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Overview
Maya’s animation key tangent parameters are based on frames while Houdini’s are based on seconds instead. Except for this difference, Maya’s tangent "angle" corresponds to Houdini’s "slope" while Maya’s tangent "weight" corresponds to Houdini’s "acceleration". In both cases, the units for a key’s "value" are the same.
The formulas below show how to convert between Maya’s angle/weight and
Houdini’s slope/acceleration parameters for bezier()
expression keys, which
correspond to Maya weighted tangent keys. For Houdini cubic() expression keys
(which only uses slope values), these should be converted to Maya nonweighted
tangent keys.
Variable 
Meaning 


Key’s value. 

Frame containing key in Maya. 

Maya animation key parameter. 

Maya animation key parameter. 

Frame rate (frames per second) in Maya. 

Houdini key "slope" parameter. 

Houdini key "acceleration" parameter. 

An arbitrary time delta where DT is in seconds while DF is in frames. 

An arbitrary value delta. 
Note
Make sure when using trig functions your inputs are in the correct unit (radians or degrees) depending on which tan()
function you use in which software package. For example, VEX and Python tan()
functions expect radians, while the HScript expression tan()
expects degrees.
Maya to Houdini
Although we're using Maya as an example, the formulas below apply to any animation software that expresses their key tangent parameters in frames instead of seconds. Houdini’s animation keys are expressed in seconds so that they are independent of the scene’s frame rate.
The formulas below assume that the converted values are put into Houdini keys
using the bezier()
expression which corresponds to Maya’s weighted tangent
keys. For Maya’s nonweighted tangent keys, these correspond to Houdini
cubic()
expression keys, which only uses slope values.
Angle to slope
Given:
DF = FPS * DT (1) tan(Angle) = DV / DF (2) S = DV / DT (3)
We can derive the formula for slope by rearranging these and substituting:
S = DV / DT (3) = (DF * tan(Angle)) / (DF / FPS) (from 2 and 1 respectively) = (DF * tan(Angle)) * (FPS / DF) = FPS * tan(Angle) (4)
The final formula for slope is:
S = FPS * tan(Angle)
Weight to acceleration
Given:
DF = FPS * DT (1) tan(Angle) = DV / DF (2) tan(Angle) = S / FPS (5, from 4 above) Weight^2 = DF^2 + DV^2 (6) A^2 = DT^2 + DV^2 (7)
We can derive the formula for acceleration by rearranging these and substituting:
DV^2 / DF^2 = S^2 / FPS^2 (8, from 2 and 5) Weight^2 / DF^2 = 1 + DV^2 / DF^2 (6 divided by DF^2) = 1 + S^2 / FPS^2 (from 8) = (FPS^2 + S^2) / FPS^2 ==> DF^2 = (Weight^2 * FPS^2) / (S^2 + FPS^2) (9) A^2 / DF^2 = DT^2 / DF^2 + DV^2 / DF^2 (7 divided by DF^2) = 1 / FPS^2 + DV^2 / DF^2 (from 1, since DT^2 = DF^2 / FPS^2) = 1 / FPS^2 + S^2 / FPS^2 (from 8) = (S^2 + 1) / FPS^2 ==> A^2 = DF^2 * (S^2 + 1) / FPS^2 = ((Weight^2 * FPS^2) * (S^2 + 1)) / ((S^2 + FPS^2) * FPS^2) (from 9) = (Weight^2 * (S^2 + 1)) / (S^2 + FPS^2) ==> A = sqrt( (Weight^2 * (S^2 + 1)) / (S^2 + FPS^2) ) (10)
The final formula for acceleration is:
A = sqrt( (Weight^2 * (S^2 + 1)) / (S^2 + FPS^2) )
Note
Weight cannot be negative.
Houdini to Maya
Slope to angle
We can convert slope to angle by rearranging the slope (S) formula from above to get:
Angle = atan2(S, FPS)
Note
atan2(S, FPS)
is equivalent to atan(S / FPS)
except it is more robust and can compute the correct quadrant. You should use atan2
instead of atan
when possible.
Acceleration to weight
We can rearrange the acceleration (A) formula from above to get:
Weight = sqrt( (A^2 * (S^2 + FPS^2)) / (S^2 + 1) )