# SceneGraph Coordinate Systems

Each renderable node has a local coordinate system associated with it with an origin at (0,0) with x increasing left-to-right and y increasing top-to-bottom. Each node can also have a 2D transformation specified that transform its local coordinate system into a transformed coordinate system. In the Roku SceneGraph implementation a node transformation matrix is specified by setting the values of four fields:

FieldDescription
translation2D vector that describes an [x, y] offset of the local coordinate system origin
scale2D vectors that describes an [x, y] scaling of the local coordinate system
rotationFloating point value that describes a Z-axis rotation of the local coordinate system. The value is specified in radians with positive values representing a counter-clockwise rotation.
scaleRotateCenter2D vector that describes a point in the local coordinate system that serves as the center of scaling and rotation

Each of these fields can be combined into an overall 2D transformation for the node by first applying these steps:

1. Translate by the inverse of the scale/rotate center
2. Multiplying by the scale amount
3. Apply the Z-axis rotation
4. Translate by the scale/rotate center
5. Translate by the translation amount.

In matrix math, the overall matrix is:

```   M = C(-1) S R C T
```

Where M is the total matrix, C is a 2D translation matrix that describes the location of the scale/rotation center in the node local coordinate system, C(-1) is the inverse of C, S is a 2D scaling matrix, R is a 2D rotation matrix, and T is a 2D translation matrix.

As the SceneGraph is traversed, 2D transformations are accumulated so that each child local coordinate system is transformed not only by its own 2D transformation matrix, but also the accumulated transformation matrix of all of its ancestors in the tree structure. This allows logical groupings of nodes to be positioned/animated by changing the transformation fields of nodes at various levels in the tree.

The transformation accumulation allows node classes to be developed without regard to their absolute pixel coordinates. Instead, each node can be have a layout relative to its local coordinate system, with its absolute on-screen position, size and orientation determined by the accumulated transformation matrix. For example, in a PanelSet node screen, each Panel node has a local origin of (0,0) at the top/left corner of the panel. The PanelSet node is the parent of each Panel node in the tree hierarchy, and animates the translation field of the Panel nodes to cause them to slide on/off screen. Each Panel node has a subtree of nodes that draw its contents. Since these nodes inherit the Panel node translation, they all slide together as the Panel node translation field is modified.

• No labels