plot::Sweep – sweep surface from the deformation of a 3D curve

$plot::Sweep([x_1(u), y_1(u), z_1(u)], u = `u_{min}`..`u_{max}`)$ creates the surface swept out by the (linear) deformation of the parameterized curve to its projection to the --plane.

$plot::Sweep([x_1(u), y_1(u), z_1(u)], [x_2(u), y_2(u), z_2(u)], u = `u_{min}`..`u_{max}`)$ creates the surface swept out by the (linear) deformation of the parameterized curve to the parameterized curve .

→ Examples

Calls:

plot::Sweep([x1, y1, z1], <Ground = g>, u = $`u_{min}`$ .. $`u_{max}`$ , <a = amin .. amax>, Options)

plot::Sweep(A1, <Ground = g>, u = $`u_{min}`$ .. $`u_{max}`$ , <a = amin .. amax>, Options)

plot::Sweep(C1, <Ground = g>, Options)

plot::Sweep([x1, y1, z1], [x2, y2, z2], u = $`u_{min}`$ .. $`u_{max}`$ , <a = amin .. amax>, Options)

plot::Sweep(A1, A2, u = $`u_{min}`$ .. $`u_{max}`$ , <a = amin .. amax>, Options)

plot::Sweep(C1, C2, Options)

Parameters:

x1, y1, z1:	the parametrization of the initial 3D curve: real-valued expressions in u (and possibly the animation parameter). x1, y1, z1 are equivalent to the attributes XFunction1, YFunction1, ZFunction1.
x2, y2, z2:	the parametrization of the “target curve”: real-valued expressions in u (and possibly the animation parameter). x2, y2, z2 are equivalent to the attributes XFunction2, YFunction2, ZFunction2.
u:	the curve parameter: an identifier or an indexed identifier. u is equivalent to the attribute UName.
$`u_{min}`$ , $`u_{max}`$ :	real-valued expressions (possibly in the animation parameter). $`u_{min}`$ , $`u_{max}`$ are equivalent to the attributes UMin, UMax.
g:	real-valued expression (possibly in the animation parameter). g is equivalent to the attribute Ground.
A1, A2:	matrices of category Cat::Matrix with three entries that provide the parametrizations x1, y1, z1 and x2, y2, z2, respectively.
C1, C2:	curves of type plot::Curve3d. C1 provides the “initial curve” , C2 provides the “target curve” .

Details:

plot::Sweep creates the parametrized surface

with the two surface parameters (ranging from $`u_{min}`$ to $`u_{max}`$ ) and (ranging from to ). This is the linear deformation of the curve defining one border of the surface to the curve defining the other border of the surface.
If no “target curve” is specified, the projection , , of the “source curve” to the --plane with constant value is used. The value is set by the attribute Ground = g. The default value is g = 0.

When a target curve is specified, the Ground attribute does not have any effect.
If the curves are specified by objects of type plot::Curve3d, the graphical attributes of the object created by plot::Sweep are copied from C1. The parametrization of C2 is automatically rewritten in terms of the curve parameter used in the definition of C1. This, however, will only work if the parametrization of C2 is defined by symbolic expressions.