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wolf_lib
wolf
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5b946ac7
Commit
5b946ac7
authored
8 years ago
by
Joan Solà Ortega
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Docuementation of interpolate()
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src/processor_motion.h
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5b946ac7
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@@ -427,7 +427,7 @@ class ProcessorMotion : public ProcessorBase
* ```
* where again the operator (*) needs to be defined properly.
*
* ### Defining the operators (*) and (
+
)
* ### Defining the operators (*)
, (+),
and (
-
)
*
* We often break down these 'd' and 'D' deltas into chunks of data, e.g.
*
...
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@@ -438,7 +438,9 @@ class ProcessorMotion : public ProcessorBase
* etc...
*
* which makes it easier to define the operators (+) and (*).
* In effect, defining (*) is now easy:
* In effect, defining (*) is now easy. We examine them below.
*
* #### Operator (*)
*
* - for linear magnitudes, (*) is the regular product *:
* ```
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@@ -452,20 +454,34 @@ class ProcessorMotion : public ProcessorBase
* ```
* dq_I = 1.slerp(tau, dq_F) // '1' is the unit quaternion
* ```
* As for the operator (+), we simply make use of `deltaPlusDelta()`, which is implemented in each derived class.
*
* ###
Computing `d_S`
* ###
# Operator (+)
*
* A
pplying (1), we can define
* A
s for the operator (+), we simply make use of `deltaPlusDelta()`, which is implemented in each derived class.
*
* d_S = d_F (-) d_I
*
* where the operator (-) might be implemented explicitly,
* #### Operator (-)
*
* For the operator (-) we have two options. We might implement it explicitly inside interpolate(),
* or through a `deltaMinusDelta()` defined akin to `deltaPlusDelta()`.
*
* By now, this `deltaMinusDelta()` is not enforced by this class as an abstract method,
* and its implementation in derived classes is up to the user.
*
* The general rule for the operator (-) is that it is the inverse of (+).
* But this needs to be taken carefully, since (+) is not commutative in the general case.
* therefore, we must define this inverse in the following way:
*
* C = B (-) A <==> A (+) C = B (4)
*
* ### Computing `d_S`
*
* Applying (1), we can define
*
* d_S = d_F (-) d_I
*
* with the (-) operator defined according to (4), that is, `d_F = d_I (+) d_S`, as can be also observed in the sketch above.
*
* For simple pose increments, we can use a local implementation:
*
* - for 2D
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