# Wonky Rectilinear Treats by Jonathan Polkest

jonathanpolkest on July 28, 2011

The term "isometric" comes from the Greek for "equal measure", reflecting that the scale along each axis of the projection is the same (unlike some other forms of graphical projection). An isometric view of an object can be obtained by choosing the viewing direction in a way that the angles between the projection of the x, y, and z axes are all the same, or 120°. For example when taking a cube, this is done by first looking straight towards one face. Next the cube is rotated ±45° about the vertical axis, followed by a rotation of approximately ±35.264° (precisely arcsin(tan 30°) or arctan(sin 45°) ) about the horizontal axis. Note that with the cube (see image) the perimeter of the 2D drawing is a perfect regular hexagon: all the black lines are of equal length and all the cube's faces are the same area. In a similar way an isometric view can be obtained for example in a 3D scene editor. Starting with the camera aligned parallel to the floor and aligned to the coordinate axes, it is first rotated downwards around the horizontal axes by about 35.264° as above, and then rotated ±45° around the vertical axis. Another way in which isometric projection can be visualized is by considering a view within a cubical room starting in an upper corner and looking towards the opposite, lower corner. The x-axis extends diagonally down and right, the y-axis extends diagonally down and left, and the z-axis is straight up. Depth is also shown by height on the image. Lines drawn along the axes are at 120° to one another. The term "isometric" is often mistakenly used to refer to axonometric projections in general. (There are three types of axonometric projections: isometric, dimetric and trimetric.

David Wilson on July 31, 2011

Hmm.. not really isometric, more of a 'wonky rectilinear'

jonathanpolkest on August 1, 2011

I prefer your suggested title, the ironic idea of dispensing treats from such a device could be considered wonky, clunky or even dare I say, dodgy..

David Wilson on August 4, 2011

:-)

Photo taken in Victoria Embankment Gardens, Victoria Embankment, London, Westminster, Greater London WC2N 6PB, UK

## Photo details

• Uploaded on July 28, 2011