Is there a polar parametric equation

Equation curves are used to model complex geometry, e.g. B. To model tooth profiles or sweeping paths for hydraulic pumps. When you create an equation curve, you identify the equations that define the curve and an area to evaluate the equations.

The equations can be parametric, where X and Y vary as a function of a variable t, or explicit, where Y varies as a function of X. To model a parabola you can e.g. B. use the following equations:
  • Parametric:
  • or

  • Explicit:

2D equation curves support Cartesian and polar coordinate systems. The coordinate system is specified in the mini toolbar for the equation curves.

Polar equation curves indicate coordinates as distance (r) and as angle (a). Parametric equation curves use equations to define r and θ as a function of a variable t. Explicit equation curves use a single equation to define r as a function of a.

Cartesian equation curves use X and Y coordinates. Parametric equation curves use equations to define x and y as a function of a variable t. Explicit equation curves use a single equation to define y as a function of x.

Units, parameters and functions in equation curves

The units in equations must be balanced. To balance the units in equations, it is often necessary to multiply or divide by one or more length units. If the units do not have a common unit of length, the equation text is highlighted in red and an error icon appears next to the mini toolbar.

Equation curves support parameters and functions. However, parameters cannot have the name t because this letter is used as an equation variable. Unsupported functions are:
  • Lower limit
  • blanket
  • Section
  • sign
  • Modulo
  • Rounding

Example equations

Parametric Cartesian
x (t): 4 * cos (1 rad * t) / sqrt (t) * 1 mm

y (t): 4 * sin (1 rad * t) / sqrt (t) * 1 mm

tmin: 0.01

tmax: 6 * PI

Explicitly Cartesian
y (x): x * sin (1 rad * x / 1 mm)

xmin: -1 * PI

xmax: 6 * PI

Parametric polar
r (t): t * 1 mm

θ (t): cos (t * 1 rad) * 1 rad * 5 * PI / 4

tmin: -5 * PI

tmax: 5 * PI

Explicitly polar
r (a): sqrt (a / 1 rad)

amine: 0.01

amax: 12 rad * PI

Examples of the format of equation curves

The following are some formatting examples that are required by certain operators and functions.

Addition / subtraction
Cartesian
x (t): 1 mm * t + 1

y (t): 1 mm * t - 1

Polar
r (t): 1 mm * t + 1

θ (t): 1 rad * t - 1 rad

Explicitly Cartesian
y (x): x + 1
Explicitly polar

r (a): 1 mm * a / 1 rad + 1

Multiplication / division
Cartesian
x (t): 2 mm * t

y (t): 2 mm / t

Polar
r (t): 2 mm * t

θ (t): 2 rad / t

Explicitly Cartesian
y (x): 3 * x / 2
Explicitly polar

r (a): 3 mm * a / 2 rad

Exponentiation
Cartesian
x (t): (t ^ 2) * 1 mm

y (t): 1 mm * pow (t; 2)

Polar
r (t): 1 mm * (t ^ 2)

θ (t): 1 rad * pow (t; 2)

Explicitly Cartesian
y (x): 1 in * (x / 1 mm) ^ 3
Explicitly polar

r (a): 1 mm * ((a / 1 rad) ^ 3)

Trigonometric functions
Cartesian
x (t): 1 mm * sin (1 rad * t) + 1 mm * cos (1 rad * t

y (t): 1 mm * tan (1 rad * t)

Polar
r (t): 1 mm * cos (1 rad * t) + 1 mm * sin (1 rad * t)

θ (t): 1 rad * tan (1 rad * t)

Explicitly Cartesian
y (x): 1 mm * sin (1 rad * x / 1 mm)
Explicitly polar

r (a): 1 mm * cos (a)

Reversed trigonometric functions
Cartesian
x (t): 1 mm * asin (t) / 1 rad + 1 mm * asin (t) / 1 rad

y (t): 1 mm * atan (t) / 1 rad

Polar
r (t): 1 mm * asin (t) / 1 rad

θ (t): acos (t)

Explicitly Cartesian
y (x): 1 mm * acos (x / 1 mm) / 1 rad
Explicitly polar

r (a): 1 mm * acos (a / 1 rad) / 1 rad

Hyperbolic
Cartesian
x (t): 1 mm * sinh (1 rad * t) + 1 mm * cosh (1 rad * t)

y (t): 1 mm * tanh (1 rad * t)

Polar
r (t): 1 mm * cosh (1 rad * t

θ (t): 1 rad * sinh (1 rad * t)

Explicitly Cartesian
y (x): 1 mm * tanh (1 rad * x / 1 mm)
Explicitly polar

r (a): 1mm * cosh (a)

logarithm
Cartesian
x (t): 1 mm * ln (t))

y (t): 1 mm * log (t)

Polar
r (t): 1 mm * log (t

θ (t): 1 rad * ln (t

Explicitly Cartesian
y (x): 1 mm * ln (x / 1 mm)
Explicitly polar

r (a): 1 mm * ln (a / 1 rad)