Cylinder
The generating curve of a cylinder is a line, parallel to the axis, at a distance R from the axis. The radial distance of a point is constant, and the height of the point is 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 cylinder
radius Radius of the cylinder
e2[3] Unit vector, in the v direction
e3[3] Normal to the plane
origin[3] Origin of the cylinder
radius Radius of the cylinder
Parameterization:
(x, y, z) = radius * [cos(u) * e1 + sin(u) * e2] +
v * e3 + origin
v * e3 + origin
Engineering Notes:
For the cylinder, cone, torus, and general surface of revolution, a local coordinate system is used that consists of three orthogonal unit vectors (e1, e2, and e3) and an origin. The curve lies in the plane of e1 and e3, and is rotated in the direction from e1 to e2. The u surface parameter determines the angle of rotation, and the v parameter determines the position of the point on the generating curve.