how to convert world space transform to object space transform?

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.

Just use vector3 position objects in word space for transform to local space. Why you want to use matrices? — OnionFan, Mar 12 '17 at 13:31
hi V. Borodinov , my object has been rotated and translated , cause of this , i need to calculate new position and rotation in new coordinate system. — masoud khanlo, Mar 12 '17 at 13:38

score 6 · Accepted Answer · answered Mar 12 '17 at 14:13

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

@Amadeus Isn't clip space an intermediate step between view and ndc? — KeyC0de, Oct 12 '19 at 21:28

how to convert world space transform to object space transform?

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