Knowledge Base

12 Analysis variables

12 Analysis Variables

The Track3D results file is an Excel file containing the 3D coordinates of the samples collected by EthoVision, and a number of position and movement variables calculated from those coordinates.

Raw Data

Block #

Indicates the block number the sample belongs to. A block is a set of successive valid samples. Within a block there may be samples interpolated using adjacent samples. Interpolation can be done for missing samples (see page 71). Whether a missing sample was replaced by interpolated values is indicated by the interpolation code (see below). Different blocks are separated by a number of missing samples. This is why there is a time gap between the end of a block and the start of the next one (Figure 22). Those missing samples were not interpolated as 12 Analysis variables they formed a sequence longer than the limits specified at interpolation (see page 71). Analysis variables are calculated for each sample using the coordinate values of that sample and at least one preceding sample. Because the samples immediately preceding the first sample of a block are missing by definition, the variables are not calculated for that sample.

Line #

Indicates the line number of the original sample. In a boundary between blocks the line numbers differ by more than one since a number of missing, non-interpolated samples have been removed.

Time

Indicates the time the sample was collected relative to the start of the EthoVision trial. If you started a trial from a specific time or frame number of the video file, the time is still the time since the start of the trial, not from the begin of the video file! It can happen that the first lines of the recording are not included in the file. This depends on your interpolation settings which may exclude those points. Figure 22 Boundary between two successive blocks 1 and 2. The end time of block 1 is 21.32 s, while the start time of block 2 is 21.56 s. This means that an interval of 0.24 s has been excluded from analysis. 12 Analysis variables

x, y, z columns

Indicate the 3D coordinates in mm of the supposed center of the tracked animal. The axis origin (0,0,0) and the axis orientation depend on the calibration used to obtain the 3D data. Inters. err. Indicates the intersection error, in pixels, for that sample. Intersection error is the distance between two lines in the 3D space connecting each camera with the object found. If the two cameras provide two values of distance, the smallest value is taken. This value is always lower than the maximum intersection error, because If this distance is greater than the sample is removed from the results file.

Plume code

Indicates where the subject is located relative to the supposed plume cone (see Figure Figure 24): Figure 23 Example of x coordinate of a sample. Figure 24 Examples of plume codes for three data points. 12 Analysis variables

Interp. code

Indicates whether the current 3D coordinates were obtained from measured 2D coordinates (that is, values exported by EthoVision) or interpolated 2D coordinates. 1 - 2D coordinates Interpolated for both cameras 2 - 2D coordinates measured for one camera and interpolated for the other 12 Analysis variables

Path Shape

Path 3d

The distance moved from the starting point of the present block up to the current sample. It measured as the sum of the segments joining adjacent samples and is expressed in mm. Figure 25 Example of Path 3d. Dots are sample points in the 3D space. The sample s0 is the start of the block. Path 3d equals: d1 for sample s1, d1+d2 for sample s2, d1+d2+d3 for sample s3, etc. 12 Analysis variables

Path xy

The distance moved (in mm) up to the current sample projected on the x-y plane. Figure 26 Example of Path xy. Dark dots are the projection of the samples on the x-y plane. Path xy equals: d1 for sample s1, d1+d2 for sample s2. d1+d2+d3 for sample s3, etc. 12 Analysis variables

Path xz

The distance moved (in mm) up to the current sample projected on the x-z plane. Figure 27 Example of Path xz. Dark dots are the projection of the samples on the x-z plane. Path xz equals: d1 for sample s1, d1+d2 for sample s2, d1+d2+d3 for sample s3, etc. 12 Analysis variables

Tortuosity 3d

Equals the value of Path 3d divided by the length of the straight line connecting the starting sample of the block and the current sample. Tortuosity 3d is a dimensionless number. It can only be equal to or larger than 1. When the samples in a block form a perfectly straight line, tortuosity is 1. Figure 28 Example of Tortuosity 3d. l3 is the straight line connecting the starting sample of the block and sample s3. See also Figure 25. Tortuosity 3d for sample s3= (d1+d2+d3)/ l3 12 Analysis variables

