HallsofIvy said:What do you mean by "A's local coordinates"?
To calculate the transformation matrix of an object in world coordinates, you first need to know the object's position, rotation, and scale in relation to the world. Then, you can use mathematical operations such as translation, rotation, and scaling to transform the object's local coordinates into world coordinates.
To solve for the transformation matrix of an object in world coordinates, you need to know the object's local coordinates, as well as its position, rotation, and scale in relation to the world. This information is typically provided in the form of a 3D model or a set of transformation parameters.
Solving for the transformation matrix of an object in world coordinates is important because it allows you to accurately position and orient the object in the world. This is crucial for tasks such as animation, simulation, and computer graphics, where the object's position and orientation need to be precisely defined.
Local coordinates refer to the position and orientation of an object relative to its own origin point. World coordinates, on the other hand, refer to the position and orientation of an object relative to the world origin point. This means that world coordinates take into account the object's position and orientation in relation to other objects in the world, while local coordinates do not.
Yes, for example, let's say we have a cube with a position of (3, 2, 1), a rotation of (45, 30, 10), and a scale of (2, 2, 2) in relation to the world. To solve for the transformation matrix, we would first translate the cube by (3, 2, 1) units, then rotate it by 45 degrees around the X-axis, 30 degrees around the Y-axis, and 10 degrees around the Z-axis, and finally, scale it by a factor of 2 in all directions. This would result in a transformation matrix that can be used to transform the cube's local coordinates into world coordinates.