# 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

Contributed by:
Utkarsh Bajaj (Junior Research Affiliate in the Wolfram Physics Project)

ResourceFunction["RelativisticInertialDeformedRegion"][ gives the deformed visual shape of | |

ResourceFunction["RelativisticInertialDeformedRegion"][ ϕ,tObs,accuracyGoal]gives the deformed visual shape when ϕ. | |

ResourceFunction["RelativisticInertialDeformedRegion"][ ϕ,tObs,accuracyGoal]gives the deformed visual shape when |

The result will be a DiscretizedRegion.

The input *region* is the actual shape as seen in the moving frame of reference.

The value of *accuracyGoal* can be set between 0 and ∞. High accuracy goals might not work for some objects.

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:

In[1]:= |

Out[1]= |

If we use Graphics3D with visible axes, we can see that the sphere is only stretched or contracted in the *x* direction:

In[2]:= |

Move the sphere diagonally up and to the right, with a speed of 0.7:

In[3]:= |

Out[3]= |

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:

In[4]:= |

Out[4]= |

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:

In[5]:= |

Out[5]= |

Simulate the visual appearance of different objects when traveling downwards with a speed of 0.95:

In[6]:= |

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:

In[7]:= |

Show an icosahedron traveling with different speeds, observed at time 0:

In[8]:= |

In[9]:= |

We can also find the apparent shape of an implicit region:

In[10]:= |

Show the shape of this region traveling upwards with a velocity of 0.8 at different times:

In[11]:= |

Out[11]= |

Show a torus moving at different speeds. Note that the centroid approaches the left edge of the torus as the speed increases:

In[12]:= |

Out[12]= |

Plot the apparent length of a horizontal line versus time, when moving with a speed of 0.9 along the positive *x*-axis:

In[13]:= |

Out[13]= |

Use a vertical line:

In[14]:= |

Out[14]= |

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.

- 1.0.0 – 28 December 2020

This work is licensed under a Creative Commons Attribution 4.0 International License