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Computer Graphics Through OpenGL: From Theory to Experiments, Second Edition Chapter 6
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Figure 6.1: Screenshot of spaceTravel.cpp with a 100 x100 array of asteroids.
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Figure 6.2: (a) Projection of the asteroids and the frustum of spaceTravel.cpp onto the xz-plane. (b) Corresponding quadtree squares (the root square is bold) (c) The tree structure with children at each node drawn SW, NW, NE, SE from left to right; the nodes in the red circle are some of those pruned.
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Figure 6.3: Spacecraft carrying a viewing frustum "attached" to its front.
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Figure 6.4: An octree cube and one of its 8 octants.
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Figure 6.5: Two rooms off a hall. A dashed bounding box is shown containing the first object.
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Figure 6.6: Screenshot of occlusion.cpp.
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Figure 6.7: Video camera and spacecraft.
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Figure 6.8: (a) Orienting an object in space with respect to fixed axes – the fixed reference orientation of the L is shown in bold (b) Orientation of an aircraft with respect to local axes “carried” by it.
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Figure 6.9: Screenshot of eulerAngles.cpp.
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Figure 6.10: The bold blue start orientation is given by the Euler angle tuple (0, 0, 0) and the bold blue destination one by either (0, 90, 0) or (-90, 90, 90). Intermediate orientations (green) in the linear interpolation between (0, 0, 0) and (0, 90, 0) all lie on the xz-plane, while those (red) between (0, 0, 0) and (-90, 90, 90) arc above it.
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Figure 6.11: Screenshot of interpolateEuler- Angles.cpp.
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Figure 6.12: The vector f(X) is obtained by rotating X about the line l.
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Figure 6.13: The unit sphere S 3 in R 4 with a radial line l, representing a rotation of R 3, passing through a pair of antipodal points.
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Figure 6.14: (a) Conceptual plan to use quaternion space to interpolate in orientation space (numbers in parentheses indicate steps) (b) The geodesic path from q 1 to q 2 on S 3 (c) Slerping from q 1 to q 2.
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Figure 6.15: Changing the orientation from AB to AB’ is inherently ambiguous.
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Figure 6.16: Screenshot of quaternionAnimation-.cpp.
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