: Transitions of the box, the box's local coordinates system (bold) and thesphere. The world coordinate system, which never changes, coincides with the box'sinitial local.

Figure 4.18: Screenshotof relativePlacement.cppafter all transformationsfrom the scaling down havebeen executed.

Figure 4.19: Planning a head on a torso: (a) The plan (b) Drawn without isolating thescaling (c) After isolating the scaling.

Figure 4.20: Transitions of the modelview matrix stack.

Figure 4.21: Screenshotof rotatingHelix1.cpp.

Figure 4.22: Animationcontrol inrotatingHelix3.cpp.

Figure 4.23: Successivecycles in double buffering.

Figure 4.24: Screenshotof ballAndTorus.cpp.

Figure 4.25: The ball's axis of latitudinal rotation from its start position is L.

Figure 4.26: Screenshotfrom Experiment 4.21.

Figure 4.27: Screenshotof throwBall.cpp.

Figure 4.28: Ballbouncing off wall.

Figure 4.29: Screenshot of (a) clown1.cpp (b) clown2.cpp (c) clown3.cpp.

Figure 4.30: (a) Cone drawn by glutWireCone(base, height, slices, stacks) (b)Torus drawn by glutWireTorus(inRadius, outRadius, sides, rings). Note that the axesare depicted differently in each diagram.

Figure 4.31: Screenshotof floweringPlant.cpp inmid-bloom.

Figure 4.32: (a) Ball rolling down one plane (b) Ball rolling down two planes (c) Ballbouncing on a box (d) Ball traveling along a helix (e) Four segments opening from asquare into a straight line (f) Solar system with a sun, one planet and two moons (g)Pool table with one ball.

Figure 4.33: (a) The (conceptual) OpenGL camera's default pose (b) A (conceptual)point camera at the origin with film on the viewing plane of the frustum.

Figure 4.34: Camera pose determined by gluLookAt(eyex, eyey, eyez, centerx,centery, centerz, upx, upy, upz).

Figure 4.35: (a) gluLookAt(): the broken frustum is the original viewing frustum, theunbroken one is where it's translated by the gluLookAt() call, the box doesn't move. (b)glTranslatef(): the viewing frustum doesn't move, rather the box is translated by theglTranslatef() call.

Figure 4.36: Sectional diagrams of the (simulated) conguration of the eye and frustumfor various gluLookAt() calls in boxWithLookAt.cpp.

Figure 4.37: Screenshots from Experiment 4.28.

Figure 4.38: Taking thedot product:u·v = |u||v|cos θ .

Figure 4.39: (a)Splitting v intocomponents v1 and v2,parallel and perpendicularto u, respectively (b) v2 asthe “shadow” of v on aplane p perpendicular to u.

Figure 4.40: The camera is seen face-forward so that its back-plane p lies on the page.The line of sight los comes perpendicularly up from the page toward the reader. Thecomponents of the vector up, parallel and perpendicular to los, respectively, are up1 andup2 (the latter lying on the page).

Figure 4.41: Solution to Exercise 4.44(a).

Figure 4.42: Checkingthe solution toExercise 4.44(a).

Figure 4.43: Camera flying over balls.

Figure 4.44: Camerarotated on an imaginarysphere enclosing a teapot.

Figure 4.45: Relative movement of the camera and scene.

Figure 4.46: Restoring the camera to its default pose: broken arrows indicatemovements which applied take the camera to the next conguration in the sequence(a)-(d).

Figure 4.47: Screenshotfrom Experiment 4.30.

Figure 4.48: Viewing transformation equivalent to a sequence of modelingtransformations.

Figure 4.49: Applying a translation (1) and rotations (2)-(4) about the threecoordinate axes to bring the camera back to its default pose. The original line of sight isbold. The up direction is shown only at the end.

Figure 4.50: Solution to Example 4.6: the configuration of the camera given bygluLookAt(0.0, 0.0, 0.0, 1.0, 1.0, 0.0, -1.0, 1.0, 0.0) is at left; the line ofsight and up vectors are indicated by blue arrows; rotations are both annotated at thetop and indicated in the figures themselves by broken arrows, the result of each rotationbeing the next configuration.

Figure 4.51: Screenshot of spaceTravel.cpp.

Figure 4.52: Spacecraft diagrams.

Figure 4.53: Ball rollingtoward a box.

Figure 4.54: Screenshotof animateMan1.cpp.

Figure 4.55: Screenshotof animateMan1.cpp indevelop mode.

Figure 4.56: Screenshotof animateMan2.cpp.

Figure 4.57: Screenshotof ballAndTorus-Shadowed.cpp.

Figure 4.58: OpenGL's synthetic-camera pipeline (highly simplified!).

Figure 4.59: Screenshotfrom selection.cpp.

Figure 4.60: Name stack configurations: (a) Initial (b) When the red rectangle isdrawn (c) When the green rectangle is drawn.

Figure 4.61: Clicking P “hits” the aircraft because the latter intersects V’.

Figure 4.62: Screenshotof ballAndTorus-Picking.cpp momentsafter the ball has beenclicked.

Figure 4.63: Color coding.