- #1
tanus5
- 52
- 0
Please excuse my terminology as I am teaching myself linear algebra.
I am attempting to construct a vector which can provide reflection from the origin, eventually I want to be able to move this point of reflection anywhere (translation and rotation) but I'm starting at the origin since that is the simplest case. Let's say my object, the "reflectee", is defined as G(t) where t is time. The only real constraint on G(t) seems to be that it produces a m x n matrix that matches my reflection vector such that the reflection vector is a m x 1 matrix. I've found that when |G(0)| < 1 the reflection vector can be assigned as the column vector (tanh(t),...) but when |G(0)| >= 1 the reflection vector is an identity column vector (1,...). What options are available to meet these constraints as a single vector to eliminate the conditionals?
|G(0)| < 1 → (tanh(t),...) * G(t)
|G(0)| >= 1 → (1,...) * G(t)
I am attempting to construct a vector which can provide reflection from the origin, eventually I want to be able to move this point of reflection anywhere (translation and rotation) but I'm starting at the origin since that is the simplest case. Let's say my object, the "reflectee", is defined as G(t) where t is time. The only real constraint on G(t) seems to be that it produces a m x n matrix that matches my reflection vector such that the reflection vector is a m x 1 matrix. I've found that when |G(0)| < 1 the reflection vector can be assigned as the column vector (tanh(t),...) but when |G(0)| >= 1 the reflection vector is an identity column vector (1,...). What options are available to meet these constraints as a single vector to eliminate the conditionals?
|G(0)| < 1 → (tanh(t),...) * G(t)
|G(0)| >= 1 → (1,...) * G(t)
Last edited: