#### Best Practice - How to create 3D curves & useful equations to create forms

This guide shows equations that can be used to create curves and how to creating a Curve from Equation in Creo Parametric.

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1. Best Practise How to create 3D curves and useful equations to create forms

2. EQUATIONS – Equations that can be used to create curves and more in Creo Tutorial how to create 3D - curves: https://learningconnector.ptc.com/content/tut - 394/creating - a - curve - from - equation Cartesian Coordinates: x, y, & z The z variable is not necessary, but when used will give the curve that extra dimension. If in doubt, try z = t*10. Sine Cartesian coordinates x = 50 * t y = 10 * sin (t * 360 ) Rhodonea Cartesian coordinates theta = t * 360 * 4 x = 25 + (10 - 6) * cos (theta) +10 * cos ((10/6 - 1) * theta) y = 25 + (10 - 6) * sin (theta) - 6 * sin ((10/6 - 1) * theta) Involute Cartesian coordinates r = 1 ang = 360 * t s = 2 * pi * r * t x0 = s * cos ( ang ) y0 = s * sin ( ang ) x = x0 + s * sin ( ang ) y = y0 - s * cos ( ang ) Logarithmic Cartesian coordinates z = 0 x = 10 * t y = log (10 * t +0.0001 )

4. Talbots /* "c" is a scaling variable. c=10 a= cos (t*360) b=sin(t*360) x=C*a*(1+exp(2)*(b^2)) y=C*b*(1+exp(2)*(b^2 )) Cylindrical Coordinates: r, theta, & z Spiral Cylindrical coordinates r = t theta = 10 + t * (20 * 360) z = t * 3 Circle Spiral Column Cylindrical coordinates theta = t * 360 r = 10 +10 * sin (6 * theta) z = 2 * sin (6 * theta) Helical Wave Cylindrical coordinates r = 5 theta = t * 3600 z = (sin (3.5 * theta - 90)) +24 * t Basket Cylindrical coordinates r = 5 + 0.3 * sin (t * 180) + t theta = t * 360 * 30 z = t * 5 Disc Spiral 2 Cylindrical coordinates R = 50 + t * (120) Theta = t * 360 * 5 Z = 0 Apple Cylindrical coordinates a = 10 r = a * (1 + cos (theta)) theta = t * 360 Spherical Coordinates: rho, theta, & phi Butterfly Ball Spherical coordinates rho = 8 * t theta = 360 * t * 4 phi = - 360 * t * 8 Spherical Helix Spherical coordinates rho = 4 theta = t * 180 phi = t * 360 * 20 UFO Spherical coordinates rho = 20 * t ^ 2 theta = 60 * log (30) * t phi = 7200 * t Unnamed Spherical coordinates rho = 200 * t theta = 900 * t phi = t * 90 * 10

3. Double Arc Epicycloid Cartesian coordinate l = 2.5 b = 2.5 x = 3 * b * cos (t * 360) + l * cos (3 * t * 360) Y = 3 * b * sin (t * 360) + l * sin (3 * t * 360 ) Star Southbound Cartesian coordinate a = 5 x = a * ( cos (t * 360)) ^ 3 y = a * (sin (t * 360)) ^ 3 Leaf Cartesian coordinates a = 10 x = 3 * a * t / (1 + (t ^ 3)) y = 3 * a * (t ^ 2) / (1 + (t ^ 3)) Helix Cartesian coordinates x = 4 * cos (t * (5 * 360)) y = 4 * sin (t * (5 * 360)) z = 10 * t Parabolic Cartesian coordinates x = (4 * t) y = (3 * t) + (5 * t ^ 2) z = 0 Eliptical Helix Cartesian coordinates X = 4 * cos (t * 3 * 360) y = 2 * sin (t * 3 * 360) z = 5 Disc Spiral 1 Cartesian coordinates /* Inner Diameter d = 10 /* Pitch p = 5 /* Revolutions r = 5 /* Height; use 0 for a 2D curve h = 0 x = ((d/2 + p * r * t) * cos ((r * t) * 360)) y = ((d / 2 + p * r * t) * sin ((r * t) * 360)) z = t * h Butterfly a= cos (t*360) b=sin(t*360) c= cos (4*t*360) d=(sin((1/12)*t*360))^5 x=b*( exp (a) - 2* c+d ) y=a*( exp (a) - 2* c+d ) Fish a = cos (t * 360) b = sin (t * 360) /* As "c" increases the fish gets fatter until it transforms into a figure 8. c = 10 x = (C*a - 20*((b)^2)/1.5) y = c * a * b Cappa /* "c" is a scaling variable c=20 /* Revolutions r=1 /* Height h=0 x=c* cos (t*r*360)*sin(t*r*360) y=c* cos (t*r*360) z=t*h Star /* "a" & "b" are scaling variables a=2 b=2 /* If, r=2/3 ---- > astroid /* If, r=2 ---- > ellipse; when a=b, its a circle /* r cannot equal 1 r=2/3 x=a*( cos (t*360))^(2/r) y=b*(sin(t*360))^(2/r) z=0 Bicorn /* "c" is a scaling variable. c=5 a= cos (t*360) b=sin(t*360) x=c*a y=c*(a^2)*(2+a)/(3+b^2)

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