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tetravolume_2.py
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"""
3-13-2024 - DAF heavily modified from https://github.com/4dsolutions/MartianMath/blob/master/tetravolume.py
"""
from math import sqrt, pi, e
from qrays import Qvector, Vector
import sys
# Constants for volume calculations
S3 = sqrt(9/8)
ROOT2 = sqrt(2)
ROOT5 = sqrt(5)
class Triangle:
"""
Represents a triangle, facilitating the calculation of areas in both IVM and XYZ coordinate systems.
Assumes an equilateral triangle for simplification.
"""
def __init__(self, a, b, c):
self.a = a
self.b = b
self.c = c
def ivm_area(self):
"""Calculates area using the IVM system."""
s = (self.a + self.b + self.c) / 2
return sqrt(s * (s - self.a) * (s - self.b) * (s - self.c))
def xyz_area(self):
"""Calculates area using the XYZ system."""
return self.ivm_area() / S3
def make_tri(v0, v1):
"""Generates a triangle from two vectors and calculates its areas."""
tri = Triangle(v0.length(), v1.length(), (v1 - v0).length())
return tri.ivm_area(), tri.xyz_area()
class Tetrahedron:
"""
Represents a tetrahedron, facilitating the calculation of volumes in both IVM and XYZ coordinate systems.
"""
def __init__(self, a, b, c, d, e, f):
self.edges = [a, b, c, d, e, f]
self.edges_squared = [edge ** 2 for edge in self.edges]
print(f"Initialized Tetrahedron with edges: {', '.join(map(str, self.edges))}")
def ivm_volume(self):
"""Calculates volume using the IVM system."""
ivmvol = sqrt((self._addopen() - self._addclosed() - self._addopposite()) / 2)
print(f"IVM Volume Calculation:")
print(f" Sum of open products: {self._addopen():.6f}")
print(f" Sum of closed products: {self._addclosed():.6f}")
print(f" Sum of opposite products: {self._addopposite():.6f}")
print(f" IVM Volume: {ivmvol:.6f}")
return ivmvol
def xyz_volume(self):
"""Calculates volume using the XYZ system."""
xyzvol = self.ivm_volume() / S3
print(f"XYZ Volume Calculation:")
print(f" XYZ Volume: {xyzvol:.6f}")
return xyzvol
def _addopen(self):
"""Calculates the sum of open products for volume calculation."""
sumval = sum(self.edges_squared[i] * self.edges_squared[j] * self.edges_squared[k]
for i in range(6) for j in range(i + 1, 6) for k in range(j + 1, 6))
print(f"Sum of open products: {sumval}")
return sumval
def _addclosed(self):
"""Calculates the sum of closed products for volume calculation."""
sumval = sum(self.edges_squared[i] * self.edges_squared[(i + 1) % 6] * self.edges_squared[(i + 2) % 6]
for i in range(0, 6, 2))
print(f"Sum of closed products: {sumval}")
return sumval
def _addopposite(self):
"""Calculates the sum of opposite products for volume calculation."""
sumval = sum(self.edges_squared[i] * self.edges_squared[i + 3] * (self.edges_squared[i] + self.edges_squared[i + 3])
for i in range(3))
print(f"Sum of opposite products: {sumval}")
return sumval
def make_tet(v0, v1, v2):
"""Generates a tetrahedron from three vectors and calculates its volumes."""
tet = Tetrahedron(v0.length(), v1.length(), v2.length(),
(v0 - v1).length(), (v1 - v2).length(), (v2 - v0).length())
print(f"Making tetrahedron with vertices: {v0}, {v1}, {v2}")
return tet.ivm_volume(), tet.xyz_volume()
PHI = (1 + ROOT5) / 2.0
# Simplified constants
R = 0.5
D = 1.0
ROOT3 = sqrt(3)
import unittest
class Test_Tetrahedron(unittest.TestCase):
# Unit tests for Tetrahedron and Triangle classes
def test_unit_volume(self):
"""Tests unit volume calculation."""
tet = Tetrahedron(D, D, D, D, D, D)
self.assertAlmostEqual(tet.ivm_volume(), 1, msg="Volume not 1")
# Additional tests omitted for brevity
def command_line():
"""Processes command-line arguments to calculate tetrahedron volumes."""
args = sys.argv[1:]
if len(args) == 6:
try:
args = [float(x) for x in args]
t = Tetrahedron(*args)
print(f"IVM Volume (from command line): {t.ivm_volume():.6f}")
print(f"XYZ Volume (from command line): {t.xyz_volume():.6f}")
except ValueError:
print("Error: All arguments must be numbers.")
else:
print("Usage: python tetravolume.py <a> <b> <c> <d> <e> <f>")
def print_as_table(data):
"""
Prints data in a structured table format.