Tortuosity xy

Equals the value of Path xy divided by the length of the straight line connecting the projection of the starting sample of the block and the current sample on the x-y plane. Tortuosity xy is a dimensionless number. It can only be >= 1. Figure 29 Example of Tortuosity xy. l3 is the straight line connecting the projection of the starting sample of the block and the sample s3 on the x-y plane. See also Figure 26. Tortuosity xy for sample s3= (d1+d2+d3)/ l3. 12 Analysis variables

Tortuosity xz

Equals the value of Path xz divided by the length of the straight line connecting the projection of the starting sample of the block and the current sample on the x-z plane. Tortuosity xz is a dimensionless number. It can only be >= 1. Figure 30 Example of Tortuosity xz. l3 is the straight line connecting the projection of the starting sample of the block and the sample s3 on the x-z plane. See also Figure 27. Tortuosity xz for sample s3= (d1+d2+d3)/ l3. 12 Analysis variables

Speed

Velocity x

The component on the x axis of the velocity vector calculated for the current sample. This vector is calculated from a number of samples around the current one using a cubic spline function (see page 98). Velocity x is expressed in mm/s and can be negative or positive: Positive values when the animal is moving in the positive direction of the x axis (the x coordinate is increasing), negative in the other case. Figure 31 Example of Velocity x. For each sample sk a velocity vector vk is computed. Velocity x is the component of vk on the x axis. 12 Analysis variables

Velocity y

The component on the y axis of the velocity vector calculated for the current sample (see Speed on page 98). Velocity y is expressed in mm/s and can be negative or positive: Positive values when the animal is moving in the positive direction of the y axis (the y coordinate is increasing), negative in the other case. Figure 32 Example of Velocity y. For each sample sk a velocity vector vk is computed. Velocity y is the component of vk on the y axis. 12 Analysis variables

Velocity z

The component on the z axis of the velocity vector calculated for the current sample (see Speed on page 98). Velocity z is expressed in mm/s and can be negative or positive: Positive values when the animal is moving in the positive direction of the z axis (the z coordinate is increasing), negative in the other case. Figure 33 Example of Velocity z. For each sample sk a velocity vector vk is computed. Velocity z is the component of vk on the z axis. 12 Analysis variables

Speed

The scalar, absolute value of the velocity vector in the 3D space. The velocity vector is calculated for each sample sk with one of the following formulas, according to how many samples are present around it. When only 1 sample sk-1 occurs before sk: Velocity vk = (pk - pk-1)/ (tk - tk-1). When 1 sample sk-1 occurs before and another sk+1 occurs after sk: Velocity vk = (pk+1 - pk-1)/ (tk+1 - tk-1) When more samples are available around sk (as in most cases): Velocity is the value of the derivative of a cubic spline function through all samples of that block, at sample sk. Figure 34 Example of Speed. vk is the velocity vector calculated for each sample sk. See the text for details. 12 Analysis variables Where p is the X,Y,Z coordinates and t is the time of the sample. Speed is expressed in mm/s, and can only have positive values.

Speed xy

The scalar, absolute value in mm/s of the component of velocity on the x-y plane. It is calculated with the formula of the Pythagorean theorem from Velocity x and Velocity y. Speed xy is expressed in mm/s. Because of the way it is defined, Speed xy can only have positive values. Figure 35 Example of Speed xy. Speed xy is the absolute value of the vector obtained from the components of vk on the x-y plane. 12 Analysis variables

Heading Angles

Track xv

The angle in the 3D space formed by the velocity vector vk (see Speed

above) and the x axis. Track xv is expressed in degrees and can only be positive, no matter wether the animal is moving to higher or lower y or z values. Frequent angles being around 90 degrees may indicate cross-wind flight. Because Track3D assumes the wind is going in the direction of the x axis defined in calibration, it follows that: When the animal is pointing exactly against the wind (less positive x values), then Track xv =0. When the animal is pointing in the same direction as the wind, Track xy = 180. Contrary to Course xv (see page 102), Track xv does not consider any effect of the air flow inside the test chamber. Figure 36 Example of Track xv. Note that the angle formed by the velocity vector and the x direction can lay on any plane passing by x, depending on the orientation of the vector. 12 Analysis variables

