Toroidal Coordinates

Three linked views of the standard toroidal coordinate system around a circular focal ring.

Coordinates Coordinate system Ring radius Eta min Eta max Eta count Alpha count Beta count

Second Space Operation B offset X B offset Y B offset Z B axis tilt

Detail Curve samples Surface samples Surface levels Opacity Surface wire overlay Ray contour shading Ray free march

Families Eta shells Alpha family Beta family Foci / axes

Angular Basis Mode Shear k Alpha vector Beta twist

Slice Plane Offset X Offset Y Offset Z Pitch Yaw Roll Slice size Slice thickness Eta spacing Alpha spacing Beta spacing

Camera Projection Auto B rotation Auto surface phase

Left-drag rotates, wheel zooms, and right/middle-drag pans. The 3D panes share one camera; the slice pane keeps its own.