Law Curves



Law Curve


Law curves are an extremely powerful way to integrate mathematical relationships into a CAD model. Law curves are 3D curves that are defined mathematically by entering an expression based on a parameter that cycles through an ordinate or baseline of a function. This parameter cycles from 0 to 1 — in other words, from 0% to 100% of your function.  Values for various axes can be built around this baseline parameter.  For example, if a sine wave across a full revolution (in degrees) is to be modeled, its X axis, or its Xt value will take values from 0 to 360, this means Xt will be defined as Xt = t * 360.

At t=0, Xt will equal 0

At t=.5, Xt will equal 180

at t =1, Xt will equal 360

t will automatically increment across the range from 0 to 1.

Yt and even Zt values for “each” value of Xt can then be assigned.  The result is a a curve that can be used to generate solids or surfaces.


Parabolic trough reflector

Chipping Hammer Handle (.zip)

Sinusoidal Corrugation

Gear Generator (source?)


t will take “all” values from zero to one

Angles are in degrees.

Simple sine wave:

    • a=20
    • t=1
    • xt=t*360
    • yt = a*cos(xt) //in degrees
    • zt = 0 //or some other function

Sample Test Questions

  • What is an example of a component (product, etc.) that might be defined by a law curve (other than a parabolic solar heater).
  • What is the purpose of the “t” parameter?
  • What would be the equation for xt if I wanted to graph a function from xt = -5 to xt = +5?
  • When I generate the sine wave below, I get a very thin, flat wave.  Why does it not look like the sine wave I see in my Trig book?
    • a=1
    • t=1
    • xt=t*360
    • yt = a*sin(xt)
    • zt = 0


Using a Law Curve as a guide:

Sweep_with_a_twist (By John Baker )

Law curve to define helix diameter & pitch