Tool: Axes/Planes/Centroids

Axes/Planes/Centroids allows defining axis, plane, and centroid objects from sets of atoms and/or markers and using them for measurements. Axis and plane objects are created as cylindrical surface models and centroid objects as markers in the coordinate system of the lowest-numbered model involved in their calculation. They are listed in the Axes/Planes/Centroids table as well as in the Model Panel.

Axis, plane, and centroid objects can also be created with the command define, and they are saved in sessions. See also: distance, angle, reorienting the view, measurements

Axes/Planes/Centroids is tabbed together with the Distances and Angles/Torsions tools into a Structure Measurements window. It can be opened from the Structure Analysis section of the Tools menu and manipulated like other panels (more...).

Define axes...
Define plane...
Define centroid...
Table of Objects

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Axes

Clicking Define axes... opens a dialog for defining axis objects (the equivalent command is define axis). Eigenvectors/values are calculated from the coordinates of each set of atoms/centroids after subtracting the position of their collective centroid. Each axis is anchored at the corresponding collective centroid and aligned with the principal (largest) eigenvector of the corresponding coordinates. There are four main choices of how to define axes, each with associated Axis Parameters:

Each helix in structure – define an axis for each peptide/protein helix in the atomic model(s) chosen in the list of Structures. Peptide/protein helix assignments are taken from the input structure file or generated with dssp. Only the backbone atoms N, CA, C are used to define the axes. Sometimes two helices are adjacent in sequence (not separated by any other residues), and the integer-valued residue attribute ss_id is used to distinguish them. Although such cases are detected automatically, ss_id can also be set manually with setattr.
- Color
  - atom-based (default) – the most prevalent color among the atoms used to define the axis, if at least 30% share that color, otherwise #909090
  - a color well (click to change)
- Name [ model-name ]
- Radius method
  - Average atom-axis distance (default) – average distance between the axis and the atoms used to define it
  - Fixed value
    - Radius (default 2.0 Å)
- Length method
  - Enclose atom/point projections (default) – the minimum needed to span the projections of the atoms used to define the axis
    - Length padding (default 0.0 Å) – additional length on each end
  - Fixed value
    - Length (default 10.0 Å)
Selected atoms/centroids – define a single axis using all selected atoms (including centroids or other markers)
- Color
  - atom-based (default) – the most prevalent color among the atoms used to define the axis, if at least 30% share that color, otherwise #909090
  - a color well (click to change)
- Name [ model-name ]
- Radius method
  - Average atom-axis distance (default) – average distance between the axis and the (three or more) atoms used to define it; for axes defined by two atoms, half of the smaller atom's radius
  - Fixed value
    - Radius (default 2.0 Å)
- Length method
  - Enclose atom/point projections (default) – the minimum needed to span the projections of the atoms used to define the axis
    - Length padding (default 0.0 Å) – additional length on each end
  - Fixed value
    - Length (default 10.0 Å)
- Mass weighting (default off) – calculate major inertial axis with mass weighting; requires the selection to contain either only “real” atoms or only markers (which could include centroid objects). The radius of a marker (Å) is used as its “mass” (daltons).
Plane normals – define a normal (perpendicular) axis for each plane chosen in the list of Planes
- Color
  - plane color (default)
  - a color well (click to change)
- Name [ model-name ]
- Radius method
  - 5% of plane radius (default)
  - Fixed value
    - Radius (default 2.0 Å)
- Length method
  - Equal to plane radius (default)
    - Length padding (default 0.0 Å) – additional length on each end
  - Fixed value
    - Length (default 10.0 Å)
Two points – between two points given as X, Y, and Z in scene coordinates.
- Color – a color well (click to change)
- Name [ model-name ]
- Radius (default 2.0 Å)
- Length method
  - Enclose atom/point projections (default) – span the two points
    - Length padding (default 0.0 Å) – additional length on each end
  - Fixed value
    - Length (default 10.0 Å)

Only one color-well color, fixed radius, and fixed length can be given at a time, but axes with different values can be created in successive uses of the tool. Clicking Apply (or OK, which also closes the dialog) calculates the axes, adds them to the table, and generates the corresponding objects. Axis parameters are reported in the Log.

