API Reference / radialScale · function

Function: radialScale()

function radialScale(shape): (thetaRad) => number;

One-parameter family of azimuthal radial scales r(theta), theta the angle from the aim in radians. Landmarks: shape -1 is gnomonic (tan theta, the rectilinear lens), -0.5 stereographic, 0 equidistant (the fisheye lens), +0.5 equal-area, +1 orthographic (sin theta, the exterior view of a glass sphere). The family is r = k tan(theta / k) with k = -1/shape on the negative side and r = k sin(theta / k) with k = 1/shape on the positive side; both limits at shape 0 are r = theta, so the family is continuous in shape. A continuous camera pull-back (a lens view widening into the exterior sphere view) is one pass of shape from -1 or 0 up to +1.

On the negative side the scale diverges at theta = k pi/2 (the gnomonic horizon); past it the function returns Infinity. On the positive side the scale folds past theta = k pi/2: for orthographic the far hemisphere maps back into the same disc, which is the fold a see-through sphere shows.

Parameters

ParameterType
shapenumber

Returns

(thetaRad) => number

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