gearbox.mathutils#

Small geometry and trigonometry helpers shared across the package.

Unless a name says otherwise, angles passed to or returned by public functions are in degrees, which is the convention used by gear standards and by the user-facing models.

involute(angle)[source]#

Return the involute function inv(alpha) = tan(alpha) - alpha.

Parameters:

angle (float) – Pressure angle in degrees.

Returns:

The involute function value (dimensionless, i.e. an angle in radians).

Return type:

float

inverse_involute(value, tolerance=0.0)[source]#

Return the angle whose involute function equals value.

Solved by bisection on [0, pi/2], down to machine precision unless a looser tolerance is requested.

Parameters:

  • value (float) – Involute function value (radians).

  • tolerance (float) – Optional absolute tolerance on the involute function to stop earlier.

Returns:

The pressure angle in degrees.

Return type:

float

sign(number)[source]#

Return -1, 0 or 1 according to the sign of number.

Return type:

int

cartesian_to_polar(x, y)[source]#

Convert a Cartesian vector to polar coordinates.

Parameters:

  • x (float) – Component along the x axis.

  • y (float) – Component along the y axis.

Returns:

[radius, angle] with the angle in radians, measured from the x axis. The angle of the null vector is arbitrarily 0.

Return type:

list[float]

polar_to_cartesian(radius, angle)[source]#

Convert polar coordinates to a Cartesian vector.

Parameters:

  • radius (float) – Radial coordinate.

  • angle (float) – Angular coordinate in radians.

Returns:

[x, y].

Return type:

list[float]

rotate(coords, angle, center=(0, 0))[source]#

Rotate points counter-clockwise around center.

Parameters:
Returns:

The rotated points as [x, y] lists.

Return type:

list[list[float]]