Torus Knot

Torus Knot Coord

from pynodes import *
from pynodes.math import *

@tree
def torus_knot_coord(Φ: Float, p: Integer, q: Integer):
    # The name of the function decorated by the decorator is treated as the name of the node tree

    r = cos(q * Φ) + 2

    x = r * cos(p * Φ)

    y = r * sin(p * Φ)

    z = -sin(q * Φ)

    return CombineXYZ(x, y, z)

Torus Knot Curve

@tree
def torus_knot_curve(
    p: Integer = 2,
    q: Integer = 3,
    # End factor for trim curve (name, default, min, max)
    e: Float = ("End", 1, 0, 1),
    # The larger the value, the smoother the curve (name, default))
    n: Integer = ("Sample", 128)
):
    # Create a primitive curve circle node and assign the geometry of the output socket to `curve`
    curve = CurveCircle(resolution=n)

    # Call the node tree defined above as a function
    pos = torus_knot_coord(curve.parameter.factor * 2 * pi, p, q)

    # Use the obtained coordinates to set the position of the curve,
    # and then create a trim curve node to trim the curve by the end factor.
    curve = curve.set_position(position=pos).trim_factor(end=e)

    # Create a frame, pass in the label of the frame.
    with frame("Deal with the connection of endpoints problem"):
        # All nodes created in the scope of the with statement will embeded in this frame
        curve = curve.to_mesh().merge_by_distance().to_curve()
        # The above operation is actually to align the normal lines
        # at the beginning and end of the curve, so that when the mesh
        # surface is generated later, it will not break

    return curve

Version with material

@tree
def torus_knot_mesh(
    p: Integer = 3,
    q: Integer = 7,
    e: Float = ("End", 1, 0, 1),
    n: Integer = ("Sample", 256),
    # The radius of the profile curve circle
    r: Float = ("Profile Radius", 0.3)
):
    # Call the node tree defined above
    curve = torus_knot_curve(p, q, e, n)

    # Store the parameter factor of the curve for shading
    curve.store_named_attribute("factor", curve.parameter.factor)

    # Sweep the curve to mesh with a profile curve
    mesh = curve.to_mesh(CurveCircle(radius=r))
    # return mesh

    # Optional: set the shade smooth and set the material
    return mesh.set_shade_smooth().set_material("Torus Knot")


@tree
def torus_knot():
    """@Material"""

    shader = BsdfPrincipled()

    factor = Shader.attribute(name="factor").fac

    color = GradientTexture(vector=factor).color

    color = color.mix("#117f0f")

    shader['Base Color'] = color

    return shader