Affine linear transformation of 3D objects
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a = amin .. amax>,
plot::Transform3d(b, A, objects) with a vector b and
a matrix A applies the affine linear transformation to
The transformation matrix
A may be specified
by a list of lists, with the sublists representing the rows:
[[A1, 1, A1, 2,
…], [A2, 1, A2, 2,
A plain list
[A1, 1, A1,
2, …, A3, 2, A3,
3] represents the matrix row by row.
Transform objects can transform several graphical objects simultaneously. Plotting the transform object renders all graphical objects inside.
Transformed objects have a tendency to overestimate their
In such cases, specify a suitable
Transformation objects can be used inside transformation objects. If they are animated, the animations run simultaneously.
Animated transform objects are rather “cheap” concerning computing and storing costs. For more complex graphical objects, it is more efficient to use an animated transform object than to redefine the object for each frame.
to extract the graphical objects inside a transformation object.
|influence of objects on the |
|the number of frames in an animation|
|the name of a plot object (for browser and legend)|
|end value of the animation parameter|
|name of the animation parameter|
|initial value of the animation parameter|
|range of the animation parameter|
|end time of the animation|
|start time of the animation|
|the real time span of an animation|
For some applications, it is very popular to plot a function
in 3D together with a projection of its contour lines onto the lower
or upper bounding plane. MuPAD® has no direct option for this,
plot::Transform3d, it is possible to achieve
the same effect. Suppose that you have the function under consideration
f := plot::Function3d(sin(x*y)+cos(x^2-y), x=-3..3, y=-3..3, Submesh=[1,1]):
plot(plot::modify(f, ZContours = [Automatic, 10]))
To only get contour lines, change a few more parameters: switch
off the surface and the parameter lines. Then, add height coloring
to the lines and use
plot::Transform3d to project them
onto the plane z = - 2.5.
Finally, plot these lines together with the original function:
plot(f, plot::Transform3d([0, 0, -2.5], // shift vector [1, 0, 0, // transformation matrix 0, 1, 0, 0, 0, 0], plot::modify(f, Filled = FALSE, XLinesVisible = FALSE, YLinesVisible = FALSE, ZContours = [Automatic, 10], LineColorFunction = // height coloring ((x, y, z) -> [(z+2)/4, 0, (2-z)/4]))))
The 3D transformation matrix: a 3×3 matrix,
a 3×3 array, a list
of 3 lists, or a plain list with 9 entries. The entries must be numerical
values or arithmetical
expressions of the animation paramater
Animation parameter, specified as