Cinema 4D Tutorial - Formula Spline Control

Published: 18 April 2020
on channel: Pappy's Tutorials

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This tutorial shows you how you can use Xpresso to explore variations in parametric equations, and how to animate the formula spline (xt, yt, zt) parameters.

Intro: 0:00
Basics: 2:18
Complex Formula: 26:00
Complete Animation Tutorial: 47:03
Other Formulas: 1:08:23

You can download a C4D library with example formula splines with parameters here: https://gumroad.com/l/splineformulas

Links:
https://en.wikipedia.org/wiki/Paramet...
https://mathworld.wolfram.com/topics/...
https://en.wikipedia.org/wiki/NACA_ai...

Here are some equations you can paste into a python Xpresso node:

Sin Wave on Cone
#R=Radius, a=frequency, c=wave height, p=position
global xt,yt,zt
#b*c*[p+cos(a*t)]*cos(t)
xt = str(R)+"*"+str(c)+"*["+str(p)+"+cos("+str(a)+"*t)]*cos(t)"
#b*c*[p+cos(a*t)]
yt = str(R)+"*"+str(c)+"*["+str(p)+"+cos("+str(a)+"*t)]"
#b*c*[p+cos(a*t)]*sin(t)
zt = str(R)+"*"+str(c)+"*["+str(p)+"+cos("+str(a)+"*t)]*sin(t)"

Sin Wave on Cylinder
#R=Radius, F=frequency, H=wave height, P=position
global xt,yt,zt
xt = str(R)+"*cos(t)"
yt = str(H)+"*cos(t*"+str(F)+")+"+str(P)
zt = str(R)+"*sin(t)"

Sin Wave on Hyperboloid
#R=Radius, a=frequency, c=wave height
global xt,yt,zt
#b*sqrt[1-sqr(c)*sqr(cos(a*t))]*cos(t)
xt = str(R)+"*sqrt[1+sqr("+str(c)+")*sqr(cos("+str(a)+"*t))]*cos(t)"
yt = str(R)+"*"+str(c)+"*cos("+str(a)+"*t)"
#b*sqrt[1-sqr(c)*sqr(cos(a*t))]*sin(t)
zt = str(R)+"*sqrt[1+sqr("+str(c)+")*sqr(cos("+str(a)+"*t))]*sin(t)"

Sin Wave on Sphere
#R=Radius, a=frequency, c=wave height
global xt,yt,zt
#b*sqrt[1-sqr(c)*sqr(cos(a*t)])*cos(t)
xt = str(R)+"*sqrt[1-sqr("+str(c)+")*sqr(cos("+str(a)+"*t))]*cos(t)"
yt = str(R)+"*"+str(c)+"*cos("+str(a)+"*t)"
#b*sqrt[1-sqr(c)*sqr(cos(a*t))]*sin(t)
zt = str(R)+"*sqrt[1-sqr("+str(c)+")*sqr(cos("+str(a)+"*t))]*sin(t)"

Helix on Sphere
#R=Radius, L=Loops, tn links to Tmin, tx links to Tmax
global xt,yt,zt,tn,tx
xt = "sqrt(1-sqr(t/"+str(L)+"))*cos(t*1*pi)*"+str(R)
if (L==0): yt = "t*0"
else: yt = "t*"+str(R/L)
zt = "sqrt(1-sqr(t/"+str(L)+"))*sin(t*1*pi)*"+str(R)
tn = -L
tx = L

Torus
#R=Radius, P=Pipe Radius, L=Loops
global xt,yt,zt
xt = "("+str(P)+"*sin("+str(L)+"*t)+"+str(R)+")*cos(t)"
yt = ""+str(P)+"*cos("+str(L)+"*t)"
zt = "("+str(P)+"*sin("+str(L)+"*t)+"+str(R)+")*sin(t)"

Cone
#R=Radius, H=Height, L=Loops, W=Wave
global xt,yt,zt
xt = str(R)+"*t/2/pi*cos(t*"+str(L)+")"
yt = str(H)+"*t/2/pi*cos(t*"+str(W)+")"
zt = str(R)+"*t/2/pi*Sin(t*"+str(L)+")"

Rhodenea
#S=Size, mx=x multiplier, my=y multiplier
global xt, yt
xt = "cos("+str(x)+"*t)*cos(t) * "+str(S)
yt = "cos("+str(y)+"*t)*sin(t) * "+str(S)

Wavey Spiral
#parameters are xa,xb, ya,yb, za,zb
global xt,yt,zt
xt = "sin(t/"+str(xa)+")*"+str(xb)+"*t"
yt = "sin(t*"+str(ya)+")*"+str(yb)
zt = "cos(t/"+str(za)+")*"+str(zb)+"*t"

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