How do I create a view matrix directly from a quaternion and a position vector?

Question

Given a quaternionic camera such that:

typedef struct
{
    vector3 upReference;
    vector3 rightReference;
    vector3 forwardReference;

    vector3 position;
    quaternion orientation;

    float pov;
} camera_t;

Where:

• upReference, rightReference, forwardReference are always (0,1,0, 1,0,0, 0,0,-1) respectively
• pov is the viewing angle

and quaternion is:

typedef struct 
{
    float x, y, z, w;
} quaternion;

Is there some way to create a view matrix directly from all of this and skip gluLookAt?

Answer 1

Try this below:

XMMATRIX is transpose of the transform matrix, so you read it as column,row

XMMATRIX viewMatrix = XMMatrixRotationQuaternion(v_quaterion);
XMFLOAT4X4 f_view;
XMStoreFloat4x4(&f_view, viewMatrix);
f_view._41 = mPosition.x * f_view._11 + mPosition.y * f_view._21 + mPosition.x * f_view._31;
f_view._42 = mPosition.x * f_view._12 + mPosition.y * f_view._22 + mPosition.x * f_view._32;
f_view._43 = mPosition.x * f_view._13 + mPosition.y * f_view._23 + mPosition.x * f_view._33;
viewMatrix = XMLoadFloat4x4(&f_view);

You need to multiply the translation vector by the rotation first

Answer 2

Another way to do it, if you already have the quaternion-rotation of a vector:

x = q.rotate (1,0,0)
y = q.rotate (0,1,0)
z = crossprod(x,y)
matrix = { x,y,z,p };

It's definitely not the fastest way to do it. But it's one that is easy to understand.