Math Functions

PythonSCAD provides trigonometric and vector math functions that mirror OpenSCAD's built-in math functions. The trigonometric functions use degrees (not radians), matching OpenSCAD convention.

For standard Python math (radians), use Python's built-in math module instead.

Trigonometry

Sin

Calculate the sine of an angle in degrees.

Python

from pythonscad import *

y = Sin(45)   # 0.7071...
y = Sin(90)   # 1.0

Cos

Calculate the cosine of an angle in degrees.

Python

from pythonscad import *

y = Cos(60)   # 0.5
y = Cos(0)    # 1.0

Tan

Calculate the tangent of an angle in degrees.

Python

from pythonscad import *

y = Tan(45)   # 1.0

Asin

Calculate the arc sine, returning degrees.

Python

from pythonscad import *

angle = Asin(0.5)   # 30.0

Acos

Calculate the arc cosine, returning degrees.

Python

from pythonscad import *

angle = Acos(0.5)   # 60.0

Atan

Calculate the arc tangent, returning degrees.

Python

from pythonscad import *

angle = Atan(1.0)   # 45.0

OpenSCAD reference: Mathematical Functions

norm

Calculate the Euclidean length (magnitude) of a vector.

Syntax:

Python

length = norm(vec)

Parameters:

Parameter	Type	Description
`vec`	list of numbers	Input vector

Examples:

Python

from pythonscad import *

length = norm([3, 4])       # 5.0
length = norm([1, 2, 3])    # 3.7416...

OpenSCAD reference: norm

dot

Calculate the dot product of two vectors.

Syntax:

Python

result = dot(vec1, vec2)

Parameters:

Parameter	Type	Description
`vec1`	list of numbers	First vector
`vec2`	list of numbers	Second vector

Examples:

Python

from pythonscad import *

d = dot([1, 0, 0], [0, 1, 0])   # 0.0
d = dot([1, 2, 3], [4, 5, 6])   # 32.0

cross

Calculate the cross product of two 3D vectors.

Syntax:

Python

result = cross(vec1, vec2)

Parameters:

Parameter	Type	Description
`vec1`	`[x, y, z]`	First vector
`vec2`	`[x, y, z]`	Second vector

Returns: A 3D vector perpendicular to both inputs.

Examples:

Python

from pythonscad import *

c = cross([1, 0, 0], [0, 1, 0])   # vector(0, 0, 1)
c = cross([0, 1, 0], [1, 0, 0])   # vector(0, 0, -1)

Vector functions

There are many places, where PythonSCAD accepts vectors which are supplied as Python lists with 2 or 3 numbers. Alernatively, PythonSCAD also accepts PythonSCAD Vector objects with calculating capabilities

Vector addition

Python

from pythonscad import *

vec1 = vector(1,2,3)
vec2 = vector(1,1,1)
print(vec1 + vec2)

Vector subtraction

Python

from pythonscad import *

vec1 = vector(3,3,3)
vec2 = vector(1,2,4)
print(vec1 - vec2)

Vector scaling

Python

from pythonscad import *

dim = sphere(1).size * 2.5
print(dim)

Cross Product

Python

from pythonscad import *

vec1 = vector(1,0,0)
vec2 = vector(0,1,0)

print(vec1 * vec2)

Dot Product

Python

from pythonscad import *

vec1 = vector(1,4,7)
vec2 = vector(1,2,4)

print(vec1.dot(vec2))

Values access

Python

from pythonscad import *

vec1 = vector(1,4,7)
vec1[1] = -3.5
print(vec1[0], vec1[1],vec1[2])

OpenSCAD reference: cross