plot::Translate2d – translation of 2D objects

plot::Translate3d – translation of 3D objects

shifts a 2D object by units along the -axis and units along the -axis.

shifts a 3D object.

Calls:

plot::Translate2d([dx, dy], obj1, <obj2, ...>, <a = amin .. amax>, Options)

plot::Translate3d([dx, dy, dz], obj1, <obj2, ...>, <a = amin .. amax>, Options)

Parameters:

dx, dy, dz:	the components of the shift vector: numerical real values or arithmetical expressions of the animation parameter a. dx, dy, dz are equivalent to the attribute Shift.
obj1, obj2, ...:	arbitrary plot objects of the appropriate dimension

Details:

Translate objects can translate several graphical objects simultaneously. Plotting the translate object renders all graphical objects inside.
Transformation objects can be used inside translation objects. If they are animated, the animations run simultaneously.
Animated translate objects are rather “cheap” concerning computing and storing costs. For more complex graphical objects, it is more efficient to use an animated translate object than to redefine the object for each frame.
The function op allows to extract the graphical objects inside a translate object.

Example 1

We use an animated translation object to shift a vector to the tip of another vector:

A1 := plot::Arrow2d([0, 0], [2, 1], Color = RGB::Red):
A2 := plot::Arrow2d([0, 0], [2, 3], Color = RGB::Green):
plot(A1, plot::Translate2d([2*a, a], A2, a = 0..1,
                           TimeRange = 0..4),
     plot::Arrow2d([0, 0], [4, 4], Color = RGB::Blue,
                   VisibleFromTo = 4..6),
     Header = "how to add 2 vectors"):

MuPAD graphics

delete A1, A2:

Example 2

Note that plot::Translate2d and plot::Translate3d do not actually change the objects translated, so it is possible to use the same object in different places in the same plot. As an example, we show an intuitive way of constructing the Sierpinski carpet, a flat version of the Menger sponge.

The Sierpinski carpet is a fractal with the general shape of a square and the property that the following operation maps it onto itself: Take eight copies, scale them by , and arrange them in a square with the middle left unfilled. Now, this can be directly written in MuPAD code:

Carpet := proc(iter)
local square;
begin
if iter <= 1 then
    return(plot::Polygon2d([[0,0], [0,1], [1,1], [1,0]],
                           Closed, Filled, FillPattern = Solid,
                           FillColor = [0.2234, 0.4563, 0.4568],
                           LinesVisible, LineColor = RGB::White,
                           Scaling = Constrained, Axes = None));
else
    square := plot::Scale2d([1/3, 1/3], Carpet(iter-1));
    return(plot::Group2d(
                 plot::Translate2d([ 0,   0], square),
                 plot::Translate2d([ 0, 1/3], square),
                 plot::Translate2d([ 0, 2/3], square),
                 plot::Translate2d([1/3,   0], square),
               //   plot::Translate2d([1/3, 1/3], square),
                 plot::Translate2d([1/3, 2/3], square),
                 plot::Translate2d([2/3,   0], square),
                 plot::Translate2d([2/3, 1/3], square),
                 plot::Translate2d([2/3, 2/3], square)));
end_if;
end_proc:

plot(Carpet(3))

MuPAD graphics

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