Provide the Matrix3D class and functions for performing matrix and vector operations. Here's an example to build a translation matrix for translating a point.
from cqmore.matrix import translation
point = (10, 10, 10)
m = translation((10, 0, 0)) # return a Matrix3D instance
new_point = m.transform(point) # (20, 10, 10)
Matrix3D supports matrix multiplication. You can combine multiple transformations in a single matrix. Say you have a point (10, 0, 0) and you want to translate it by (5, 0, 0) and then rotate it around the z-axis by 45 degrees. You can do it like:
from cqmore.matrix import translation, rotationZ
point = (10, 0, 0)
m = rotationZ(45) @ translation((5, 0, 0))
new_point = m.transform(point)
The right-most matrix is first multiplied with the point so you should read the multiplications from right to left.
| Signature | Description |
|---|---|
Matrix3D(m) |
Create a matrix from an array-like object. |
| Signature | Description |
|---|---|
transform(point) |
Use the current matrix to transform a point. |
transformAll(points) |
Use the current matrix to transform a list of points. |
| Signature | Description |
|---|---|
identity() |
Create an identity matrix. |
scaling(v) |
Create a scaling matrix. |
translation(v) |
Create a translation matrix. |
mirror(v) |
Create a mirror matrix. |
rotationX(angle) |
Create a rotation matrix around the x-axis. |
rotationY(angle) |
Create a rotation matrix around the y-axis. |
rotationZ(angle) |
Create a rotation matrix around the z-axis. |
rotation(direction, angle) |
Create a rotation matrix around the given direction. |
Create a matrix from an array-like object.
m: an array-like object.
from cqmore.matrix import Matrix3D
v = (5, 5, 5)
# Create a translation matrix
translation = Matrix3D([
[1, 0, 0, v[0]],
[0, 1, 0, v[1]],
[0, 0, 1, v[2]],
[0, 0, 0, 1]
])
Use the current matrix to transform a point.
point: the point to transform.
from cqmore.matrix import Matrix3D
translation = Matrix3D([
[1, 0, 0, 5],
[0, 1, 0, 5],
[0, 0, 1, 5],
[0, 0, 0, 1]
])
point = (10, 20, 30)
translated = translation.transform(point) # (15, 25, 35)
Use the current matrix to transform a list of points.
points: a list of points to transform.
from cqmore.matrix import Matrix3D
translation = Matrix3D([
[1, 0, 0, 5],
[0, 1, 0, 5],
[0, 0, 1, 5],
[0, 0, 0, 1]
])
points = [(10, 20, 30), (0, 0, 0), (-10, -20, -30)]
# ((15, 25, 35), (5, 5, 5), (-5, -15, -25))
translated = translation.transformAll(points)
Create an identity matrix.
from cqmore.matrix import identity
m = identity()
Create a scaling matrix.
v: scaling vector.
from cqmore.matrix import scaling
from cqmore.polyhedron import uvSphere
from cqmore import Workplane
sphere = uvSphere(1, widthSegments = 12, heightSegments = 6)
m = scaling((2, 1, 1))
scaled_points = m.transformAll(sphere.points)
r = Workplane().polyhedron(scaled_points, sphere.faces)
Create a translation matrix.
v: translation vector.
from cqmore.matrix import scaling, translation
from cqmore.polyhedron import uvSphere
from cqmore import Workplane
sphere = uvSphere(1, widthSegments = 12, heightSegments = 6)
r1 = Workplane().polyhedron(*sphere)
s = scaling((2, 2, 2))
t = translation((3, 0, 0))
transformed_pts = (t @ s).transformAll(sphere.points)
r2 = Workplane().polyhedron(transformed_pts, sphere.faces)
Create a mirror matrix.
v: mirror vector.
from cqmore.matrix import mirror, translation
from cqmore.polyhedron import tetrahedron
from cqmore import Workplane
t = tetrahedron(1)
pts = translation((1, 0, 0)).transformAll(t.points)
r1 = Workplane().polyhedron(pts, t.faces)
mirrored_pts = mirror((1, 0, 0)).transformAll(pts)
r2 = Workplane().polyhedron(mirrored_pts, t.faces)
Create a rotation matrix around the x-axis.
angle: angle degrees.
from cqmore.matrix import translation, rotationX
from cqmore.polyhedron import tetrahedron
from cqmore import Workplane
t = tetrahedron(1)
pts = translation((0, 3, 0)).transformAll(t.points)
for a in range(0, 360, 30):
rotated_pts = rotationX(a).transformAll(pts)
show_object(Workplane().polyhedron(rotated_pts, t.faces))
Create a rotation matrix around the y-axis.
angle: angle degrees.
from cqmore.matrix import translation, rotationY
from cqmore.polyhedron import tetrahedron
from cqmore import Workplane
t = tetrahedron(1)
for i in range(20):
rotated_pts = (rotationY(i * 36) @ translation((3, i, 0))).transformAll(t.points)
show_object(Workplane().polyhedron(rotated_pts, t.faces))
Create a rotation matrix around the z-axis.
angle: angle degrees.
from cqmore import Workplane
from cqmore.matrix import translation, rotationX, rotationZ
from cqmore.polyhedron import sweep
def mobius_strip(radius, frags):
profile = [(10, -1, 0), (10, 1, 0), (-10, 1, 0), (-10, -1, 0)]
translationX20 = translation((radius, 0, 0))
rotationX90 = rotationX(90)
angle_step = 360 / frags
profiles = []
for i in range(frags):
m = rotationZ(i * angle_step) @ translationX20 @ rotationX90 @ rotationZ(i * angle_step / 2)
profiles.append(m.transformAll(profile))
return Workplane().polyhedron(*sweep(profiles, closeIdx = 2))
radius = 20
frags = 24
strip = mobius_strip(radius, frags)
Create a rotation matrix around the given direction.
direction: axis of rotation.angle: angle degrees.
from cqmore.matrix import rotation, translation, rotationY
from cqmore.polyhedron import tetrahedron
from cqmore import Workplane
t = tetrahedron(1)
pts = translation((6, 6, 3)).transformAll(t.points)
direction = (10, 10, 10)
for a in range(0, 360, 30):
rotated_pts = rotation(direction, a).transformAll(pts)
show_object(Workplane().polyhedron(rotated_pts, t.faces))
show_object(
Workplane().polylineJoin(
[(0, 0, 0), direction],
Workplane().box(.1, .1, .1)
)
)
