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
| Parameter | Type |
|---|---|
shape | number |
Returns
(thetaRad) => number