## Choosing the Plotting Backend

Since version 2.2.0, you can choose between two plotting backends: `matplotlib` and `plotly`. By default the `matplotlib` backend is used for quick and simple plotting. If you want to create advanced interactive HTML reports, you can switch to the `plotly` backend by clicking "Plotting" in the menu bar and selecting the desired backend.

## Processing Settings

Trajectopy offers a range of processing options that can be applied to the imported trajectories. These options are:

| Option     | Description                                                                                                                                                                                                                                                                                                                                                                                                                           |
| ---------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Alignment  | Alignment of two trajectories using least squares adjustment. The implemented approach can handle a similarity transformation (translation, rotation, scale), a lever arm (3d vector), and a time shift (scalar). Each parameter can be included or exluded from the adjustment depending on the individual sensor modalities using the `AlignmentSettings`. In addition, preprocessing steps and stochastics can also be configured. |
| Matching   | Matching of two trajectories to establish pose-to-pose correspondencies. After matching both trajectories will have the same number of poses. You can choose from different matching methods in the `MatchingSettings`.                                                                                                                                                                                                               |
| Comparison | Comparison of two trajectories using absolute (ATE) and relative (RPE) metrics. The relative comparison can be configured using the `RelativeComparisonSettings`.                                                                                                                                                                                                                                                                     |

## Alignment Settings

### Preprocessing Settings

- `min_speed` (float): Only poses with a speed above this threshold are considered for alignment.
- `time_start` (float): Only poses with a timestamp above this threshold are considered for alignment. The timestamp is given in seconds and is relative to the first common timestamp of both matched trajectories.
- `time_end` (float): Only poses with a timestamp below this threshold are considered for alignment. The timestamp is given in seconds and is relative to the first common timestamp of both matched trajectories.

### Estimation Settings

- `translation_x` (boolean): Enable or disable x-translation of the similarity transformation.
- `translation_y` (boolean): Enable or disable y-translation of the similarity transformation.
- `translation_z` (boolean): Enable or disable z-translation of the similarity transformation.
- `rotation_x` (boolean): Enable or disable rotation around the X-axis of the similarity transformation.
- `rotation_y` (boolean): Enable or disable rotation around the Y-axis of the similarity transformation.
- `rotation_z` (boolean): Enable or disable rotation around the Z-axis of the similarity transformation.
- `scale` (boolean): Enable or disable scaling of the similarity transformation.
- `time_shift` (boolean): Enable or disable the estimation of time shift.
- `leverarm_x` (boolean): Enable or disable estimation of lever arm in the X-axis.
- `leverarm_y` (boolean): Enable or disable estimation of lever arm in the Y-axis.
- `leverarm_z` (boolean): Enable or disable estimation of lever arm in the Z-axis.
- `sensor_rotation` (boolean): Enable or disable estimation of sensor rotation. Independent of the least squares adjustment, a constant rotational offset can be computed between the rotations of both trajectories after the alignment.

### Stochastics Settings

- `std_xy_from` (float): Standard deviation of XY source position components in meters.
- `std_z_from` (float): Standard deviation of Z source position component in meters.
- `std_xy_to` (float): Standard deviation of XY target position components in meters.
- `std_z_to` (float): Standard deviation of Z target position component in meters.
- `std_roll_pitch` (float): Standard deviation of roll and pitch in radians.
- `std_yaw` (float): Standard deviation of yaw in radians.
- `std_speed_to` (float): Standard deviation of platform speed in (meters per second).
- `error_probability` (float): Probability of error used for stochastic testing.
- `variance_estimation` (boolean): Enable or disable the estimation of the variance factor for a-posteriori variance computation.

### Threshold Settings

Usually, these settings can be left at their default values.

- `metric_threshold` (float): Iteration threshold for the least squares adjustment regarding the metric parameters.
- `time_threshold` (float): Iteration threshold for the least squares adjustment regarding the time shift parameter.


## Matching Settings

- `method` (`MatchingMethod`): The method used for trajectory matching. Choices: `MatchingMethod.NEAREST_SPATIAL`, `MatchingMethod.NEAREST_TEMPORAL`, `MatchingMethod.INTERPOLATION`, `MatchingMethod.NEAREST_SPATIAL_INTERPOLATED`. The methods are described below.
- `max_time_diff` (float): Maximum allowed time difference when matching two trajectories using their timestamps.
- `max_distance` (float): Maximum allowed distance between matched positions during spatial matching.
- `k_nearest` (integer): The number of nearest neighbors to consider during spatial interpolation matching.

