Polar Coordinate Illustrating

Concentric Circles

concentric_circles

from pynodes import *
from pynodes.math import *

@tree
def concentric_circles(band_width: Float = 0.02, count: Integer = (20, 0, 100)):

    points = InputPoints(count=count)

    circle = CurveCircle().set_spline_type("CATMULL_ROM")

    with frame("Clone circles and set scale"):

        circles = circle.on_points(points, scale=(points.index + 1, points.index + 1, 1)).realize_instances()

    with frame("Curve to Mesh and Set material"):

        mesh = circles.to_mesh(CurveLine((-band_width, 0, 0), (band_width, 0, 0))).set_material("Cerulean")

    return mesh

Axis Slices

Slice the plane radially, except the x,y-axis.

axis_slices

@tree
def axis_slices(width: Float = 0.05, length: Float = 50):

    line = Rectangle(length, width).filled_ngons

    lines = [line.Mesh.transform(rotation=(0, 0, pi / 8 * i)) for i in range(8) if i % 4 != 0]

    return join(lines).Mesh.set_material("Cerulean")

Angle Spiral

The Spiral to illustrate the rotation of coordinate.

angle_spiral

@tree
def angle_spiral(end: Float = (1, 0, 1)):

    with frame("Spiral"):

        curve = CurveSpiral(64, 1, 1, 1.08, -0.01, True).set_spline_type("CATMULL_ROM")

    with frame("Trim Spiral"):

        curve = curve.trim_factor(end=end.float_curve(points=[(0, 0.001), (0.53, 0.52), (1, 1)]))

    with frame("Curve to Mesh"):

        mesh = curve.to_mesh(CurveLine((-0.03, 0, 0), (0.03, 0, 0)))

    return mesh.set_material("Cerise")

Text of Polar Coord

radial_coord_text

# Times New Roman Bold
font = bpy.data.fonts.load("C:\\Windows\\Fonts\\" + "timesbd.ttf", check_existing=True)

@tree
def get_position(r: Float = 2.2, θ: Float = 0):

    return CombineXYZ(r * cos(θ), r * sin(θ), 0)

@tree
def radial_coord_text(r: Float = 2.2, θ: Float = 0, decimals: Integer = 2, scale: Float = 1):

    with frame("Get Position"):

        pos = get_position(r, θ)

    with frame("Radius String"):

        string_r = r.to_string(decimals)

    with frame("Angle String"):

        string_θ = θ.to_string(decimals)

    with frame("String Length"):

        length_r = string_r.length

        length_θ = string_θ.length

    with frame("Join String"):

        string = InputString("(").join(string_r, InputString(", "), string_θ, InputString(")"))

    with frame("String to Curve Instances"):

        instances = string.to_curves(align_x="CENTER", size=0.5 * scale, font=font).curve_instances

        instances.transform(pos).transform((0, 0.2, 0.01))

    with frame("Seperate String Curves"):

        text1, text2 = instances[0, length_r + 1, length_r + length_θ + 3].separate()

    text1 = text1.Curve.filled_mesh.set_material("Black")

    with frame("Seperate Float String Curves"):

        text2, text3 = text2[:length_r].separate()

    text2 = text2.Curve.filled_ngons.set_material("Green")

    text3 = text3.Curve.filled_ngons.set_material("Cerise")

    return text1.join(text2, text3)

Line from origin to dot

line_from_origin_to_dot

@tree
def line_from_origin_to_dot(r: Float = 2.2, θ: Float = 0):

    pos = (r * cos(θ), r * sin(θ), 0)

    with frame("Line and Dots"):

        line = CurveLine(end=pos).to_mesh(CurveLine((-0.02, 0, 0), (0.02, 0, 0)))

        dot1 = CurveCircle(0.05)

        dot2 = dot1.Curve.transform(pos)

        dot = dot1.join(dot2).filled_ngons

        line = line.join(dot).set_material("Green")

    text = radial_coord_text(r, θ)

    return line.join(text)

Dot with Coord Text

dot_with_coord_text

@tree
def dot_with_coord_text(r: Float = 2.2, θ: Float = 0, decimals: Integer = 2, scale: Float = 1, material: Material = None):

    pos = (r * cos(θ), r * sin(θ), 0)

    with frame("Dot"):

        dot = CurveCircle(0.05 * scale).transform(pos).filled_ngons.set_material(material)

    text = radial_coord_text(r, θ, decimals, scale)

    return dot.join(text)

Materials

Materials

@tree
def cerulean():
    """@material"""
    return BsdfPrincipled(base_color="#0070A8", alpha=0.5)

bpy.data.materials["Cerulean"].blend_method = "BLEND"

@tree
def cerise():
    """@material"""
    return BsdfPrincipled(base_color="#CE009E")

@tree
def green():
    """@material"""
    return Bsdf.Principled(base_color="#158C00")

@tree
def black():
    """@material"""
    return BsdfPrincipled(base_color="#000000")

The Result Illustration

polar_coordinates

@tree
def polar_coordinates(radius: Float = 1.33, factor: Float = (0.3, 0, 1), r: Float = 1.5, θ: Float = pi / 4):

    meshes = [concentric_circles(), axis_slices()]

    meshes.append(line_from_origin_to_dot(r=radius, θ=factor * tau))

    meshes.append(angle_spiral(factor))

    meshes.append(dot_with_coord_text(r, θ, material="Black"))

    return join(meshes)