To calculate affine transformation parameters with six free parameters.

## Project Description

## affine6p

To calculate affine transformation parameters with six free parameters.

## nudged^{0.3.1}

A Python lib to estimate scale, rotation, and translation between two sets of 2D points. Applicable for example in cases where one wants to move objects by multiple fingers or where a large number of points from an eye tracker device are wanted to be corrected based on a few calibration points. In general, you can apply nudged in any situation where you want to move a number of points based on a few sample points.

Mathematically speaking, nudged is an optimal least squares estimator for affine transformation matrices with uniform scaling, rotation, and translation and without reflection or shearing. The estimation has time complexity of O(*n*) that consists of *6n+22* multiplications and *11n+19* additions, where *n* is the cardinality (size) of the point sets. In other words, nudged solves an affine 2D to 2D point set registration problem in linear time.

Available also in JavaScript.

### Install

`$ pip install nudged`

### Usage

You have lists of points for the **domain** and **range** of the tranformation function to be estimated:

dom = [[0,0], [2,0], [ 1,2]] ran = [[1,1], [1,3], [-1,2]]

Compute optimal tranformation based on the points:

trans = nudged.estimate(dom, ran);

Apply the transformation to other points:

trans.transform([2,2]) # [-1,3]

To explore the estimated transformation, you can:

trans.get_matrix() # [[0,-1, 1], # [1, 0, 1], # [0, 0, 1]] trans.get_rotation() # 1.5707... = π / 2 (radians) trans.get_scale() # 1.0 trans.get_translation() # [1, 1]

### API

#### nudged.estimate(domain, range)

**Parameters**

*domain*: list of [x,y] points*range*: list of [x,y] points

The *domain* and *range* should have equal length. Different lengths are allowed but additional points in the longer list are ignored.

**Return** a new *nudged.Transform(…)* instance.

#### nudged.estimate_error(transform, domain, range)

Compute mean squared distance between the point pairs of the domain after the given transformation and the range. If the transform was estimated with the given domain and range, then the result is the mean squared error (MSE) of the estimation.

**Parameters**

*transform*: a*nudged.Transform*instance*domain*: list of [x,y] points*range*: list of [x,y] points

**Return** a float, the mean squared distance between the range and transformed domain point pairs.

**Usage example**:

dom = [[0, 0], [1, 1], [2, 2]] ran = [[0,-1], [1, 2], [2,-1]] t = nudged.estimate(dom, ran) mse = nudged.estimate_error(t, dom, ran) # mse == 2.0

#### nudged.version

Contains the module version string equal to the version in *setup.py*.

#### nudged.Transform(s, r, tx, ty)

An instance returned by the *nudged.estimate(…)*.

In addition to the methods below, it has attributes *s*, *r*, *tx*, *ty* that define the augmented transformation matrix:

|s -r tx| |r s ty| |0 0 1|

##### nudged.Transform#transform(points)

**Return** an list of transformed points or single point if only a point was given. For example:

trans.transform([1,1]) # [2,2] trans.transform([[1,1]]) # [[2,2]] trans.transform([[1,1], [2,3]]) # [[2,2], [3,4]]

##### nudged.Transform#get_matrix()

**Return** an 3x3 augmented transformation matrix in the following list format:

[[s,-r, tx], [r, s, ty], [0, 0, 1]]

##### nudged.Transform#get_rotation()

**Return** rotation in radians.

##### nudged.Transform#get_scale()

**Return** scaling multiplier, e.g. `0.333` for a threefold shrink.

##### nudged.Transform#get_translation()

**Return** `[tx, ty]` where `tx` and `ty` denotes movement along x-axis and y-axis accordingly.

### For developers

Follow instructions to install pyenv <http://sqa.stackexchange.com/a/15257/14918>`_ and then either run quick tests:

$ python2.7 setup.py test

or comprehensive tests for multiple Python versions in `tox.ini`:

$ eval "$(pyenv init -)" $ pyenv rehash $ tox

### Versioning

### License

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Wheel | py2.py3 | Mar 1, 2018 |