## Matching Methods

### Nearest Spatial

This method matches two trajectories by finding the nearest pose in the target trajectory for each pose in the source trajectory. The distance between two poses is computed using the Euclidean distance between their positions.

### Nearest Temporal

This method matches two trajectories using their timestamps by finding the nearest timestamp in the target trajectory for each timestamp in the source trajectory.

### Interpolation

This method matches two trajectories by interpolating the timestamps of one trajectory to the timestamps of the other trajectory. The interpolation is linear for both positions and rotations (SLERP).

### Nearest Spatial Interpolated

This method matches both trajectories spatially by requesting the nearest k positions from the reference trajectory for each pose in the test trajectory. Then, an interpolation is performed using a 3d line fit of the k nearest positions. After this operation, both trajectories will have the length of the test trajectory. This method does not support rotation matching.


## Relative Comparison Settings

- `pair_min_distance` (float): Minimum pose pair distance to be considered during RPE (Relative Pose Error) computation.

- `pair_max_distance` (float): Maximum pose pair distance to be considered during RPE computation.

- `pair_distance_step` (float): Step in which the pose pair distance increases.

- `pair_distance_unit` (`Unit`): Unit of the pose pair distance. Choices: `Unit.METER`, `Unit.SECOND`.

- `use_all_pose_pairs` (boolean): If enabled, overlapping pose pairs will be used for relative metrics calculation.


### RPE Background

For this metric, relative pose-pair differences are compared. The distance between two poses can be specified by the user and can be either time- or distance-based. The comparison involves finding pose pairs separated by a specific distance or time interval, computing the relative translation and rotation between the reference and estimated pose pairs, and calculating the translational and rotational difference normalized by the distance or time that separated the poses.

1. Find pose pair separated by e.g. 100 m in reference trajectory. This pair represents the start and end poses of a sequence of size $N$.
2. Find the corresponding pose pair in estimated trajectory
3. Compute relative translation and rotation between the reference pose pair

    $\Delta_{P~ref} = P_{ref, 1}^{-1} \cdot P_{ref, N}$

4. Compute relative translation and rotation between the estimated pose pair

    $\Delta_{P~est} = P_{est, 1}^{-1} \cdot P_{est, N}$

5. Compute transformation between 3) and 4)

6. Compute translation and rotation error from 5)

7. Divide 6) by the distance or the time that separated both poses (e.g. 100 m).

This metric does not require both trajectories to be aligned. Units are m/m: %, deg/m for distance based comparison and m/s, deg/s for time-based comparison. 

Example:

- Minimum pose distance: 100
- Maximum pose distance: 800
- Distance step: 100
- Distance unit: Meter

Results in pose distances: [100 m, 200 m, 300 m, 400 m, 500 m, 600 m, 700 m, 800 m]

Furthermore, the user can choose to either use consecutive pose pairs (non-overlapping) or all posible pairs (overlapping).

## Report Settings

### Visualization Settings

- `single_plot_height` (int): The height of a single plot. Default value is 450.
- `two_subplots_height` (int): The height of two subplots. Default value is 540.
- `three_subplots_height` (int): The height of three subplots. Default value is 750.
- `scatter_max_std` (float): The upper colorbar limit is set to the mean plus this value times the standard deviation of the data. This is useful to prevent outliers from dominating the colorbar. Default value is 4.0.
- `ate_unit_is_mm` (bool): Indicates whether the unit of Absolute Trajectory Error (ATE) is millimeters. Default value is False.
- `directed_ate` (bool): Indicates whether the ATE is split into along-, horizontal-cross- and vertical-cross-track direction. Default value is True.
- `histogram_opacity` (float): The opacity of the histogram bars. Default value is 0.7.
- `histogram_bargap` (float): The gap between histogram bars. Default value is 0.1.
- `histogram_barmode` (str): The mode of displaying histogram bars. Default value is "overlay".
- `histogram_yaxis_title` (str): The title of the y-axis in the histogram. Default value is "Count".
- `plot_mode` (str): The mode of displaying plots. Default value is "lines+markers".
- `scatter_mode` (str): The mode of displaying scatter plots. Default value is "markers".
- `scatter_colorscale` (str): The colorscale for scatter plots. Default value is "RdYlBu_r".
- `scatter_axis_order` (str): The order of the axes in scatter plots. Default value is "xy". If 3d plotting is desired, also specify "z".
- `scatter_marker_size` (int): The size of markers in scatter plots. Default value is 5.
- `scatter_show_individual_dofs` (bool): Indicates whether to show scatter plots for each degree of freedom. Default value is False.

