The coordinate system plays a crucial role in a rendering engine, ensuring the accuracy of rendering results and interactions. By reading this document, you can understand most of the coordinate systems involved in Galacean. It is important to note that the definitions of various spaces differ between rendering engines; this document discusses only the spatial standards within Galacean.

This document will compare various coordinate spaces in terms of definition of space and coordinate system type. The coordinate system type specifically refers to the left-handed coordinate system and right-handed coordinate system, as shown in the image below:

Defining a system as left-handed or right-handed affects the direction of forward and the direction of rotation (clockwise or counterclockwise). For the definition of direction, you can imagine overlapping your right hand with +X, and the top of your head with +Y. The direction your face points is forward. You can compare the differences between Galacean and Unity:

• Unity's local and world coordinate systems are left-handed. Rotation during transformations is done clockwise, and the forward direction corresponds to +Z. Therefore, the camera's direction (viewing direction) is +Z.

• Galacean's local and world coordinate systems are right-handed. Rotation during transformations is done counterclockwise, and the forward direction corresponds to -Z. Therefore, the camera's direction (viewing direction) is -Z.

Local Space

Local space is relative, using the object's own position as the reference coordinate system. It is usually described as "a point in the local space of node A". Local space uses a right-handed coordinate system. The Transform component automatically calculates the position of each point in world space using the following formula.

World Space

World space is absolute. The root node is placed in world space, and its child nodes inherit its spatial relationships. Like local space, world space also uses a right-handed coordinate system. When two nodes are not in the same local space, they can be converted to world space for comparison of relative positional relationships.

Editor Usage

Determine the gizmo's orientation in the scene:

View Space

View space is the local space of the camera. Taking a perspective camera as an example:

Screen Space

The definition of screen space is consistent with front-end specifications; it is a 2D coordinate system with the top-left corner of the canvas as the origin. The value range within the space is consistent with the dimensions of the canvas and is frequently used in interaction and screen space conversion.

Viewport Space

The definition of viewport space is consistent with front-end specifications. By setting the camera's viewport, you can control the target area of rendering.

2D Sprites

When rendering sprites or masks and other 2D elements, they are by default placed on the XoY plane in the local coordinate system: