3D Transform Visualization tool made by Daniel

Angle format:

Translation vector (xyz)

x
y
z

Rotation matrix

Quaternion (xyzw)

x
y
z
w

Axis-angle (xyz, angle) (radians)

Axis x
y
z
Angle (radians)

Axis with angle magnitude (radians)

Axis x
y
z

Euler angles of multiple axis rotations (radians)

x
y
z

^{parent}_{child}M =

Description

The matrix represents the pose of the child frame (bright colors) in the parent frame (greyed-out).

A transform matrix can be used to easily transform objects from a child to a parent frame

For example if we have three frames, "world", "person", and "hand" and some objects (e.g. a hat, an apple). We might know some relationships between frames and objects, for example where the person is in the world, where the hand is w.r.t. the person, where the apple is w.r.t the hand...

Here, the apple coordinates can be represented as a vector,

^{in person}X_{apple} = [x, y, z, 1]

we can use transforms to get the apple's position in another frame

^{in world}X_{apple} = ^{in world}_{person}M @ ^{in person}X_{apple}

this math also works for transforming frames

^{in world}_{arm}M = ^{in world}_{person}M @ ^{in person}_{arm}M

@ denotes the matrix multiplication operator

I am reusing the notation from this link