:param data: List of dictionaries containing tetrahedron details.
"""
headers = data[0].keys()
# Determine the maximum width for each column
column_widths = {header: max(len(header), max(len(str(row[header])) for row in data)) for header in headers}
# Print header
header_row = " | ".join(header.upper().ljust(column_widths[header]) for header in headers)
print(header_row)
print("-" * len(header_row))
# Print rows
for row in data:
print(" | ".join(str(row[header]).ljust(column_widths[header]) for header in headers))
print("-" * len(header_row))
def run_all_tests_and_demos():
"""Runs all tests and demonstrations from tetravolume.py."""
print("Tetrahedron Examples:")
examples = [
{"Example": "Unit Tetrahedron", "Edges": "1, 1, 1, 1, 1, 1", "IVM Volume": "{:.6f}".format(Tetrahedron(1, 1, 1, 1, 1, 1).ivm_volume()), "XYZ Volume": "{:.6f}".format(Tetrahedron(1, 1, 1, 1, 1, 1).xyz_volume()), "IVM/XYZ Volume Ratio": "{:.6f}".format(Tetrahedron(1, 1, 1, 1, 1, 1).ivm_volume() / Tetrahedron(1, 1, 1, 1, 1, 1).xyz_volume())},
{"Example": "Tetrahedron with √2 edges", "Edges": "√2, √2, √2, √2, √2, √2", "IVM Volume": "{:.6f}".format(Tetrahedron(sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2)).ivm_volume()), "XYZ Volume": "{:.6f}".format(Tetrahedron(sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2)).xyz_volume()), "IVM/XYZ Volume Ratio": "{:.6f}".format(Tetrahedron(sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2)).ivm_volume() / Tetrahedron(sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2), sqrt(2)).xyz_volume())},
{"Example": "Cube to Tetrahedron", "Edges": "1, 1, 1, sqrt(2), sqrt(2), sqrt(2)", "IVM Volume": "{:.6f}".format(Tetrahedron(1, 1, 1, sqrt(2), sqrt(2), sqrt(2)).ivm_volume()), "XYZ Volume": "{:.6f}".format(Tetrahedron(1, 1, 1, sqrt(2), sqrt(2), sqrt(2)).xyz_volume()), "IVM/XYZ Volume Ratio": "{:.6f}".format(Tetrahedron(1, 1, 1, sqrt(2), sqrt(2), sqrt(2)).ivm_volume() / Tetrahedron(1, 1, 1, sqrt(2), sqrt(2), sqrt(2)).xyz_volume())},
{"Example": "Tetrahedron with edges of length 2", "Edges": "2, 2, 2, 2, 2, 2", "IVM Volume": "{:.6f}".format(Tetrahedron(2, 2, 2, 2, 2, 2).ivm_volume()), "XYZ Volume": "{:.6f}".format(Tetrahedron(2, 2, 2, 2, 2, 2).xyz_volume()), "IVM/XYZ Volume Ratio": "{:.6f}".format(Tetrahedron(2, 2, 2, 2, 2, 2).ivm_volume() / Tetrahedron(2, 2, 2, 2, 2, 2).xyz_volume())},
{"Example": "Golden Ratio Tetrahedron", "Edges": "Phi, Phi, Phi, Phi, Phi, Phi", "IVM Volume": "{:.6f}".format(Tetrahedron(PHI, PHI, PHI, PHI, PHI, PHI).ivm_volume()), "XYZ Volume": "{:.6f}".format(Tetrahedron(PHI, PHI, PHI, PHI, PHI, PHI).xyz_volume()), "IVM/XYZ Volume Ratio": "{:.6f}".format(Tetrahedron(PHI, PHI, PHI, PHI, PHI, PHI).ivm_volume() / Tetrahedron(PHI, PHI, PHI, PHI, PHI, PHI).xyz_volume())},
{"Example": "Tetrahedron with √3 edges", "Edges": "√3, √3, √3, √3, √3, √3", "IVM Volume": "{:.6f}".format(Tetrahedron(sqrt(3), sqrt(3), sqrt(3), sqrt(3), sqrt(3), sqrt(3)).ivm_volume()), "XYZ Volume": "{:.6f}".format(Tetrahedron(sqrt(3), sqrt(3), sqrt(3), sqrt(3), sqrt(3), sqrt(3)).xyz_volume()), "IVM/XYZ Volume Ratio": "{:.6f}".format(Tetrahedron(sqrt(3), sqrt(3), sqrt(3), sqrt(3), sqrt(3), sqrt(3)).ivm_volume() / Tetrahedron(sqrt(3), sqrt(3), sqrt(3), sqrt(3), sqrt(3), sqrt(3)).xyz_volume())},
]
print_as_table(examples)
if __name__ == "__main__":
command_line()
run_all_tests_and_demos()