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Constants and Functions

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Jeff Hayes edited this page May 13, 2025 · 5 revisions

Table of Contents

Constants

pi
3.14159 ratio between diameter and circumference of a circle
rad
57.29578 degrees in a radian for conversions
clearance
0.2 arbitrary value for space to leave between mating gears

Functions

rad_to_deg( radians )

convert an Angle in Radians to Degrees using formula: 

 (Angle in Radians) × 180°/π = Angle in Degrees
 where 1 Radian = 180/π Degrees = 57.296 Degrees

was called grad(angle).

deg_to_rad( degrees )

convert an Angle in Degrees to Radians using formula: 

 Angle in Degrees × π/180° = Angle in Radians
 rho x π/180° = / 180°/π
 QED degrees/57.29578 --> radians

was called radian( angle )

polar_to_cartesian([radius,angle])

Convert a 2 dimensional position in polar coordinates into Cartesian coordinates.

  • The input vector must have form [radius,angle] were the angles are in degrees.
  • It returns a vector of form [X,Y]

ev(r,rho)

Adjust polar coords given by r (radius?) and rho (angle?) to by a rotation ? or a translation ? 

 return a vector [x,y] ?
 where x will be radius/cosine(rho)
 and y = rad_to_deg(tan(rho) - deg_to_rad(rho))
   i.e. polar_to_cartesian( ev(rb,rho_ra) )

sphere_ev(theta0,theta)

The two angles, theta0 and theta, are used to calculate a mystery value. === sphere_to_cartesian(XYZCoords) convert a 3 dimensional position in polar coordinates into Cartesian coordinates. 

 where XYZCoords is a vector of form [radius,angle,angle] with the angles in degrees
 it returns a vector [X,Y,Z]

is_even(number)

returns 1 when the given number is even and 0 when odd providing a value that, when multiplied by the modulus of a gear, either preserves it, or zeros it in the calculation.

spiral(a, r0, phi)

Function to calculate a scalar value using a*phi + r0.

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