Equation Curve Formula Reference

Units, Parameters, and Functions in Equation Curves

Equation curves support parameters and functions. The exception for parameters is that you cannot have a parameter named “t,” because that is used for the variable in equations. Unsupported functions are:

• Floor
• Ceiling
• Abs
• Sign
• % Modulo

2D Equation Formulas

	Cartesian	Polar	Explicit Cartesian	Explicit Polar
Addition/Subtraction	x(t): 1 mm * t + 1 y(t): 1 mm * t - 1	r(t): 1 mm * t + 1 θ(t): 1 rad * t - 1 rad	y(x): x + 1	r(a): 1 mm * a / 1 rad + 1
Multiplication/Division	x(t): 2 mm * t y(t): 2 mm / t	r(t): 2 mm * t θ(t): 2 rad / t	y(x): 3 * x / 2	r(a): 3 mm * a / 2 rad
Exponents	x(t): (t^2) * 1 mm y(t): 1 mm * pow(t;2)	r(t): 1 mm * (t^2) θ(t): 1 rad * pow(t;2)	y(x): 1 in * (x / 1 mm)^3	r(a): 1 mm * ((a / 1 rad)^3)
Trig Functions	x(t): 1 mm * sin(1 rad * t) + 1 mm * cos(1 rad * t y(t): 1 mm * tan(1 rad * t)	r(t): 1 mm * cos(1 rad * t) + 1 mm * sin(1 rad * t) θ(t): 1 rad * tan(1 rad * t)	y(x): 1 mm * sin(1 rad * x / 1 mm)	r(a): 1 mm * cos(a)
Inverse Trig Functions	x(t): 1 mm * asin(t) / 1 rad + 1 mm * asin(t) / 1 rad y(t): 1 mm * atan(t) / 1 rad	r(t): 1 mm * asin(t) / 1 rad θ(t): acos(t)	y(x): 1 mm * acos(x / 1 mm) / 1 rad	r(a): 1 mm * acos(a / 1 rad) / 1 rad
Hyperbolic	x(t): 1 mm * sinh(1 rad * t) + 1 mm * cosh(1 rad * t) y(t): 1 mm * tanh(1 rad * t)	r(t): 1 mm * cosh(1 rad * t θ(t): 1 rad * sinh(1 rad * t)	y(x): 1 mm * tanh(1 rad * x / 1 mm)	r(a): 1 mm * cosh(a)
Log	x(t): 1 mm * ln(t) ) y(t): 1 mm * log(t)	r(t): 1 mm * log(t θ(t): 1 rad * ln(t	y(x): 1 mm * ln(x / 1 mm)	r(a): 1 mm * ln(a / 1 rad)

3D Equation Formulas

This table shows examples of the formatting required to use certain operators and functions.

	Cartesian	Cylindrical	Spherical
Addition/Subtraction	x(t): 1 mm * t + 1 mm y(t): 1 mm * t - 1 mm z(t): 1 mm * t - 1 mm	r(t): 1 mm * t + 1 mm θ(t): 1 rad * t + 1 rad z(t): 1 mm * t - 2 mm	r(t): 1 mm * t + 1 mm ϕ(t): 1 rad * t + 1 rad θ(t): 1 rad + t - 1 rad
Multiplication/Division	x(t):2 mm * t y(t):2 mm / t z(t): 2 mm / t	r(t): 3 mm * t θ(t): 2 rad * t z(t): 2 mm * t / 2	r(t): 3 mm *t ϕ(t): 2 rad * t θ(t): 2 rad / 2
Exponents	x(t): (t ^ 2) * 1 mm y(t): 1 mm * pow(t;2) z(t): 1 mm * pow(t;2)	r(t): 1 mm * (t ^ 2) θ(t): 1 rad * pow(t;2) z(t): 1 mm * (t ^ (1/2))	r(t): 1 mm * (t ^ 2) ϕ(t): 1 rad * pow(t;2) θ(t): 1 rad * (t ^ (1/2))
Trig Functions	x(t): 1 mm * sin(1 rad * t) + 1 mm * cos(1 rad * t) y(t): 1 mm * tan(1 rad * t) z(t): 1 mm * tan(1 rad * t)	r(t): 1 mm * cos(1 rad * t) θ(t): 1 rad * sin(1 rad * t) z(t): 1 mm * tan (1 rad * t)	r(t): 1 mm * cos(1 rad * t) ϕ(t): 1 rad * sin(1 rad * t) θ(t): 1 rad * tan(1 rad * t)
Inverse Trig Functions	x(t): 1 mm * asin(t) / 1 rad + 1 mm * asin(t) / 1 rad y(t): 1 mm * atan(t) / 1 rad z(t): 1 mm * atan(t) / 1 rad	r(t): 1 mm * acos(t) / 1 rad θ(t): asin(t) z(t): 1 mm * atan(t) / 1 rad	r(t): 1 mm * acos(t) / 1 rad ϕ(t): asin(t) θ(t): atan(t)
Hyperbolic	x(t): 1 mm * sinh(1 rad * t) + 1 mm * cosh(1 rad * t) y(t): 1 mm * tanh(1 rad * t) z(t): 1 mm * tanh(1 rad * t)	r(t): 1 mm * cosh(1 rad * t) θ(t): 1 rad * sinh(1 rad * t) z(t): 1 mm * tanh(1 rad * t)	r(t): 1 mm * cosh(1 rad * t) θ(t): 1 rad * sinh(1 rad * t) ϕ(t): 1 rad * tanh(1 rad * t)
Log	x(t): 1 mm * ln(t) y(t): 1 mm * log(t) z(t): 1 mm * log(t)	r(t): 1 mm * log(t) θ(t): 1 rad * ln(t) z(t): 1 mm * ln(t)	r(t): 1 mm * log(t) ϕ(t): 1 rad * ln(t) θ(t): 1 rad * ln(t)