I'm guessing I'm looking for two libraries, one for matrix math and one for drawing them in 2D and 3D.
For example, enter a 3x3 matrix, see the parallelepiped it represents, enter a rotation matrix, see the rotated parallelepiped.īonus points for ability to calculate area/volume, animate, change colours, visualize higher dimensions, wash my socks. So I'd like to be able to enter a vector or matrix, see it in 2-space or 3-space, enter a transformation vector or matrix, and see the result. I've tried finding an existing tool to do this to no avail so now I'm looking for Python libraries so I can do it (almost) myself.
We can now see graphically how the column vectors get aligned as we bring the matrix to upper triangular form: Your browser does not support the video tag.I want to visualize matrix transformations in 2- and 3-space. Knowing how to work with transformation matrices is possibly the most important point when dealing with Direct3D.Using matrices, we can perform rotation, scaling, or translation of any object on the 3-D world (or in the 2-D world, if we choose to ignore the z component), and these operations, correctly applied, will heilp> u to define our projection type (as shown in the previous section) or. wait () cube = new_cube i_vec, j_vec, k_vec = i_vec_new, j_vec_new, k_vec_new self. get_run_time ()), ReplacementTransform ( k_vec, k_vec_new, rate_func = cube_anim. play around with this toy to get a sense of what different matrices do to the unit cube. Then we can see how each column of the matrix actually represents the coordinates defining the transformed basis vectors in the original frame. For the 3x3 case this is particularly intuitive, as we can visualize how a certain matrix transforms standard x/y/z basis vectors, or a unit cube defined by these. get_run_time ()), ReplacementTransform ( j_vec, j_vec_new, rate_func = cube_anim. Sometimes it's convenient to think of matrices as transformations. Click Draw button to display point cloud, Erase to hide point cloud. Reload button next to it reloads ply from disk. Go to 3d View Sidebar (N) > Point Cloud Visualizer tab, click file browser icon, select ply file, click Load PLY.
play ( cube_anim, ReplacementTransform ( i_vec, i_vec_new, rate_func = cube_anim. Basic Usage: Install and activate addon in a usual way. basis_k_color ) # prepare and run animationĬube_anim = ReplacementTransform ( cube, new_cube ) self. basis_j_color ) k_vec_new = Vector ( a np. basis_i_color ) j_vec_new = Vector ( a np. New_cube = Cube ( side_length = 1, fill_color = BLUE, stroke_width = 2, fill_opacity = 0.1 ) new_cube. Display This section allows visualization of how much and what direction of displacements specified by the transform. Values can be separated by spaces, commas, or semicolons, which allows copy/pasting numpy array from Python console or matrix from Matlab. add_fixed_in_frame_mobjects ( matrix ) # transformed cube Paste: paste transformation matrix from clipboard. wait ( 2 ) for a in gauss ( M ): a_rounded = np. wait () i_vec, j_vec, k_vec = i_vec_new, j_vec_new, k_vec_new self. get_rate_func (), run_time = matrix_anim. get_run_time ()), ReplacementTransform ( k_vec, k_vec_new, rate_func = matrix_anim. get_run_time ()), ReplacementTransform ( j_vec, j_vec_new, rate_func = matrix_anim. play ( matrix_anim, ReplacementTransform ( i_vec, i_vec_new, rate_func = matrix_anim. wait () matrix_anim = ApplyMatrix ( M, cube ) self. play ( ShowCreation ( cube ), GrowArrow ( i_vec ), GrowArrow ( j_vec ), GrowArrow ( k_vec ), Write ( basis_vector_helper ) ) self. basis_j_color ) k_vec_new = Vector ( M np. basis_i_color ) j_vec_new = Vector ( M np. basis_k_color ) i_vec_new = Vector ( M np. begin_ambient_camera_rotation ( rate = 0.15 ) cube = Cube ( side_length = 1, fill_color = BLUE, stroke_width = 2, fill_opacity = 0.1 ) cube. add_fixed_in_frame_mobjects ( matrix ) # axes & camera Basic geometric transformations in a 2D plane are called 2D transformations and those are translation, rotation, scaling, reflection and shear. add_fixed_in_frame_mobjects ( basis_vector_helper ) # matrix
set_camera_orientation ( phi = 55 * DEGREES, theta =- 45 * DEGREES ) # basis vectors i,j,kīasis_vector_helper = TextMobject ( "$i$", ",", "$j$", ",", "$k$" ) basis_vector_helper. array (,, ]) # axesĪxes = ThreeDAxes () axes. to_corner ( UP + LEFT ) return m def construct ( self ): M = np. From manimlib.imports import * class LinearTransformation3D ( ThreeDScene ): CONFIG = def create_matrix ( self, np_matrix ): m = Matrix ( np_matrix ) m.