General Surface of Revolution
Figure 238. General Surface of Revolution
A general surface of revolution is created by rotating a curve entity, usually a spline, around an axis. The curve is evaluated at the normalized parameter v, and the resulting point is rotated around the axis through an angle u. The surface of revolution data structure consists of a local coordinate system and a curve structure.
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 surface of revolution
curve Generating curve
e2[3] Unit vector, in the v direction
e3[3] Normal to the plane
origin[3] Origin of the surface of revolution
curve Generating curve
Parameterization:
curve(v) = (c1, c2, c3) is a point on the curve.
(x, y, z) = [c1 * cos(u) - c2 * sin(u)] * e1 +
[c1 * sin(u) + c2 * cos(u)] * e2 +
c3 * e3 + origin
(x, y, z) = [c1 * cos(u) - c2 * sin(u)] * e1 +
[c1 * sin(u) + c2 * cos(u)] * e2 +
c3 * e3 + origin