A Frame3d has an origin point and a set of X, Y and Z directions (which are always perpendicular to each other). It can be thought of as:

• A local coordinate system: Most geometric types have associated relativeTo and placeIn functions that convert values of that type from global coordinates to local coordinates in a particular frame, and vice versa.
• A set of axes and planes: It is often convenient to (for example) rotate around the Z axis of a frame, or mirror across its XY plane. Frames can also themselves be translated, rotated and mirrored!
• A combined 3D position and orientation: For example, a Frame3d could be used to define the position and orientation of a spaceship in a 3D game. Movement of the ship would then be done by translating and rotating the frame.

Constants

Constructors

The withXDirection, withYDirection and withZDirection functions all construct a new Frame3d with the given axis direction, having the given origin point. The other two directions will be chosen arbitrarily. This can be useful when constructing 'scratch' frames where (for example) you want a particular Z direction but the specific X/Y directions are unimportant.

No guarantees are given about the other two directions other than that the three directions will be mutually perpendicular, and will be oriented so that the resulting frame is right-handed.

Properties

Axes

Planes

The following functions all return planes with the same origin point as the given frame, but with varying normal directions. In each case the normal direction of the resulting plane is given by the cross product of the two indicated basis directions (assuming a right-handed frame).

Sketch planes

These functions all form a SketchPlane3d from two axes of the given frame. The X and Y axes of the sketch plane will correspond to the two indicated axes.

Transformations

Coordinate conversions