Geom3py

geom3py is a library developed entirely in Pure Python for analytical geometry calculations in three-dimensional space. It features its own vector and linear algebra engine and provides an object-oriented API for vectors, points, lines, planes and faces including geometric transformations such as scaling, rotation, translation and reflection.

The library has no external dependencies and is suitable for teaching and study as well as a foundation for geometric applications, visualization or CAD-related projects.

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Features

Vectors (Vector)

• Vector addition and subtraction

• Scalar multiplication

• Magnitude

• Dot product

• Cross product

• Normalization

• Angle calculation

• Transformations

  • Scale
  • Translate
  • Rotate
  • Reflect on point
  • Reflect on line
  • Reflect on plane

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Points (Point)

• Creation of points in ℝ³
• Distance between points
• Direction vector between two points
• All geometric transformations

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Lines (Line)

• Creation from

  • two points
  • support and direction vector

• Calculation of any point on the line

• Foot point of a point

• Intercept points

• Distances to

  • points
  • lines

• Intersection with lines

• Positional relationships

  • identical
  • parallel
  • intersecting
  • skew

• Angle calculations

• Geometric transformations

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Planes (Plane)

• Creation from

  • point and normal vector
  • point and two direction vectors

• Foot point of a point

• Intersection line of two planes

• Intersection with lines

• Intercept points

• Distances to

  • points
  • lines
  • planes

• Intersection angles

• Positional relationships

  • identical
  • parallel
  • intersecting

• Geometric transformations

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Faces (Face)

Representation of bounded planar quadrilaterals.

Supports among others:

• Center point

• Perimeter

• Area

• Normal vector

• Point-in-face test

• Positional relationships between faces

  • identical
  • parallel
  • intersecting
  • outside
  • coplanar intersecting
  • coplanar outside
  • on edge
  • touching
  • edge intersecting

• Distance between faces

• Intersection point (if unique)

• Geometric transformations

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Properties

• ✅ Completely in Pure Python
• ✅ No external dependencies
• ✅ Custom vector engine
• ✅ Custom linear algebra helper functions
• ✅ Object-oriented API
• ✅ Numerically robust calculations using custom tolerance functions
• ✅ Geometric transformations for all objects
• ✅ Extensive unit tests
• ✅ Suitable for teaching, study and technical applications

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Installation

pip install geom3py

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📚 Examples

Basic Geometry

from geom3py import Point, Line

A = Point([0, 0, 0])
B = Point([2, 2, 2])

g = Line.from_points(A, B)

print(A.distance_to_point(B))
print(g.point_at(0.5))
print(g.contains_point(A))

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Planes

from geom3py import Point, Plane

E = Plane([1, 2, 3], [1, 1, 1])
P = Point([4, 5, 6])

print(E.distance_point(P))
print(E.contains_point(P))
print(E.intercept_points())

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Transformations

from geom3py import Line

g = Line(Point(1, 2, 3), Point(1, 0, 0))

g2 = g.scale(2)
g3 = g.translate(Point(5, 0, 0))
g4 = g.rotate(90, "z")
g5 = g.reflect_on_point(Point(0, 0, 0))

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Face

from geom3py import Point, Face

face = Face(
    [0, 0, 0],
    [10, 0, 0],
    [10, 8, 0],
    [0, 8, 0]
)

print(face.area())
print(face.perimeter())
print(face.center)

P = Point([5, 4, 0])
print(face.contains_point(P))

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Intersection Between Line and Plane

from geom3py import Line, Plane

g = Line([0, 0, 0], [1, 1, 1])
E = Plane([1, 0, 0], [0, 1, 0])

print(E.position_line(g))
print(E.intersection_line(g))

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Angle Calculations

from geom3py import Line, Plane

g1 = Line([0, 0, 0], [1, 0, 0])
g2 = Line([0, 0, 0], [1, 1, 0])

print(g1.angle_lines(g2, deg=True))

E = Plane([0, 0, 0], [0, 0, 1])
print(E.angle_line(g1, deg=True))

E2 = Plane([0, 0, 0], [1, 1, 0])
print(E.angle_plane(E2, deg=True))

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Dependencies

• Python ≥ 3.10

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License

MIT License.