What transformations are carried out below mannequin house?

Mannequin house is the title of the house you’re in earlier than you might have utilized any of S, R, or T.

World house is the title of the house you’re in after you might have utilized all of S, R, and T.

We do not typically title the areas for every step of the transformation between the 2. Usually, all three are concatenated into one matrix M = T * R * S, so we’re not making use of them as particular person steps in any respect however , and a vector by no means exists in an intermediate house:

p_world = M * p_model

A “house” isn’t just the route of its foundation vectors, but in addition its scaling and absolute place / “reference zero”. So we won’t actually say the vector is in both mannequin ot world house once we’ve utilized a few of these steps however not all of them.

What we are able to say is…

• The primary three diagonal parts of the S matrix (S[0,0], S[1,1] and S[2,2]) are the size components to use to the mannequin’s u, v, and w axes, respectively.

  The consequence could possibly be known as “scaled mannequin house”

• The primary three columns of the R matrix are the unit route vectors in world house that you really want the mannequin’s u, v, and w axes to level alongside after rotation. This rotation doesn’t change the placement of the mannequin’s origin (the purpose u = v = w = 0) — we pivot round this origin level.

  The consequence could possibly be known as “scaled and rotated mannequin house” or “unshifted world house” because it doesn’t incorporate translation but.

• The final column of the T matrix is level in world house the place you need the mannequin’s pivot/origin to maneuver to, after rotation.

Does that reply what you wanted to know?