Example: Cone Data Format
The generating curve of a cone is a line at an angle α to the axis of revolution which 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 (α). The following illustration shows a cone.
Data format:
e1[3] | (dbl) | |
e2[3] | (dbl) | |
e3[3] | (dbl) | |
origin[3] | (dbl) | Origin of the local coordinate system |
a | (dbl) | The angle between the axis of the cone and the generating line |
Parameterization:
(x, y, z) = v * tan(α) * [cos(u) * e1 + sin(u) * e2] + v * e3 + origin