This problem is intended to follow Min and Max Regular Tetrahedral Shadows.
Now let's imagine an opaque irregular tetrahedron, having edges of somewhat random lengths.
This tetrahedron may rotate along any axis, and as it does the shape and size of the shadow cast onto the ground changes.
Sometimes the changes can be quite dramatic, if the tetrahedron is highly irregular.
Input data will contain the number of testcases T in the first line.
The following T lines will each contain 12 space-separated decimal values corresponding to xyz
coordinates of the vertices of a tetrahedron, given in the format x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4.
Answer
Should be a string of space-separated value pairs corresponding to the minimum and maximum possible areas of the shadow cast by the given tetrahedron.
Round all answers to the nearest integer.
Example
In this example each line with test-case is further sub-split into four lines (all except first indented) to simplify human reading.
To feed these data to your program you may need remove these extra line breaks (depending on your chosen language and input method).
input data:
124.505471 -169.257075 362.025425
191.150081 -202.822632 395.169294
117.056519 -223.908481 422.228445
149.15761 -98.581877 484.601749
655.742148 -191.036593 -846.572974
711.090649 -223.87769 -796.326856
643.486942 -121.682616 -721.403079
776.273121 -114.705966 -863.113431
answer:
2727 5863 3983 10283