5.1.8 Lathe

The syntax of a lathe object is:

LATHE:
  lathe { [LATHE_SPLINE_TYPE] NUM_POINTS, POINT_LIST 
    [LATHE_MODIFIERS] }

LATHE_SPLINE_TYPE:
  linear_spline | quadratic_spline | cubic_spline | bezier_spline

LATHE_MODIFIERS:
  [sturm [BOOL]] | [UV_MAPPING] | [OBJECT_MODIFIERS]

See also:

• [pov:6.5.1.7]Lathe
• [pov:3.4.1]Lathe Object; See also for intro to splines

This describes an object obtained by rotating the area between the $y$-axes and the spline given by the NUM_POINTS many 2d-points in POINT_LIST around the $y$-axes.

Figure: Lathe objects with linear and with Bezier splines

    

For the spline type linear_spline we need NUM_POINTS$\geq 2$, and for the spline type quadratic_spline we need $n=$NUM_POINTS$\geq 3$, where from $P_k$ to $P_{k+1}$ we use the quadratic spline constructed for $P_{k-1},P_{k},P_{k+1}$. Thus the curve will start only at $P_1$ and end at $P_n$, and $P_0$ is just a control point.

For cubic_splines we need $n=$NUM_POINTS$\geq 4$, where from $P_k$ to $P_{k+1}$ we use the cubic spline constructed for $P_{k-1},P_{k},P_{k+1},P_{k+2}$. Thus the curve will start only at $P_1$ and end at $P_{n-1}$, and both $P_0$ and $P_n$ are just control points.

Finally for bezier_spline we need $4n=$NUM_POINTS, where we use the cubic Bezier curve through the points $P_{4n},P_{4n+1},P_{4n+2},P_{4n+3}$ from $P_{4n}$ to $P_{4n+3}=P_{4(n+1)}$. Thus only the points $P_0,P_3=P_4,\dots,P_{4n-1}$ will ly on the curve, the others are just control points.