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PyAnsys Geometry 101: Math

The math module is the foundation of PyAnsys Geometry. This module is built on top of NumPy, one of the most renowned mathematical Python libraries.

This example shows some of the main PyAnsys Geometry math objects and demonstrates why they are important prior to doing more exciting things in PyAnsys Geometry.

Perform required imports

Perform the required imports.

import numpy as np

from ansys.geometry.core.math import Plane, Point2D, Point3D, Vector2D, Vector3D, UnitVector3D

Create points and vectors

Everything starts with Point and Vector objects, which can each be defined in a 2D or 3D form. These objects inherit from NumPy’s ndarray, providing them with enhanced functionalities. When creating these objects, you must remember to pass in the arguments as a list (that is, with brackets [ ]).

Create 2D and 3D point and vectors.

Point3D([x, y, z])
Point2D([x, y])

Vector3D([x, y, z])
Vector2D([x, y])

You can perform standard mathematical operations on points and vectors.

Perform some standard operations on vectors.

vec_1 = Vector3D([1,0,0]) # x-vector
vec_2 = Vector3D([0,1,0]) # y-vector

print("Sum of vectors [1, 0, 0] + [0, 1, 0]:")
print(vec_1 + vec_2) # sum

print("\nDot product of vectors [1, 0, 0] * [0, 1, 0]:")
print(vec_1 * vec_2) # dot

print("\nCross product of vectors [1, 0, 0] % [0, 1, 0]:")
print(vec_1 % vec_2) # cross

Sum of vectors [1, 0, 0] + [0, 1, 0]:
[1 1 0]

Dot product of vectors [1, 0, 0] * [0, 1, 0]:
0

Cross product of vectors [1, 0, 0] % [0, 1, 0]:
[0 0 1]

Create a vector from two points.

p1 = Point3D([12.4, 532.3, 89])
p2 = Point3D([-5.7, -67.4, 46.6])

vec_3 = Vector3D.from_points(p1, p2)
vec_3

Vector3D([ -18.1, -599.7,  -42.4])

Normalize a vector to create a unit vector, which is also known as a direction.

print("Magnitude of vec_3:")
print(vec_3.magnitude)

print("\nNormalized vec_3:")
print(vec_3.normalize())

print("\nNew magnitude:")
print(vec_3.normalize().magnitude)

Magnitude of vec_3:
601.4694173438911

Normalized vec_3:
[-0.03009297 -0.99705818 -0.07049402]

New magnitude:
1.0

Use the UnitVector class to automatically normalize the input for the unit vector.

uv = UnitVector3D([1,1,1])
uv

UnitVector3D([0.57735027, 0.57735027, 0.57735027])

Perform a few more mathematical operations on vectors.

v1 = Vector3D([1, 0, 0])
v2 = Vector3D([0, 1, 0])

print("Vectors are perpendicular:")
print(v1.is_perpendicular_to(v2))

print("\nVectors are parallel:")
print(v1.is_parallel_to(v2))

print("\nVectors are opposite:")
print(v1.is_opposite(v2))

print("\nAngle between vectors:")
print(v1.get_angle_between(v2))
print(f"{np.pi / 2} == pi/2")

Vectors are perpendicular:
True

Vectors are parallel:
False

Vectors are opposite:
False

Angle between vectors:
1.5707963267948966 radian
1.5707963267948966 == pi/2

Create planes

Once you begin creating sketches and bodies, Plane objects become very important. A plane is defined by these items:

• An origin, which consists of a 3D point

• Two directions (direction_x and direction_y), which are both UnitVector3Dobjects

If no direction vectors are provided, the plane defaults to the XY plane.

Create two planes.

plane = Plane(Point3D([0,0,0])) # XY plane

print("(1, 2, 0) is in XY plane:")
print(plane.is_point_contained(Point3D([1, 2, 0]))) # True

print("\n(0, 0, 5) is in XY plane:")
print(plane.is_point_contained(Point3D([0, 0, 5]))) # False

(1, 2, 0) is in XY plane:
True

(0, 0, 5) is in XY plane:
False

Perform parametric evaluations

PyAnsys Geometry implements parametric evaluations for some curves and surfaces.

Evaluate a sphere.

from ansys.geometry.core.shapes import Sphere, SphereEvaluation
from ansys.geometry.core.math import Point3D
from ansys.geometry.core.misc import Distance

sphere = Sphere(Point3D([0,0,0]), Distance(1)) # radius = 1

eval = sphere.project_point(Point3D([1,1,1]))

print("U Parameter:")
print(eval.parameter.u)

print("\nV Parameter:")
print(eval.parameter.v)

U Parameter:
0.7853981633974483

V Parameter:
0.6154797086703873

print("Point on the sphere:")
eval.position

Point on the sphere:

Point3D([0.57735027, 0.57735027, 0.57735027])

print("Normal to the surface of the sphere at the evaluation position:")
eval.normal

Normal to the surface of the sphere at the evaluation position:

UnitVector3D([0.57735027, 0.57735027, 0.57735027])

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