Computer Graphics Through
OpenGL: From Theory to
Experiments, Second Edition
Chapter 4
Figure 4.1: Screenshot of
box.cpp.
Figure 4.2: Translation: glTranslatef(p, q, r).
Figure 4.3: Translating into the viewing frustum.
Figure 4.4: Screenshot of
Experiment 4.3.
Figure 4.5: Scaling:
glScalef(u, v, w).
Figure 4.6: Screenshot of
initial configuration of
Experiment 4.4.
Figure 4.7: Reflection in
the yz-plane.
Figure 4.8: Screenshots of Experiment 4.5: (a) before scaling (b) after.
Figure 4.9: Screenshot
for Experiment 4.6.
Figure 4.10: Turning
along a cylinder.
Figure 4.11: Rotation: glRotatef(A, p, q, r). The point P is rotated according to
the 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 system
is fixed.
Figure 4.17: Transitions of the box, the box's local coordinates system (bold) and the
sphere. The world coordinate system, which never changes, coincides with the box's
initial local.
Figure 4.18: Screenshot
of relativePlacement.cpp
after all transformations
from the scaling down have
been executed.
Figure 4.19: Planning a head on a torso: (a) The plan (b) Drawn without isolating the
scaling (c) After isolating the scaling.
Figure 4.20: Transitions of the modelview matrix stack.
Figure 4.21: Screenshot
of rotatingHelix1.cpp.
Figure 4.22: Animation
control in
rotatingHelix3.cpp.
Figure 4.23: Successive
cycles in double buffering.
Figure 4.24: Screenshot
of ballAndTorus.cpp.
Figure 4.25: The ball's axis of latitudinal rotation from its start position is L.
Figure 4.26: Screenshot
from Experiment 4.21.
Figure 4.27: Screenshot
of throwBall.cpp.
Figure 4.28: Ball
bouncing 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 axes
are depicted differently in each diagram.
Figure 4.31: Screenshot
of floweringPlant.cpp in
mid-bloom.
Figure 4.32: (a) Ball rolling down one plane (b) Ball rolling down two planes (c) Ball
bouncing on a box (d) Ball traveling along a helix (e) Four segments opening from a
square 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, the
unbroken 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 the
glTranslatef() call.
Figure 4.36: Sectional diagrams of the (simulated) conguration of the eye and frustum
for various gluLookAt() calls in boxWithLookAt.cpp.
Figure 4.37: Screenshots from Experiment 4.28.
Figure 4.38: Taking the
dot product:
u·v = |u||v|cos θ .
Figure 4.39: (a)
Splitting v into
components v1 and v2,
parallel and perpendicular
to u, respectively (b) v2 as
the “shadow” of v on a
plane 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. The
components of the vector up, parallel and perpendicular to los, respectively, are up1 and
up2 (the latter lying on the page).
Figure 4.41: Solution to Exercise 4.44(a).
Figure 4.42: Checking
the solution to
Exercise 4.44(a).
Figure 4.43: Camera flying over balls.
Figure 4.44: Camera
rotated on an imaginary
sphere 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 indicate
movements which applied take the camera to the next conguration in the sequence
(a)-(d).
Figure 4.47: Screenshot
from Experiment 4.30.
Figure 4.48: Viewing transformation equivalent to a sequence of modeling
transformations.
Figure 4.49: Applying a translation (1) and rotations (2)-(4) about the three
coordinate axes to bring the camera back to its default pose. The original line of sight is
bold. The up direction is shown only at the end.
Figure 4.50: Solution to Example 4.6: the configuration of the camera given by
gluLookAt(0.0, 0.0, 0.0, 1.0, 1.0, 0.0, -1.0, 1.0, 0.0) is at left; the line of
sight and up vectors are indicated by blue arrows; rotations are both annotated at the
top and indicated in the figures themselves by broken arrows, the result of each rotation
being the next configuration.
Figure 4.51: Screenshot of spaceTravel.cpp.
Figure 4.52: Spacecraft diagrams.
Figure 4.53: Ball rolling
toward a box.
Figure 4.54: Screenshot
of animateMan1.cpp.
Figure 4.55: Screenshot
of animateMan1.cpp in
develop mode.
Figure 4.56: Screenshot
of animateMan2.cpp.
Figure 4.57: Screenshot
of ballAndTorusShadowed.cpp.
Figure 4.58: OpenGL's synthetic-camera pipeline (highly simplified!).
Figure 4.59: Screenshot
from selection.cpp.
Figure 4.60: Name stack configurations: (a) Initial (b) When the red rectangle is
drawn (c) When the green rectangle is drawn.
Figure 4.61: Clicking P “hits” the aircraft because the latter intersects V’.
Figure 4.62: Screenshot
of ballAndTorusPicking.cpp moments
after the ball has been
clicked.
Figure 4.63: Color coding.