Example: Cylinder Data Format
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. The following illustration shows a cylinder.
Data format:
e1[3] | (dbl) | |
e2[3] | (dbl) | |
e3[3] | (dbl) | |
origin[3] | (dbl) | Origin of the local coordinate system |
R | (dbl) | The radius of the cylinder |
Parameterization:
(x, y, z) = R * [cos(u) * e1 + sin(u) * e2] + v * e3 + origin
For the cylinder, cone, torus, and the general surface of revolution, the system uses a local coordinate system consisting of three orthogonal unit vectors (e1, e2, and e3) and an origin. The curve lies in the plane of e1 and e3 and rotates 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.