Summary of Rigid-Body Motions and Twists. We use homogeneous transformation matrices to describe rigid-body motions. By analogy to the case of rotation matrix, we have calculate the variable that describes the velocity of the moving rigid-body from transformation/rotation matrix, which is named twist. Given a geometric model that contains 3D points p1,p2,p3 and three other points q1,q2,q3, find the total rigid body transformation that: (1) transforms p1 into q1; (2) transforms the vector (p2 - p1) into the vector (q2 - q1), direction only; (3) transforms the plane containing the three points p1,p2,p3 into the plane containing q1,q2,q3 Note ... Spatial Vector and Rigid-Body Dynamics Software. Version 2: June 2012 (latest bug fix: Feb 2015) . Released Under GNU GPL — Legal Notices — Download Spatial_v2 is a suite of functions that implement spatial vector arithmetic and dynamics algorithms in Matlab code. Mar 08, 2020 · theta = pi/2; T_x = rotx(theta); % Returns a 4x4 pose matrix. The upper-left 3x3 submatrix is the % rotation matrix representing a rotation by theta about the x-axis. R_x = tr2rt(T_x); % Returns the 3x3 rotation matrix corresponding with T_x. T_y = roty(theta); % A rotation about the y-axis.