# solvePnP rotational vector **URL:** \ **Category:** Uncategorized\ **Tags:** calib3d, solvepnp, math\ **Created:** [July 21, 2022, 3:08pm UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590 "2022-07-21T15:08:55Z")\ **Posts on this page:** 11\ **Page:** 1
**Author:** ![Carlos144Green](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/carlos144green/32/5702_2.png) [@Carlos144Green](https://forum.opencv.org/u/Carlos144Green)\ **Post date:** [July 21, 2022, 3:08pm UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/1 "2022-07-21T15:08:55Z")
So I am following [this #](https://learnopencv.com/head-pose-estimation-using-opencv-and-dlib/)project, the result video is at the end. I want a way to extract the global 3d coordinates of the nose and the vector pointing away. I understand that we get the translational vector (which is the nose coordinates… I think) and the rotational vector (I think this is the camera angle?). I just want the two points of the vector pointing away from the face in two 3D points. Can anyone help with this? ---
**Author:** ![crackwitz](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/crackwitz/32/14_2.png) [@crackwitz](https://forum.opencv.org/u/crackwitz)\ **Post date:** [July 21, 2022, 3:48pm UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/2 "2022-07-21T15:48:14Z")
rvec and tvec represent… - a transformation from the object coordinate frame to the camera coordinate frame - the pose of the object, expressed in the camera frame rvec is an axis-angle encoding. ---
**Author:** ![berak](https://avatars.discourse-cdn.com/v4/letter/b/85f322/32.png) [@berak](https://forum.opencv.org/u/berak)\ **Post date:** [July 21, 2022, 5:16pm UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/3 "2022-07-21T17:16:43Z")
> [@Carlos144Green](#): > > which is the nose coordinates… I think rvec/tvec are same for ALL the points. the tip of the nose isnt any special here ---
**Author:** ![Carlos144Green](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/carlos144green/32/5702_2.png) [@Carlos144Green](https://forum.opencv.org/u/Carlos144Green)\ **Post date:** [July 21, 2022, 6:01pm UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/4 "2022-07-21T18:01:21Z")
So how do we solve for the end point of the vector if its length is constant but location isn’t? ---
**Author:** ![crackwitz](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/crackwitz/32/14_2.png) [@crackwitz](https://forum.opencv.org/u/crackwitz)\ **Post date:** [July 21, 2022, 9:42pm UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/5 "2022-07-21T21:42:54Z")
express that point local to the “object” (face). then use projectPoints on that data, along with rvec and tvec, and out comes the screen-space point for that 3D point. if you want to explore what’s going on… use the following combined with `cv.perspectiveTransform()` ```python def rtvec_to_matrix(rvec, tvec): """ Convert rotation vector and translation vector to 4x4 matrix """ rvec = np.asarray(rvec) tvec = np.asarray(tvec) T = np.eye(4) R, jac = cv.Rodrigues(rvec) T[:3, :3] = R T[:3, 3] = tvec return T def matrix_to_rtvec(matrix): """ Convert 4x4 matrix to rotation vector and translation vector """ rvec, jac = cv.Rodrigues(matrix[:3, :3]) tvec = matrix[:3, 3] return rvec, tvec ``` ---
**Author:** ![Carlos144Green](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/carlos144green/32/5702_2.png) [@Carlos144Green](https://forum.opencv.org/u/Carlos144Green)\ **Post date:** [July 22, 2022, 2:38am UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/6 "2022-07-22T02:38:44Z")
Sorry, I am still very new to all of this. could you explain how to use cv.perspectiveTransform() and these functions to help understand this all. Also I dabbled around with the first function and it is throwing an error: ValueError: could not broadcast input array from shape (3,1) into shape (3,) on line T[:3, 3] = tvec ---
