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Transformations in 3D Space

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Abstract

Similar to transformations in 2D space discussed in Chap. 3, transformation operations can be applied to objects in 3D space. Those operations change the status of objects. Points of interest like vertices are those that undergo the transformation operations. For example, in order to rotate a tetrahedron that is composed of four triangular faces, only its four vertices need to be rotated. The basic 3D transformation operations include translation, rotation, scaling, reflection and shearing. Many publications handled such operations (e.g., Foley et al. 1995, Vince11, Ammeraal07). We will discuss each of these operations in the rest of this chapter.

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Notes

  1. 1.

    Note that the positive direction of the rotation about the \(x\)-axis in 3D space is the direction of rotation from the \(y\)-axis to the \(z\)-axis.

  2. 2.

    Note that the positive direction of the rotation about the \(y\)-axis in 3D space is the direction of rotation from the \(z\)-axis to the \(x\)-axis.

References

  • Ammeraal, L., and K. Zhang. 2007. Computer graphics for Java programmers, 2nd ed. New York: Wiley

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  • Foley, J.D., A. van Dam, S.K. Feiner, and J. Hughes. 1995. Computer graphics: principles and practice in C, 2nd ed. The systems programming series. Reading: Addison-Wesley

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  • Vince, J. 2011. Rotation transforms for computer graphics. Berlin: Springer.

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Author information

Authors and Affiliations

  1. Digital Media Engineering and Technology, German University in Cairo, Cairo, Egypt

    Rimon Elias

Authors
  1. Rimon Elias
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Correspondence to Rimon Elias .

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© 2014 Springer International Publishing Switzerland

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Cite this chapter

Elias, R. (2014). Transformations in 3D Space. In: Digital Media. Springer, Cham. https://doi.org/10.1007/978-3-319-05137-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-05137-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-05136-9

  • Online ISBN: 978-3-319-05137-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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