Track xy

The angle in the x-y plane formed by the component of the velocity vector vk on the x-y plane and the x direction. Track xy is expressed in degrees and can be positive or negative: Positive when the y component of the velocity vector is positive (like in the figure above, where the animal is moving to the right, that is, to higher values of the y coordinate), negative in the opposite cases. Note: When the animal points exactly against the wind (less positive x values), then Track xy =0. When the animal points exactly to the same direction as the wind, Track xy = 180. When the animal moves along the x axis, Track xy may have very different values for adjacent samples, for example -170 at time k and + 170 at time k+1. The change in Track xy (= Angular change xy) is not 170-(-170) = +340, but 20 like in circular statistics. Figure 37 Example of Track xy. 12 Analysis variables

Track xz

The angle in the x-z plane formed by the component of the velocity vector vk on the x-z plane and the x direction. Track xz is expressed in degrees and can be positive or negative: Positive when the z component of the velocity vector is positive (like in the figure above, where the animal is moving to higher values of the z coordinate), negative in the other cases.

Course xv

It is calculated as Track xv, but considering the effect of air speed and direction. It is essentially the heading direction from the point of view of an observer who would move with the air. First consider the vector 'Heading relative to air', which is the 'intended' velocity and direction of movement in absence of wind. The actual heading is the resultant of this vector and the wind velocity vector. Figure 38 Example of Track xz. 12 Analysis variables Course xv is the angle in the 3D space formed by the vector 'Heading relative to air' and the x direction (see Figure 36 for an example - the vector 'Heading relative to air should replace vk). Course xv is expressed in degrees and can only be positive. Course values are calculated assuming that the wind direction is the same as the x axis. If you have made a calibration with the origin closer to the downwind screen, the wind direction is opposite to the x axis Figure 39 Course is synonymous of Heading relative to air. Track is the Actual heading. Figure 40 Example of Course xv. 12 Analysis variables direction. To obtain correct values of course, enter a negative value of wind speed (see page 64).

Course xy

It is calculated as Track xy, but considering the effect of air speed and direction. Course xy is expressed in degrees and can be positive or negative: Positive when the y component of the velocity vector is positive (like in the figure above, where the animal is moving to higher values of the y coordinate), negative in the other cases. Course values are calculated assuming that the wind direction is the same as the x axis. If you use a calibration with the origin closer to the downwind screen than to the upwind screen, the wind direction is opposite to the x axis direction. To obtain correct values of course, enter a negative value of air speed (see page 64). Figure 41 Example of Course xy. 12 Analysis variables

Course xz

It is calculated as Track xz, but considering the effect of air speed and direction. Course xz is expressed in degrees and can be positive or negative: Positive when the z component of the velocity vector is positive (like in the figure above, where the animal is moving to higher values of the z coordinate), negative in the other case. Course values are calculated assuming that the wind direction is the same as the x axis. If you have made a calibration with the origin closer to the downwind screen, the wind direction is opposite to the x axis direction. To obtain correct values of course, enter a negative value of air speed (see page 64).

Drift xv

It is calculated as the difference Track xv - Course xv. It is the change in the heading angle in the 3D space, due to the wind. Drift xv is expressed in degrees and can only be positive. Drift values are calculated assuming that the wind direction is the same as the x axis. If you have made a calibration with the origin closer to the downwind screen, the wind direction is opposite to the x axis Figure 42 Example of Course xz. 12 Analysis variables direction. To obtain correct values of drift, enter a negative value of air speed (see page 64).

Drift xy

It is calculated as the difference Track xy - Course xy. It is the change in the heading angle in the x-y plane, due to the wind. Drift xy is expressed in degrees and can be positive or negative, with the same sign as Track xy and Course xy for the same sample. This is because the wind direction coincides with the x direction, so Track xy Figure 43 Example of Drift xv. Figure 44 Example of Drift xy. 12 Analysis variables cannot be on the other side of the x axis relative to Course xy and vice versa. Drift values are calculated assuming that the wind direction is the same as the x axis. If you have made a calibration with the origin closer to the downwind screen, the wind direction is opposite to the x axis direction. To obtain correct values of drift, enter a negative value of air speed (see page 64).

