"""Fabex 'curve_cam_equation.py' © 2021, 2022 Alain Pelletier
Operators to create a number of geometric shapes with curves.
"""
from math import pi, sin, cos, sqrt
import numpy as np
import bpy
from bpy.props import (
EnumProperty,
FloatProperty,
IntProperty,
StringProperty,
)
from bpy.types import Operator
from .. import parametric
from ..utilities.geom_utils import triangle, s_sine
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class CamSineCurve(Operator):
"""Object Sine""" # by Alain Pelletier april 2021
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bl_idname = "object.sine"
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bl_label = "Periodic Wave"
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bl_options = {"REGISTER", "UNDO", "PRESET"}
# zstring: StringProperty(name="Z equation", description="Equation for z=F(u,v)", default="0.05*sin(2*pi*4*t)" )
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axis: EnumProperty(
name="Displacement Axis",
items=(
("XY", "Y to displace X axis", "Y constant; X sine displacement"),
("YX", "X to displace Y axis", "X constant; Y sine displacement"),
("ZX", "X to displace Z axis", "X constant; Y sine displacement"),
("ZY", "Y to displace Z axis", "X constant; Y sine displacement"),
),
default="ZX",
)
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wave: EnumProperty(
name="Wave",
items=(
("sine", "Sine Wave", "Sine Wave"),
("triangle", "Triangle Wave", "triangle wave"),
("cycloid", "Cycloid", "Sine wave rectification"),
("invcycloid", "Inverse Cycloid", "Sine wave rectification"),
),
default="sine",
)
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amplitude: FloatProperty(
name="Amplitude",
default=0.01,
min=0,
max=10,
precision=4,
unit="LENGTH",
)
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period: FloatProperty(
name="Period",
default=0.5,
min=0.001,
max=100,
precision=4,
unit="LENGTH",
)
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beat_period: FloatProperty(
name="Beat Period Offset",
default=0.0,
min=0.0,
max=100,
precision=4,
unit="LENGTH",
)
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shift: FloatProperty(
name="Phase Shift",
default=0,
min=-360,
max=360,
precision=4,
step=100,
unit="ROTATION",
)
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offset: FloatProperty(
name="Offset",
default=0,
min=-1.0,
max=1,
precision=4,
unit="LENGTH",
)
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iteration: IntProperty(
name="Iteration",
default=100,
min=50,
max=2000,
)
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max_t: FloatProperty(
name="Wave Ends at X",
default=0.5,
min=-3.0,
max=3,
precision=4,
unit="LENGTH",
)
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min_t: FloatProperty(
name="Wave Starts at X",
default=0,
min=-3.0,
max=3,
precision=4,
unit="LENGTH",
)
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wave_distance: FloatProperty(
name="Distance Between Multiple Waves",
default=0.0,
min=0.0,
max=100,
precision=4,
unit="LENGTH",
)
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wave_angle_offset: FloatProperty(
name="Angle Offset for Multiple Waves",
default=pi / 2,
min=-200 * pi,
max=200 * pi,
precision=4,
step=100,
unit="ROTATION",
)
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wave_amount: IntProperty(
name="Amount of Multiple Waves",
default=1,
min=1,
max=2000,
)
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def execute(self, context):
amp = self.amplitude
period = self.period
beatperiod = self.beat_period
offset = self.offset
shift = self.shift
# z=Asin(B(x+C))+D
if self.wave == "sine":
zstring = s_sine(amp, period, dc_offset=offset, phase_shift=shift)
if self.beat_period != 0:
zstring += (
f"+ {s_sine(amp, period+beatperiod, dc_offset=offset, phase_shift=shift)}"
)
# build triangle wave from fourier series
elif self.wave == "triangle":
zstring = f"{round(offset, 6) + triangle(80, period, amp)}"
if self.beat_period != 0:
zstring += f"+ {triangle(80, period+beatperiod, amp)}"
elif self.wave == "cycloid":
zstring = f"abs({s_sine(amp, period, dc_offset=offset, phase_shift=shift)})"
elif self.wave == "invcycloid":
zstring = f"-1 * abs({s_sine(amp, period, dc_offset=offset, phase_shift=shift)})"
