3D Coordinate System

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3D Mathematical Curves

Helix Spiral
x=2cos(t), y=2sin(t), z=t/2
Cylinder Helix
cos(t)+cos(3t)/3, sin(t)+sin(3t)/3, t/2
Circular Helix
cos(t), sin(t), t + sin(2t)
Spiral Wave
t·cos(t), t·sin(t), sin(5t)
Trefoil Knot
sin(t)+2sin(2t), cos(t)-2cos(2t), -sin(3t)
Figure-8 Knot
(2+cos(2t))cos(3t), (2+cos(2t))sin(3t), sin(4t)
Torus Knot
(3+cos(3t))cos(2t), (3+cos(3t))sin(2t), sin(3t)
Granny Knot
Complex 3-component knot
Solomon's Knot
sin(2t), cos(2t), sin(3t)
Celtic Knot
sin(t)+sin(3t)/3, cos(t)-cos(3t)/3, sin(2t)
Viviani's Curve
cos²(t), cos(t)sin(t), sin(t)
Spherical Spiral
r(1+sin(2φ))sin(θ)cos(φ), r cos(θ), r sin(θ)sin(φ)
Astroidal Spiral
cos³(t), sin³(t), t/2
Cardioid 3D
(1+cos(t))cos(t), (1+cos(t))sin(t), sin(2t)
Nephroid 3D
cos²(t), sin³(t), cos(3t)
Butterfly Curve
sin(t)e^(cos(t))-2cos(4t)-sin⁵(t/12)
Lissajous 3D
sin(3t+π/2), sin(2t), sin(4t+π/4)
Rose 3D
cos(5t)cos(t), cos(5t)sin(t), sin(5t)
Hypotrochoid 3D
(3-4cos(t))cos(t), (3-4cos(t))sin(t), 4sin(t)
Epitrochoid 3D
(5+2cos(5t))cos(t), (5+2cos(5t))sin(t), 2sin(5t)
Hilbert Curve 3D
Space-filling curve approximation
Dragon Curve 3D
Fractal curve in 3D space
Golden Spiral 3D
φ-based logarithmic spiral
Lemniscate 3D
Figure-eight in 3D projection
Sine Wave Helix
cos(t), sin(t), t + 0.5sin(10t)
Flower Helix
cos(t)(1+0.5cos(5t)), sin(t)(1+0.5cos(5t)), t/3

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