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Planes

Clicking Define plane... opens a dialog for defining a plane based on the selected atoms (the equivalent command is define plane). Eigenvectors/values are calculated from the atomic coordinates after subtracting the position of their non-mass-weighted centroid. The plane is anchored at the centroid and aligned with the two largest eigenvectors (the third-largest eigenvector is normal to the plane).

Plane name [ name ]
Color
- atom-based (default) – the most prevalent color among the atoms used to define the plane, if at least 30% share that color, otherwise #909090
- a color well (click to change)
Radius method
- Enclose atom projections (default) – span the projections of the atoms used to define the plane
  - Extra radius (padding) (default 0.0 Å)
- Fixed value
  - Radius (default 10.0 Å)
Disk thickness (default 0.10 Å)

Clicking Apply (or OK, which also closes the dialog) calculates the plane, adds it to the table, and generates the corresponding object. Plane parameters are reported in the Log.

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Centroids

Clicking Define centroid... opens a dialog for defining a centroid based on the selected atoms (the equivalent command is define centroid).

Centroid name [ name ]
Color
- atom-based (default) – the most prevalent color among the atoms used to define the centroid, if at least 30% share that color, otherwise #909090
- a color well (click to change)
Radius (default 2.0 Å)
Mass weighting (default off) – whether to use mass weighting, i.e., to define the centroid as the center of mass rather than center of geometry. The radius of a marker (Å) is used as its “mass” (daltons).

Clicking Apply (or OK, which also closes the dialog) calculates a centroid, adds it to the table, and generates the corresponding object. Centroid coordinates are reported in the Log.

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Axes/Planes/Centroids Table of Objects

The table of objects includes the following columns, many the same as in the Model Panel:

Name – model name; doubleclick to edit
ID – model number; doubleclick to edit
a color well; click to change color interactively
– show/hide checkbox
– selection checkbox
Length
Radius

Clicking a column header sorts the table by that column, and the table can be saved as a comma- or tab-separated file by choosing Save CSV or TSV File... from the dialog's context menu.

One or more objects can be chosen from the list by clicking and dragging with the left mouse button; Ctrl-click (or command-click if using a Mac) toggles whether an object is chosen. Chosen lines are highlighted in the dialog.

Clicking Delete removes the chosen objects.

Choosing any two objects reports their applicable geometric relationships below the table and in the Log. For angle measurements, axes and planes are treated as infinite. For distance measurements, axes are treated as finite line segments, while planes are treated as infinite.

Report distance measures distances between the chosen objects and selected atoms; the minimum, maximum, and mean distances to each chosen object are reported in the Log.

Center and align is available when a single axis or plane object is chosen. It centers and aligns the chosen axis, or centers the chosen plane and aligns its normal vector, along the specified direction in screen coordinates:

X – horizontal in the plane of the screen
Y – vertical in the plane of the screen
Z – perpendicular to the screen, along the line of sight

There is no control over which end of the axis or normal vector goes in the positive direction, but the view can be flipped 180° with a command, for example, if the axis is model #1.2.3:

turn y 180 center #1.2.3

Clicking Save Info... writes all axis/plane/centroid information to a file, regardless of which objects are chosen in the table. For each object, the information includes model name, model ID, and untransformed center coordinates (x_c,y_c,z_c). Axis information also includes length and direction (orientation) expressed as a unit vector (x_u,y_u,z_u). Axis endpoint coordinates (x₁,y₁,z₁) (x₂,y₂,z₂) can be generated as follows:

x₁ = x_c – 0.5(length)(x_u)
y₁ = y_c – 0.5(length)(y_u)
z₁ = z_c – 0.5(length)(z_u)

x₂ = x_c + 0.5(length)(x_u)
y₂ = y_c + 0.5(length)(y_u)
z₂ = z_c + 0.5(length)(z_u)

Plane information also includes radius and orientation expressed as a normal unit vector.

UCSF Resource for Biocomputing, Visualization, and Informatics / February 2024