Points, vectors and utilities

Points

point3(x, y, z) creates a three-dimensional point; point2(x, y) creates a two-dimensional point. Most geometry functions also accept coordinate tuples.

from zencad import *

p = point3(1, 2, 3)
assert p.value() == (1, 2, 3)
assert float(p.x) == 1

curve = interpolate([(0, 0, 0), (0, 0, 10), (10, 0, 10)])
display(curve)
display(p)
show()

A point is displayed as a vertex. Both rotation and translation apply when transforming it.

Vectors

vector3(x, y, z) and vector2(x, y) describe directions and displacements. Translation does not affect a vector. Use an arrow to display one.

Adding two points is not allowed. Operations create new values without changing the original coordinates.

from zencad import *

v = vector3(3, 4, 0)
assert float(v.length()) == 5
assert abs(float(v.normalized().length()) - 1) < 1e-7
assert vector3(1, 0, 0).cross(vector3(0, 1, 0)).value() == (0, 0, 1)

Arrays of points and vectors

points and vectors create lists of three-dimensional points and vectors. points2 creates a two-dimensional grid of three-dimensional points, for example for surface interpolation.

points([(0, 0, 0), (0, 0, 10), (10, 0, 10)])
vectors([(0, 0, 1), (1, 0, 0), (0, 1, 0)])
points2([
    [(0, 0, 0), (10, 0, 5)],
    [(0, 10, 0), (10, 10, 5)],
])

Numbers and evaluation

The functions point3, vector3 and scalar return Point3, Vector3 and Scalar objects. These preserve computation dependencies. .value() returns a number or coordinate tuple; .to_numpy() on a point or vector returns a NumPy array.

from zencad import *

body = box(2)
volume = body.mass()             # Scalar
moved = body.right(volume / 4)   # Translation depends on volume.
assert abs(float(volume) - 8) < 1e-7
coordinates = moved.center().to_numpy()

float, int, bool and comparisons request a numerical result. math.sin(value) also evaluates a number; ZenCad's sin(value) preserves the dependency. See Evaluation and caching.

Radians and degrees

Angles in the ZenCad API use radians. deg(180) equals math.pi; deg2rad is an alias for deg, and rad2deg performs the reverse conversion.

rotateZ(deg(45))

Empty primitive: nullshape

An empty shape can take part in boolean operations:

it = nullshape()
for i in range(7):
    it = it + box(20).translate(10*i, 10*i, 10*i)

# The same using a list:
# union([box(20).translate(10*i, 10*i, 10*i) for i in range(7)])

Registering a font

register_font(fontpath) registers a FreeType font for creating text.