Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Compute the apparent visual shape of an object or region traveling with constant velocity
gives the deformed visual shape of region, intially positioned at the origin,traveling at speed along the positive x-axis, at time tObs and with an accuracy of accuracyGoal.
gives the deformed visual shape when region is traveling in the direction defined by spherical coordinates θ and ϕ.
gives the deformed visual shape when region is intially positioned at vec.
Compute the apparent shape of a sphere with radius 2 moving with speed 0.9 in the positive x direction, as observed at different times:
If we use Graphics3D with visible axes, we can see that the sphere is only stretched or contracted in the x direction:
Move the sphere diagonally up and to the right, with a speed of 0.7:
Compute the shape of a sphere centered at (2,2,2) in the moving reference system and moving with a speed of 0.5 in the positive x direction:
Show the observed shape of a cone initially positioned at (1,1,1), moving at a speed of 0.9 in the positive x direction:
Simulate the visual appearance of different objects when traveling downwards with a speed of 0.95:
The shape of a vertical line at different times when moving in the x direction is a hyperbola, which degenerates to its asymptotes at time 0:
Show an icosahedron traveling with different speeds, observed at time 0:
We can also find the apparent shape of an implicit region:
Show the shape of this region traveling upwards with a velocity of 0.8 at different times:
Show a torus moving at different speeds. Note that the centroid approaches the left edge of the torus as the speed increases:
Plot the apparent length of a horizontal line versus time, when moving with a speed of 0.9 along the positive x-axis:
Use a vertical line:
For some objects a higher accuracy goal may not work. For example, setting an accuracyGoal above 400 for the Wolfram Spikey leads to Mathematica running the code forever.
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