print(zstring)
# make equation from string
def e(t):
return eval(zstring)
# build function to be passed to create parametric curve ()
def f(t, offset: float = 0.0, angle_offset: float = 0.0):
if self.axis == "XY":
c = (e(t + angle_offset) + offset, t, 0)
elif self.axis == "YX":
c = (t, e(t + angle_offset) + offset, 0)
elif self.axis == "ZX":
c = (t, offset, e(t + angle_offset))
elif self.axis == "ZY":
c = (offset, t, e(t + angle_offset))
return c
for i in range(self.wave_amount):
angle_off = self.wave_angle_offset * period * i / (2 * pi)
parametric.create_parametric_curve(
f,
offset=self.wave_distance * i,
min=self.min_t,
max=self.max_t,
use_cubic=True,
iterations=self.iteration,
angle_offset=angle_off,
)
return {"FINISHED"}
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class CamLissajousCurve(Operator):
"""Lissajous""" # by Alain Pelletier april 2021
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bl_idname = "object.lissajous"
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bl_label = "Lissajous Figure"
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bl_options = {"REGISTER", "UNDO", "PRESET"}
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amplitude_a: FloatProperty(
name="Amplitude A",
default=0.1,
min=0,
max=100,
precision=4,
unit="LENGTH",
)
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wave_a: EnumProperty(
name="Wave X",
items=(("sine", "Sine Wave", "Sine Wave"), ("triangle", "Triangle Wave", "triangle wave")),
default="sine",
)
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amplitude_b: FloatProperty(
name="Amplitude B",
default=0.1,
min=0,
max=100,
precision=4,
unit="LENGTH",
)
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wave_b: EnumProperty(
name="Wave Y",
items=(("sine", "Sine Wave", "Sine Wave"), ("triangle", "Triangle Wave", "triangle wave")),
default="sine",
)
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period_a: FloatProperty(
name="Period A",
default=1.1,
min=0.001,
max=100,
precision=4,
unit="LENGTH",
)
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period_b: FloatProperty(
name="Period B",
default=1.0,
min=0.001,
max=100,
precision=4,
unit="LENGTH",
)
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period_z: FloatProperty(
name="Period Z",
default=1.0,
min=0.001,
max=100,
precision=4,
unit="LENGTH",
)
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amplitude_z: FloatProperty(
name="Amplitude Z",
default=0.0,
min=0,
max=100,
precision=4,
unit="LENGTH",
)
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shift: FloatProperty(
name="Phase Shift",
default=0,
min=-360,
max=360,
precision=4,
step=100,
unit="ROTATION",
)
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iteration: IntProperty(
name="Iteration",
default=500,
min=50,
max=10000,
)
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max_t: FloatProperty(
name="Wave Ends at X",
default=11,
min=-3.0,
max=1000000,
precision=4,
unit="LENGTH",
)
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min_t: FloatProperty(
name="Wave Starts at X",
default=0,
min=-10.0,
max=3,
precision=4,
unit="LENGTH",
)
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def execute(self, context):
# x=Asin(at+delta ),y=Bsin(bt)
if self.wave_a == "sine":
xstring = s_sine(self.amplitude_a, self.period_a, phase_shift=self.shift)
elif self.wave_a == "triangle":
xstring = f"{triangle(100, self.period_a, self.amplitude_a)}"
if self.wave_b == "sine":
ystring = s_sine(self.amplitude_b, self.period_b)
elif self.wave_b == "triangle":
ystring = f"{triangle(100, self.period_b, self.amplitude_b)}"
zstring = s_sine(self.amplitude_z, self.period_z)
# make equation from string
def x(t):
return eval(xstring)
def y(t):
return eval(ystring)
def z(t):
return eval(zstring)
print(f"x= {xstring}")
print(f"y= {ystring}")
# build function to be passed to create parametric curve ()
def f(t, offset: float = 0.0):
c = (x(t), y(t), z(t))
return c
parametric.create_parametric_curve(
f, offset=0.0, min=self.min_t, max=self.max_t, use_cubic=True, iterations=self.iteration
)
return {"FINISHED"}
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class CamHypotrochoidCurve(Operator):
"""Hypotrochoid""" # by Alain Pelletier april 2021
