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```

# General info for all markers

## What a marker is

A marker is the interface between the items that have coordinates - nodes and bodies - and the items
that act on them - connectors, constraints, joints and loads. A joint does not need to know whether
it is attached to a node or to a point of a body: it asks its markers for what it needs. The
**Interface** of every connector and load names the marker types it requests, and the Interface of
every marker the items that can use it; the table below lists all markers.

## What a marker provides

A marker computes, in the current configuration, the **marker quantities** its types promise:

| type | quantities |
|---|---|
| `Position` | the global position $\LU{0}{\pv}_m$ and velocity $\LU{0}{\vv}_m$ |
| `Orientation` | the rotation matrix $\LU{0m}{\Rot}$ and the local angular velocity $\LU{m}{\tomega}$ |
| `Coordinate`, `Coordinates` | one or several coordinates and their time derivatives |
| `BodyMass` | only a Jacobian, for a load proportional to the mass |

and the **Jacobians** through which a force acts: the position Jacobian
$\LU{0}{\Jm_{pos}} = \partial \LU{0}{\vv}_m / \partial \dot\qv$, the rotation Jacobian
$\LU{0}{\Jm_{rot}} = \partial \LU{0}{\tomega}_m / \partial \dot\qv$, or for a coordinate a row of the
unit matrix. A marker on a **body** takes position, orientation, velocity and angular velocity as the
output variables of the body define them, at its local position, and the Jacobians from the body; a
marker on a **node** takes them from the node.

## How a force reaches the coordinates

The virtual work of a force $\LU{0}{\fv}$ at the marker, $\delta W = \delta \LU{0}{\pv}_m\tp
\LU{0}{\fv}$, gives the generalized forces

$$
\Qm = \LU{0}{\Jm_{pos}}\tp\, \LU{0}{\fv} ,
$$

and a torque $\LU{0}{\ttau}$ gives $\Qm = \LU{0}{\Jm_{rot}}\tp\, \LU{0}{\ttau}$; a force $f$ on a
coordinate marker gives $\Qm = \Jm\tp f$. A marker on the ground - a `NodePointGround`, an
`ObjectGround` - has an empty Jacobian, and nothing acts there.

## With or without reference values

`MarkerNodeCoordinate` and `MarkerNodeODE1Coordinate` give the **current** coordinate, without its
reference value; `MarkerNodeCoordinates`, `MarkerObjectODE2Coordinates` and the cable and beam
markers give the coordinates **including** the reference values. A coordinate constraint between two
markers therefore means something different with the one and with the other.

## Markers in sensors, and markers that are created

`SensorMarker` measures the marker quantities, in the current configuration. Most markers of a model
are added by the Create functions: `CreateRevoluteJoint` adds two `MarkerBodyRigid`, `CreateForce` a
`MarkerBodyPosition` or `MarkerBodyRigid`, `CreateRigidBody` with gravity a `MarkerBodyMass`.

(sec-drawing-markers)=
## Drawing

A marker with a position is drawn if `markers.show` and its own `show` are True: as a symbol of size
`markers.defaultSize` - a fraction of `openGL.advanced.initialMaxSceneSize` if -1 -, three crossed lines with
`markers.drawSimplified`, a cube otherwise, in `markers.defaultColor`; with `markers.showBasis` the frame of a marker
that has an orientation, of length `markers.basisSize` (`general.axesTiling`). `markers.showNumbers` writes its
number. A marker on coordinates has no position and draws nothing.

The settings: [`markers.show`](#sec-vsettingsmarkers), [`markers.defaultSize`](#sec-vsettingsmarkers), [`markers.defaultColor`](#sec-vsettingsmarkers), [`markers.drawSimplified`](#sec-vsettingsmarkers), [`markers.showNumbers`](#sec-vsettingsmarkers), [`markers.showBasis`](#sec-vsettingsmarkers), [`markers.basisSize`](#sec-vsettingsmarkers), [`general.axesTiling`](#sec-vsettingsgeneral), [`openGL.advanced.initialMaxSceneSize`](#sec-vsettingsopengladvanced).

## All markers

```{tabularcolumns} \Y{0.3}\Y{0.3}\Y{0.2}\Y{0.2}
```
| marker | attached to | provides | usable by |
|---|---|---|---|
| [](#sec-item-markerbodymass) | a body | `BodyMass` | 1 item |
| [](#sec-item-markerbodyposition) | a body | `Position` | 10 items |
| [](#sec-item-markerbodyrigid) | a body | `Position`, `Orientation` | 23 items |
| [](#sec-item-markernodeposition) | a node with `Position` or `Position2D` | `Position` | 10 items |
| [](#sec-item-markernoderigid) | a node with `Position` or `Position2D` and `Orientation` or `Orientation2D` | `Position`, `Orientation` | 23 items |
| [](#sec-item-markernodecoordinate) | a node | `Coordinate` | 5 items |
| [](#sec-item-markernodecoordinates) | a node | `Coordinates` | 1 item |
| [](#sec-item-markernodeode1coordinate) | a node | `Coordinate` | 5 items |
| [](#sec-item-markernoderotationcoordinate) | a node with `Orientation` | `Coordinate` | 5 items |
| [](#sec-item-markerbodiesrelativetranslationcoordinate) | two bodies | `Coordinate` | 5 items |
| [](#sec-item-markerbodiesrelativerotationcoordinate) | two bodies | `Coordinate` | 5 items |
| [](#sec-item-markersuperelementposition) | mesh nodes of a super element | `Position` | 10 items |
| [](#sec-item-markersuperelementrigid) | mesh nodes of a super element | `Position`, `Orientation` | 23 items |
| [](#sec-item-markerkinematictreerigid) | a link of a kinematic tree | `Position`, `Orientation` | 23 items |
| [](#sec-item-markerobjectode2coordinates) | a body | `Coordinates` | 1 item |
| [](#sec-item-markerbodycable2dshape) | a body | `Coordinate` | 5 items |
| [](#sec-item-markerbodycable2dcoordinates) | a body | `Coordinate` | 5 items |
| [](#sec-item-markerbodybeamshape) | a body | `Beam3DShape` | the items that name it |