I have tried to build lookat view matrix without library but result was wrong. Then I tried glm library `lookAt`

function and it gave me the almost the same matrix as my own function built. The only difference is in translation part.
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glm's translation part in matrix:

Result[3][0] =-dot(s, eye); Result[3][1] =-dot(u, eye); Result[3][2] = dot(f, eye);

What? Why it's uses dot product? Isn't it should be a camera position in world? Here is my code.

Camera buildCamera(glm::vec3 cameraOrigin, glm::vec3 lookAt) { Camera camera = {}; glm::vec3 up = glm::vec3(0,1,0); glm::vec3 forward = glm::normalize(cameraOrigin - lookAt); glm::vec3 right = glm::normalize(glm::cross(up, forward)); up = glm::cross(forward,right); f32 c[] = { right.x, right.y, right.z,-cameraOrigin.x, up.x, up.y, up.z, -cameraOrigin.y, forward.x, forward.y, forward.z,-cameraOrigin.z, 0, 0, 0,1 }; camera.cameraMat = glm::transpose(glm::make_mat4(c)); return camera; }

Thanks

Edited by Roman
on

LookAt matrix does two steps in this order:

- translate to origin
- rotate to match your orientation.

If you express these steps as matrix and multiply them in correct order, you will get that dot product for translation.

For your non-dot product case you are doing these steps in opposite order - first rotate, then translate. Which means position will be in wrong place.

This goes into more detail on this (Step 4): https://medium.com/@carmencincotti/lets-look-at-magic-lookat-matrices-c77e53ebdf78