Torus
The generating curve of a torus is an arc of radius R2 with its center at a distance R1 from the origin. The starting point of the generating arc is located at a distance R1 + R2 from the origin, in the direction of the first vector of the local coordinate system. The radial distance of a point on the torus is R1 + R2 * cos(v), and the height of the point along the axis of revolution is R2 * sin(v).
Data Format:
e1[3] Unit vector, in the u direction
e2[3] Unit vector, in the v direction
e3[3] Normal to the plane
origin[3] Origin of the torus
radius1 Distance from the center of the
generating arc to the axis of
revolution
radius2 Radius of the generating arc
e2[3] Unit vector, in the v direction
e3[3] Normal to the plane
origin[3] Origin of the torus
radius1 Distance from the center of the
generating arc to the axis of
revolution
radius2 Radius of the generating arc
Parameterization:
(x, y, z) = (R1 + R2 * cos(v)) * [cos(u) * e1 +
sin(u) * e2] + R2 * sin(v) * e3 +
origin
sin(u) * e2] + R2 * sin(v) * e3 +
origin