**Author:** ![Carlos144Green](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/carlos144green/32/5702_2.png) [@Carlos144Green](https://forum.opencv.org/u/Carlos144Green)\ **Post date:** [July 22, 2022, 2:40am UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/7 "2022-07-22T02:40:21Z")
Here are the values from the mona lisa image I included in the top most post. ```auto translation_vector: [[-167.53555238] [-203.05570512] [2571.1324635]] rotation_vector: [[-2.808854] [-0.01133365] [0.42841277]] ``` ---
**Author:** ![crackwitz](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/crackwitz/32/14_2.png) [@crackwitz](https://forum.opencv.org/u/crackwitz)\ **Post date:** [July 22, 2022, 10:33am UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/8 "2022-07-22T10:33:11Z")
fix: ```auto def rtvec_to_matrix(rvec, tvec): """ Convert rotation vector and translation vector to 4x4 matrix """ rvec = np.asarray(rvec) tvec = np.asarray(tvec) T = np.eye(4) R, jac = cv.Rodrigues(rvec) T[:3, :3] = R T[:3, 3] = tvec.squeeze() # this is the fix return T ``` ---
**Author:** ![crackwitz](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/crackwitz/32/14_2.png) [@crackwitz](https://forum.opencv.org/u/crackwitz)\ **Post date:** [July 22, 2022, 10:39am UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/9 "2022-07-22T10:39:23Z")
> [@Carlos144Green](#): > > the mona lisa image I included in the top most post I don’t see that picture. your first post only includes a link to a blog post. your tvec looks like the calibration might be in mm. the 4x4 transformation matrix for your rvec and tvec is: ```auto array([[0.95552, -0.03688, -0.29262, -167.53555], [0.0523 , -0.95524, 0.29118, -203.05571], [-0.29026, -0.29354, -0.91082, 2571.13246], [0. , 0. , 0. , 1.]]) ``` I’m gonna talk about “markers” purely because I’m kinda stuck in that lingo. it comes from working with AR markers. I imagine if you work with faces, the axes are placed similarly (Z is nose/forward, X to subject’s left, Y up) the rotation maps (read each column)… - X to +X, with a bit of -Z but not much - Y to -Y (so it points up/far) - Z to -Z (so it points near/up) which _rotates_ marker-local coordinates/directions into camera-local points/directions. so that means you’re facing the marker. it probably faces a little to your bottom left. the translation then simply moves all that away/far by 2571, and a little to the top left of the image center. ---
**Author:** ![Carlos144Green](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/carlos144green/32/5702_2.png) [@Carlos144Green](https://forum.opencv.org/u/Carlos144Green)\ **Post date:** [July 22, 2022, 1:28pm UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/10 "2022-07-22T13:28:03Z")
> [@crackwitz](#): > > it probably faces a little to your bottom left ![](https://us1.discourse-cdn.com/flex020/uploads/opencv/original/2X/7/78a7dd9061d064d13305fa1e05cc7277b1060f2f.png) Spot on, its pointing towards the bottom left. I am still a little confused how you read the matrix to determine the position of the vector though. ---
**Author:** ![crackwitz](https://sea2.discourse-cdn.com/flex020/user_avatar/forum.opencv.org/crackwitz/32/14_2.png) [@crackwitz](https://forum.opencv.org/u/crackwitz)\ **Post date:** [July 22, 2022, 3:34pm UTC](https://forum.opencv.org/t/solvepnp-rotational-vector/9590/11 "2022-07-22T15:34:59Z")
the matrix transforms object-local points/vectors to camera-local. you can get a sense for what it does by figuring where the (object-local) axes get mapped to. X is (1,0,0), Y is (0,1,0), Z is (0,0,1). append a 1 for points or a 0 for vectors. the +Z vector gets mapped to… \begin{pmatrix} 0.95552 & -0.03688 & -0.29262 & -167.536 \\ 0.0523 & -0.95524 & 0.29118 & -203.056 \\ -0.29026 & -0.29354 & -0.91082 & 2571.13 \\ 0 & 0 & 0 & 1 \end{pmatrix} \cdot \begin{pmatrix} 0 \\ 0 \\ 1 \\ 0 \end{pmatrix} = \begin{pmatrix} -0.29262 \\ 0.29118 \\ -0.91082 \\ 0 \end{pmatrix} so the +Z vector gets mapped to… the third column. now, where does a camera-local vector point if that is its value? a little to -X (left), a little to +Y (down), and mostly to -Z, so that’s near. and that is where the face’s +Z vector points, as viewed by the camera. same for the others.