disc

The disc variation is based on polar coordinates, where points are specified by a distance ρ and an angle θ (see polar). The basic idea is simple: it just switches ρ and θ (after scaling by π to make things work nicely). This converts wedges centered at the origin to half-rings and vice versa as shown below. The images on the left side are before and on the right side after disc is applied.

The sides of the triangles across from the center point get converted to arcs by disc because the corners are 1 unit from the origin but the middles are closer, so ρ varies from 1 to somewhat less along the sides. More importantly, the result seems sideways; the polar coordinate angle θ is normally measured from the positive x axis towards the positive y axis. In JWildfire, positive y is down so θ would be measured clockwise from the positive x axis (going right from the origin). However, disc swaps the x and y axes, so θ is instead measured counter-clockwise from the positive y axis (going down from the origin).

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