#### ATE Frame Definition

By default, the ATE is split into along-, horizontal-cross- and vertical-cross-track directions. The along-track direction is defined as positive in the direction of travel. The horizontal cross-track direction is defined as positive to the right of the along-track direction. The vertical cross-track direction is defined as positive upwards. The following image illustrates the frame definition.

<img src="https://raw.githubusercontent.com/gereon-t/trajectopy/main/.images/along_cross_frames.png" alt="ate_frames" width="400"/>

### Mapbox Settings

These settings currently only apply to trajectory only plots without deviations.

- `scatter_plot_on_map` (bool): Indicates whether the trajectory should be plotted onto a map. Default value is False.
- `scatter_mapbox_style` (str): The style of the map. For some styles, a Mapbox token is required. Default value is "open-street-map".
- `scatter_mapbox_zoom` (int): The zoom level of the map. Default value is 15.
- `scatter_mapbox_token` (str): The Mapbox token. Default value is "".

The mapbox token can be obtained from [https://www.mapbox.com/](https://www.mapbox.com/) after creating a free account. The token can be set in multiple ways:

- As a command line argument `--mapbox_token`.
- As an environment variable `MAPBOX_TOKEN`.
- Directly in the settings file.
- In the GUI settings dialog.
- By placing a file named `.mapbox_token` in the current working directory.

### Position Units and Names

- `pos_x_name` (string): Name for the X-axis position. Default: "x".
- `pos_y_name` (string): Name for the Y-axis position. Default: "y".
- `pos_z_name` (string): Name for the Z-axis position. Default: "z".
- `pos_x_unit` (string): Unit for the X-axis position, Default: "m".
- `pos_y_unit` (string): Unit for the Y-axis position, Default: "m".
- `pos_z_unit` (string): Unit for the Z-axis position, Default: "m".
- `directed_pos_dev_x_name` (string): Name for the directed position deviation in along-track direction. Default: "along".
- `directed_pos_dev_y_name` (string): Name for the directed position deviation in horizontal cross-track direction. Default: "cross-h".
- `directed_pos_dev_z_name` (string): Name for the directed position deviation in vertical cross-track direction. Default: "cross-v".

### Rotation Units and Names

- `rot_x_name` (string): Name for the roll rotation. Default: "roll".
- `rot_y_name` (string): Name for the pitch rotation. Default: "pitch".
- `rot_z_name` (string): Name for the yaw rotation. Default: "yaw".
- `rot_unit` (string): Unit symbol for rotation. Default: "°".

### Export Settings

- `single_plot_export` (ExportSettings): The export settings for single plots. Default value is an instance of ExportSettings with width=800 and height=450.
- `two_subplots_export` (ExportSettings): The export settings for two subplots. Default value is an instance of ExportSettings with width=800 and height=540.
- `three_subplots_export` (ExportSettings): The export settings for three subplots. Default value is an instance of ExportSettings with width=800 and height=750.


### Export Settings

- `format` (string): The export format. Choices: "png", "svg", "jpeg", "webp". Default: "png".
- `height` (integer): The export height in pixels. Default: 500.
- `width` (integer): The export width in pixels. Default: 800.
- `scale` (integer): The export scale. Default: 6.


## Matplotlib Plotting Settings (MPLPlotSettings)

- `colorbar_show_zero_crossing` (bool): Indicates whether the colorbar should show zero. Default value is True.
- `colorbar_steps` (int): The number of steps in the colorbar. Default value is 4.
- `scatter_hide_axes` (bool): Indicates whether the axis should be hidden. Default value is False.
- `scatter_smooth` (bool): Indicates whether the data defining the color of a scatter plot should be smoothed. Default value is False.
- `scatter_smooth_window` (int): The window size for smoothing the scatter plot. Default value is 5.
- `colorbar_max_std` (float): The upper colorbar limit is set to the mean plus this value times the standard deviation of the data. This is useful to prevent outliers from dominating the colorbar. Default value is 3.0.
- `ate_unit_is_mm` (bool): Indicates whether the unit of Absolute Trajectory Error (ATE) is millimeters. Default value is False.
- `hist_as_stairs` (bool): Indicates whether the histogram should be displayed as stairs. Default value is False.
- `directed_ate` (bool): Indicates whether the ATE is split into along-, horizontal-cross- and vertical-cross-track direction. Default value is False.
- `scatter_3d` (bool): Indicates whether the scatter plot should be 3D. Default value is False.
- `dofs_tab` (bool): Indicates whether the degrees of freedom tab should be shown. Default value is True.
- `velocity_tab` (bool): Indicates whether the velocity tab should be shown. Default value is True.
- `height_tab` (bool): Indicates whether the height tab should be shown. Default value is True.
