如何将世界空间变换转换为对象空间变换？

Question

i'm trying to implement :

transform.InverseTransformPoint(Vector3) and transform.InverseTransformDirection(Vector3) using glm library in opengl. i have view ,projection ,model matrices for each object.

actually i don't know what i must to do with this matrices for got to that methods functionality.

Answer 1

Usually, a point in local space can be transformed to NDC space by doing the following math:

Pworld = M * Plocal;
Pview = V * Pworld;
Pndc = P * Pview;

where M = model, V = view and P = projection.

So, if you have a point in world coordinate system and want to get it in local coordinate system, you just have to invert the first equation:

Plocal = inv(M) * Pworld;

This should be equivalent to transform.InverseTransformPoint(Vector3) (just add a fourth coordinate vector H = 1)

To implement transform.InverseTransformDirection(Vector3) , which is not affected by scale, you must use this equation:

Plocal = transpose(inverse(M)) * Pworld

where M is the upper-left 3x3 matrix from your original Model. To understand why you sould use this math, I invite you to look at this page: normal transformation