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3D graphics eBook - Course Materials Repository

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Conversion between quaternions and Euler angles 33<br />

External links<br />

• Q60. How do I convert Euler rotation angles to a quaternion? [2] and related questions at The Matrix and<br />

Quaternions FAQ<br />

References<br />

[1] http:/ / www. euclideanspace. com/ maths/ geometry/ rotations/ conversions/ quaternionToEuler/<br />

[2] http:/ / www. j3d. org/ matrix_faq/ matrfaq_latest. html#Q60<br />

Cube mapping<br />

In computer <strong>graphics</strong>, cube mapping is a method of<br />

environment mapping that uses a six-sided cube as the<br />

map shape. The environment is projected onto the six<br />

faces of a cube and stored as six square textures, or<br />

unfolded into six regions of a single texture. The cube<br />

map is generated by first rendering the scene six times<br />

from a viewpoint, with the views defined by an<br />

orthogonal 90 degree view frustum representing each<br />

cube face. [1]<br />

In the majority of cases, cube mapping is preferred<br />

over the older method of sphere mapping because it<br />

eliminates many of the problems that are inherent in<br />

sphere mapping such as image distortion, viewpoint<br />

dependency, and computational efficiency. Also, cube<br />

mapping provides a much larger capacity to support<br />

real-time rendering of reflections relative to sphere<br />

mapping because the combination of inefficiency and<br />

viewpoint dependency severely limit the ability of<br />

sphere mapping to be applied when there is a<br />

consistently changing viewpoint.<br />

History<br />

The lower left image shows a scene with a viewpoint marked with a<br />

black dot. The upper image shows the net of the cube mapping as seen<br />

from that viewpoint, and the lower right image shows the cube<br />

superimposed on the original scene.<br />

Cube mapping was first proposed in 1986 by Ned Greene in his paper “Environment Mapping and Other<br />

Applications of World Projections” [2] , ten years after environment mapping was first put forward by Jim Blinn and<br />

Martin Newell. However, hardware limitations on the ability to access six texture images simultaneously made it<br />

infeasible to implement cube mapping without further technological developments. This problem was remedied in<br />

1999 with the release of the Nvidia GeForce 256. Nvidia touted cube mapping in hardware as “a breakthrough image<br />

quality feature of GeForce 256 that ... will allow developers to create accurate, real-time reflections. Accelerated in<br />

hardware, cube environment mapping will free up the creativity of developers to use reflections and specular lighting<br />

effects to create interesting, immersive environments.” [3] Today, cube mapping is still used in a variety of graphical<br />

applications as a favored method of environment mapping.

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