Understanding Ray Casting and Isovists

 Ray Casting and Isovists

The Science Behind Isovists: A Short History

Although isovists are considered to have been first set in theory by Benedikt in 1979 [1] (a first mention of them was made by the same author in 1977 [2]), their first appearance in scientific litterature was a paper by Tandy [3], itself based on writings from on AC Hardy [4]. This concept sprouted from JJ Gibson’s work [5] on “optic arrays”. Benedikt and Burnham [6] give a good explanation of the difference between optic rays and isovists :

Imagine a rectangle (representing a room) and the space within it. Draw a straight line between two points on the rectangle; draw another, and another, until the space of the rectangle is effectively filled with criss-crossing lines between all pairs of points. Now chose an point within the rectangle and you find that a large number of lines pass through that point, one of which is shared with another different set of lines passing through a point nearby. If we consider these lines to represent light rays (i.e., photon streams) of varying wavelength and intensity scattered and bounced by the edges of the rectagle (i.e., the walls of the room), then you have an optic array – a set of rays that pass through the point of interest.

But where does the otic ray start and end? Is a ray that happens to pass through our point the same ray that it was before it bounced off the wall? If it is, then almost every ray in the room qualifies as belonging to our optic array, as it would eventually pass through our point. Clearly this isn’t going to work. The solution lies in concidering a ray only after its “last bounce”, that is, in concidering only the set of lines – rays – joining our point to the nearest light-scattering surface in every direction. Now, the isovist is simply this optic array, with wavelength and intensity information omitted. In other words,

To every bearing (omega, phi) from a point of observation x in the world there corresponds a distance l, from the point to the nearest surface such that we have a unique ordered set

Several equations derived from isovists and isovist fields (that is, when caculating the isovist for each point in space), mainly from it’s perimeter and area, which an be discretized. We can produce a number of morphological indicators from isovists, including :

  • Mean Depth
  • Compactness fields
  • Occlusivity, occlusivity fields
  • Visible Perimeter Fields

Isovist Moments can be derived into three types :

M1 represents represents the derivation from the mean of the perimeter’s distance to x.
M2 represented the derivation from the variance of the perimeter’s distance to x.
M3 represents the derivation from the skewness of the perimeter’s distance to x. This last formulae can be used to find areas which can see well but remain hidden.

[1] ML Benedikt, 1979, “To Take Hold of Space : Isovists and Isovist Fields”, Environment and Planning B, vol 6, pp. 46 – 65
[2] ML Benedikt, 1977, “Path-dependence and position-dependence in isovist fields”, research report for the Council of Advanced Transportation Studies, University of Texas Austin, Austin, Texas.
Tandy, C. R. V. (1967). The isovist method of landscape survey. Methods of Landscape Analysis. London, Landscape Research Group, 9-10.
[4] AC Hardy, University of Newcastle, unpublished
[5] JJ Gibson, 1966, The Ecological Approach to Visual Perception, Psychology Press Classic Editions
Benedikt, M. L., & Burnham, C. A. (1985). Perceiving architectural space: from optic arrays to isovists. Persistence and change, 103-114.

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