Editing Scientific visualization (section)

=== In mathematics ===

{{main|Mathematical visualization}}

Scientific visualization of mathematical structures has been undertaken for purposes of building intuition and for aiding the forming of mental models.<ref>[[Andrew J. Hanson]], [[Tamara Munzner]], George Francis: ''Interactive methods for visualizable geometry'', Computer, vol.&nbsp;27, no.&nbsp;7, pp.&nbsp;73–83 ([https://ieeexplore.ieee.org/document/299415/ abstract])</ref>

[[File:Domain coloring x2-1 x-2-i x-2-i d x2+2+2i.xcf|120px|right|thumb|[[Domain coloring]] of 
{{math|''f''(''x'') {{=}} {{sfrac|(''x''<sup>2</sup>−1)(''x''−2−''i'')<sup>2</sup>|''x''<sup>2</sup>+2+2''i''}}}}]]

Higher-dimensional objects can be visualized in form of projections (views) in lower dimensions. In particular, 4-dimensional objects are visualized by means of projection in three dimensions. The lower-dimensional projections of higher-dimensional objects can be used for purposes of virtual object manipulation, allowing 3D objects to be manipulated by operations performed in 2D,<ref>[[Andrew J. Hanson]]: ''Constrained 3D navigation with 2D controller'', Visualization '97., Proceedings, 24 October 1997, pp.&nbsp;175-182 ([https://ieeexplore.ieee.org/document/663876/ abstract])</ref> and 4D objects by interactions performed in 3D.<ref>Hui Zhang, [[Andrew J. Hanson]]: ''Shadow-Driven 4D Haptic Visualization'', IEEE Transactions on Visualization and Computer Graphics, vol.&nbsp;13, no.&nbsp;6, pp.&nbsp;1688-1695 ([https://ieeexplore.ieee.org/document/4376203/ abstract])</ref>

In [[complex analysis]], functions of the complex plane are inherently 4-dimensional, but there is no natural geometric projection into lower dimensional visual representations. Instead, colour vision is exploited to capture dimensional information using techniques such as [[domain coloring]].