Drift xz

It is calculated as the difference Track xz - Course xz. It is the change in the heading angle in the x-z plane, due to the wind. Figure 45 Example of Drift xz. 12 Analysis variables Drift xz is expressed in degrees and can be positive or negative, and has the same sign as Track xz and Course xz. Drift values are calculated assuming that the wind direction is the same as the x axis. If you have made a calibration with the origin closer to the downwind screen, the wind direction is opposite to the x axis direction. To obtain correct values of drift, enter a negative value of air speed (see page 64).

Angular Changes (turns)

General information

Contrary to heading variables, which are calculated from velocity vectors, angular changes are calculated from the coordinates of the samples. In Track3D, any turn to the right of the segment joining sk to sk-1 results in a positive angular change for the sk sample point. Any turn to the left results in a negative value. This is independent of the direction of movement (e.g. towards lower/higher values of x). Figure 46 Please take this picture into account when interpreting angular change values. 12 Analysis variables

Ang. ch. xv

Stands for Angular change xv. It is calculated as the difference between the angles in the 3D space formed by the segments joining sk to sk-1 and sk to sk+1, and the x direction (see the figure below). Angular change xv can also be seen as: Figure 47 Example of Angular change xv. Figure 48 Example of Angular change xv calculated by translating the vector sk - sk+1 in such a way that it starts from sk-1. (the translated point s'k+1 is shown in grey). Angular change xv is the difference between the two highlighted angles. 12 Analysis variables Angular change xv is expressed in degrees and can be positive or negative. Its sign depends on which heading value is bigger between the two, and therefore does not contain information about the direction of movement, it gives an indication on how strongly the animal make turns (see also Track xv).

Ang. ch. xy

Stands for Angular change xy. It is calculated as the difference between the angles in the x-y plane formed by the projection of the segments joining sk to sk-1 and sk to sk+1 on the x-y plane, and the x direction. Angular change xy is expressed in degrees and can be positive or negative: Positive for a right turn, negative for a left turn. See also the notes on page 113. Figure 49 Left: Example of Angular change xy. Right: The angles formed by the segments sk-sk-1 and sk-sk+1 with the x direction are both positive (right turns). The difference is positive. 12 Analysis variables

Ang. ch. xz

Stands for Angular change xz. It is calculated as the difference between the angles in the x-z plane formed by the projection of the segments joining sk to sk-1 and sk+1 on the x-z plane, and the x direction. Angular change xz is expressed in degrees and can be positive or negative: Positive when the turn is towards more positive values of the z coordinate (right turn), negative in the other cases. See also the notes on page 113. Figure 50 Left: Example of Angular change xz. Right: The angles formed by the segments sk-sk-1 and sk-sk+1 with the x direction are positive and negative, respectively. Tip: rotate mentally the x-z plane in such a way that the x axis points to your right (see the picture at the bottom). You see that the first angle is positive (right turn) and the second negative (left turn). The difference is more negative (seen from the x-z plane, the overall turn is to the left). 12 Analysis variables

Ang. ch. 3d

Stands for Angular change 3d. It is calculated as the angle in the 3D space formed by the segment joining sk and sk+1 and the prolongation of the segment joining sk and sk-1. Angular change 3d can also be seen as: Angular change 3d is expressed in degrees and can only be positive. Figure 51 Example of Angular change 3d. Angular change 3d is the angle in the 3D space formed by the velocity vector and the prolongation of the previous velocity vector. Figure 52 Example of Angular change 3d, calculated by translating the vector sk - sk+1 in such a way that it starts from sk-1. (the translated point s'k+1 is shown in grey). Angular change 3d is the highlighted angle. 12 Analysis variables

Questions About Angular Changes

How are track and angular changes related?

In general, angular change is the change in heading (track) between that sample and the previous, for the corresponding plane. For

example, angular change xy at sample k corresponds to track xy at

sample k minus track xy at sample k-1. However, when the track value changes sign from one sample to the next, Angular change follows the rule of circular statistics. For example, when the animal moves along the x axis, Track xy may have very different values for adjacent samples, for example -170 at time k and + 170 at time k+1. The change in Track xy (= Angular change xy) is not 170- (-170) = +340, but 20 like in circular statistics. In many cases there is a slight difference between angular change and the change in track. This is due to the fact that track is based on the velocity vector (see for example Track xy on page 101), while angular Figure 53 In this example, a fish is making a turn to the left. The scatterplot shows the x-y position of the fish (the arrow shows the direction of movement). For a specific sample, the value of angular change xy (leftmost column) is equal to the difference in track xy between that sample and the previous: -142 - (-126) = -16. 12 Analysis variables change is based on the actual point's coordinates. Because of the way the vector is calculated, this may not exactly overlap with the segments joining the data points.

