Cone
The generating curve of a cone is a line at an angle alpha to the axis of revolution that intersects the axis at the origin. The v parameter is the height of the point along the axis, and the radial distance of the point is v * tan(alpha).
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 cone
alpha Angle between the axis of the cone
and the generating line
e2[3] Unit vector, in the v direction
e3[3] Normal to the plane
origin[3] Origin of the cone
alpha Angle between the axis of the cone
and the generating line
Parameterization:
(x, y, z) = v * tan(alpha) * [cos(u) * e1 +
sin(u) * e2] + v * e3 + origin
sin(u) * e2] + v * e3 + origin