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bl_idname = "object.hypotrochoid"
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bl_label = "Spirograph Type Figure"
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bl_options = {"REGISTER", "UNDO", "PRESET"}
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typecurve: EnumProperty(
name="Type of Curve",
items=(
("hypo", "Hypotrochoid", "Inside ring"),
("epi", "Epicycloid", "Outside inner ring"),
),
)
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R: FloatProperty(
name="Big Circle Radius",
default=0.25,
min=0.001,
max=100,
precision=4,
unit="LENGTH",
)
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r: FloatProperty(
name="Small Circle Radius",
default=0.18,
min=0.0001,
max=100,
precision=4,
unit="LENGTH",
)
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d: FloatProperty(
name="Distance from Center of Interior Circle",
default=0.050,
min=0,
max=100,
precision=4,
unit="LENGTH",
)
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dip: FloatProperty(
name="Variable Depth from Center",
default=0.00,
min=-100,
max=100,
precision=4,
)
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def execute(self, context):
r = round(self.r, 6)
R = round(self.R, 6)
d = round(self.d, 6)
Rmr = round(R - r, 6) # R-r
Rpr = round(R + r, 6) # R +r
Rpror = round(Rpr / r, 6) # (R+r)/r
Rmror = round(Rmr / r, 6) # (R-r)/r
maxangle = 2 * pi * ((np.lcm(round(self.R * 1000), round(self.r * 1000)) / (R * 1000)))
if self.typecurve == "hypo":
xstring = f"{Rmr} * cos(t) + {d} * cos({Rmror} * t)"
ystring = f"{Rmr} * sin(t) - {d} * sin({Rmror} * t)"
else:
xstring = f"{Rpr} * cos(t) - {d} * cos({Rpror} * t)"
ystring = f"{Rpr} * sin(t) - {d} * sin({Rpror} * t)"
zstring = f"({round(self.dip, 6)} * (sqrt((({xstring})**2) + (({ystring})**2))))"
# make equation from string
def x(t):
return eval(xstring)
def y(t):
return eval(ystring)
def z(t):
return eval(zstring)
print(f"x= {xstring}")
print(f"y= {ystring}")
print(f"z= {zstring}")
print(f"maxangle {maxangle}")
# build function to be passed to create parametric curve ()
def f(t, offset: float = 0.0):
c = (x(t), y(t), z(t))
return c
iter = int(maxangle * 10)
if iter > 10000: # do not calculate more than 10000 points
print("limiting calculations to 10000 points")
iter = 10000
parametric.create_parametric_curve(
f, offset=0.0, min=0, max=maxangle, use_cubic=True, iterations=iter
)
return {"FINISHED"}
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class CamCustomCurve(Operator):
"""Object Custom Curve""" # by Alain Pelletier april 2021
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bl_idname = "object.customcurve"
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bl_label = "Custom Curve"
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bl_options = {"REGISTER", "UNDO", "PRESET"}
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x_string: StringProperty(
name="X Equation",
description="Equation x=F(t)",
default="t",
)
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y_string: StringProperty(
name="Y Equation",
description="Equation y=F(t)",
default="0",
)
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z_string: StringProperty(
name="Z Equation",
description="Equation z=F(t)",
default="0.05*sin(2*pi*4*t)",
)
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iteration: IntProperty(
name="Iteration",
default=100,
min=50,
max=2000,
)
[docs]
max_t: FloatProperty(
name="Wave Ends at X",
default=0.5,
min=-3.0,
max=10,
precision=4,
unit="LENGTH",
)
[docs]
min_t: FloatProperty(
name="Wave Starts at X",
default=0,
min=-3.0,
max=3,
precision=4,
unit="LENGTH",
)
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def execute(self, context):
print("x= " + self.x_string)
print("y= " + self.y_string)
print("z= " + self.z_string)
# make equation from string
def ex(t):
return eval(self.x_string)
def ey(t):
return eval(self.y_string)
def ez(t):
return eval(self.z_string)
# build function to be passed to create parametric curve ()
def f(t, offset: float = 0.0):
c = (ex(t), ey(t), ez(t))
return c
parametric.create_parametric_curve(
f, offset=0.0, min=self.min_t, max=self.max_t, use_cubic=True, iterations=self.iteration
)
return {"FINISHED"}