What is the difference between Angular change xv and Angular

change 3d?

Consider Angular change xv: Now consider, for the same data points, Angular change 3d: If we overlap the two pictures, the three highlighted angles can be seen as: 12 Analysis variables Where A = Angular change 3d, and B-C = Angular change xv. For the same reason why, in a triangle the following inequality is valid: Then Angular change 3D is always greater than or equal to the absolute value of Angular change xv.

Angular Velocities

Ang. vel. xv

Stands for Angular velocity xv. It is the Angular change xv per time unit. It is expressed in degrees/s.

Ang. vel. xy

Stands for Angular velocity xy. It is the Angular change xy per time unit. It is expressed in degrees/s.

Ang. vel. xz

Stands for Angular velocity xz. It is the Angular change xz per time unit. It is expressed in degrees/s.

Ang. vel. 3d

Stands for Angular velocity xv. It is the Angular change 3d per time unit. It is expressed in degrees/s. 12 Analysis variables

3d Zones

The columns Zone x ind. through Zone cyl. mark each data point with

numeric codes, based on the coordinates relative to the defined three- dimensional zones. With Excel, you can easily filter those codes to analyze the data points that occur in a specific zone, or in a combination of zones. The ranges of coordinates that are assigned to a zone are open to the lower limit (low limit, high limit]. For example: If the values entered as limits of zones parallel to the z axis are 100 and 200 mm, then a data point with z=100 mm gets the code 1 for the zone (-, 100], a data point with z=200 gets the code 2 for the zone (100-200]. For a cylinder zone, if a data point falls exactly on a cylinder (boundary between two zones), it is assigned to the inner zone. For the odour plume cone, see page 65. Figure 54 The four columns in the results file mark each sample with a code indicating the presence of the data point in a 3D zone. The sixth row in the column zone z ind. marks the transition from one zone (1) to another (2). 12 Analysis variables Zone x ind. Indicates where the animal is located relative to the zones perpendicular to the x axis (see page 67). 1 - In the first zone (x ordinates below the first limit entered; 2 - In the second zone (x ordinates falling between the first and the second limit entered) 3 - In the third zone (x ordinates between the second and the third limit entered) The highest number - Last zone, with the x ordinates exceeding the highest limit entered. Zone y ind. Indicates where the animal is located relative to the zones perpendicular to the y axis (see page 69). 1 - In the first zone (y ordinates below the first limit entered; 2 - In the second zone (y ordinates falling between the first and the second limit entered) 3 = In the third zone (y ordinates between the second and the third limit entered); The highest number - Last zone, with the y ordinates exceeding the highest limit entered. Zone z ind. Indicates where the animal is located relative to the zones perpendicular to the z axis (see page 69). 1 - In the first zone (z ordinates below the first limit entered; 2 - In the second zone (z ordinates falling between the first and the second limit entered); 3 - In the third zone (z ordinates between the second and the third limit entered); The highest number - Last zone, with the z ordinates exceeding the highest limit entered. 12 Analysis variables Zone cyl. Indicates where the animal is located relative to the concentric cylinders (see page 70). 1 - In the inner cylinder (indicated by the first diameter entered); 2 - In the zone between the first and the second cylinder; 3 - In the zone between the second and the third cylinder; The highest number - Last zone, outside the outer cylinder.

Example of data selection based on a cylindric zone

The following picture shows the data points for a zone defined by two cylinders of 200 mm and 400 mm diameter, respectively. Figure 55 In this example, the data of a Track3D results file have been filtered in Excel (Data menu). The chart shows the y and z coordinates (like in a cross section of the wind tunnel). Data points are selected that have code =2 for zone defined by two cylinders. The cylinders have center at y=200 and z=300. The inner cylinder has a 200 mm diameter, the outer cylinder a 400 mm diameter. Because of the selection, only data points in the zone defined between the two cylinders are displayed.

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Source: Track3D 2 - Reference Manual (March 2025)