From 17985bd6a0fe36c3adafc9bfcb468d25948d77aa Mon Sep 17 00:00:00 2001 From: Dave <davepreiss@gmail.com> Date: Mon, 5 Jun 2023 16:38:44 -0400 Subject: [PATCH] after hard reset --- final/.gitignore | 8 + final/README.MD | 58 +++++- final/csv_export/slice_0.5.png | Bin 0 -> 121798 bytes final/img/asd.gif | Bin 0 -> 1035975 bytes final/img/molded_part_flipped.jpg | Bin 0 -> 87841 bytes final/img/molded_part_front.jpg | Bin 0 -> 127657 bytes final/img/molded_part_rear.jpg | Bin 0 -> 116532 bytes final/img/rotor_both.jpg | Bin 0 -> 45646 bytes final/img/rotor_sideby.jpg | Bin 0 -> 59164 bytes final/mesh_compare.py | 311 ++++++++++++++++++++++++++++++ final/numpy_stl_experiment.py | 34 ---- final/stanford.stl | Bin 15534 -> 0 bytes final/step_gui.py | 19 -- 13 files changed, 369 insertions(+), 61 deletions(-) create mode 100644 final/.gitignore create mode 100644 final/csv_export/slice_0.5.png create mode 100644 final/img/asd.gif create mode 100644 final/img/molded_part_flipped.jpg create mode 100644 final/img/molded_part_front.jpg create mode 100644 final/img/molded_part_rear.jpg create mode 100644 final/img/rotor_both.jpg create mode 100644 final/img/rotor_sideby.jpg create mode 100644 final/mesh_compare.py delete mode 100644 final/numpy_stl_experiment.py delete mode 100644 final/stanford.stl delete mode 100644 final/step_gui.py diff --git a/final/.gitignore b/final/.gitignore new file mode 100644 index 0000000..9017e53 --- /dev/null +++ b/final/.gitignore @@ -0,0 +1,8 @@ +*.mp4 +*.swo +*.blend +*.blend1 +*.csv +*.stl +.venv +__pycache__ diff --git a/final/README.MD b/final/README.MD index 2d2ba5b..cbde466 100644 --- a/final/README.MD +++ b/final/README.MD @@ -1,14 +1,56 @@ -# Final Project - Heatmapping CT Data +# Final Project - Metrology Analysis of CT Data -Given a CT scan of a material with constant material density, fit a 3D model (.step file) to that data and characterize error in the scanned part. +At the CBA we've struggled to find a good solution to the problem of performing metrology analysis on CT scanned data. The two most common data types obtained from a 3D scan: .tif stacks in the case of a CT and point clouds in the case of lidar are typically scanned in a coordinate system with no bearings to an actual solid model. On the diamond rotors project a common workflow will be to run a reconstruction, orient a rendered 2D cross section of the model by hand, and then bring a screenshot of that cross section into imageJ where a new scale must be established off of some existing feature. There are a number of problems with this approach, and plenty of opportunities for errors to creep into the measurement, and this is where analysis in a native 3D file format would be particularly useful. -Is the part larger or smaller than the intended CAD, is that difference isotropic? For example is error coming from over-extruding in a 3D-printed part (XY error), or poor layer height calibration (Z error). +There are a lot of starting-off points for the project. CT scans are reconstructed as stacks of uncompressed image files (.tif), which are typically on the order of ~1Gb. At the end of the day for scans of uniform material density, what we want is to discard all of that density information, and just put as accurate as possible a boundary around whatever your target material density is, then we can store a much sparser mesh of these coordinates as a .stl (or maybe someday something a little more sophisticated + unit retaining). -For diamond rotors is the ID concentric with the OD? Is there taper in either? Are the ID or OD lobed, and if so at what angular frequency? +Because I've been learning Blender and wanting to get more into computational design, I chose to assume that we are dealing with a mesh or point cloud that can be brought into Blender. I've been getting there by opening .tif stacks in [TomViz](https://tomviz.org/) (which is open source/freeware) and contouring them into .stl files. Blender has a robust python API, and has all of the mesh manipulation/repair tools we could want built directly in. -## Planning 4/13/23 +With that said, here are some examples of the project output: -For visualzing a .tiff stack: +### Injection Molded Scan -- pygfx -- pytorch 3d has lots of libraries for visualizing 3d data from MRI machines etc +<img src="img/molded_part_front.jpg" width="700"> + +Above is a scan I did for a friend who was having tolerance issues with an injection molded part they're working on. On the left is a mesh output of the original CAD file (remeshed in Blender for more point density which can lead to some strange but small artifacts). In the middle is a mesh reconstruction of a ~1 hour CT scan where you can see a number of deviations from the original part design, including ejector pin tooling marks, as well as some mold/run stamps on the top and bottom faces. On the right is a copy of the original mesh with "error" information overlaid as a shader, where you can see deviations highlighted in red. + +I thought it was neat that on the back you can see sink marks from the ejector pins (or maybe they're inverse material that's been pushed out while still in the borderline plastic phase). + +<img src="img/molded_part_rear.jpg" width="700"> + +When I first ran the script on this part I confused myself into thinking the tab on the top was something not reflected in the 3D model, but it turns out I had just let ICP converge to a flipped orientation and it was stuck in a local minimum. It turns out something in my pre-blender workflow was giving mirrored and incorrectly scaled meshes (I strongly suspect the .stl conversion). + +<img src="img/molded_part_flipped.jpg" width="700"> + +### Diamond Rotor Scans + +For lack of a better place to put it, below is an animation of the iterative closest point (ICP) algorithm converging. I've had a hard time getting good reconstructions into meshes due to how x-ray transparent diamond is, and how close it is to fixturing foam and wax in density. You can see some artifacts as a result of this in the scans below. + +<img src="img/asd.gif" width="700"> + +I find something about the shader on this one deeply unsettling, but you can see the largest errors are all on one end the rotor. This is partially because of scaling issues and partially because we make a nominal move along the length of the rotor when parting when we should really be accounting for beam width. (especially with a deep kerf). The large length error sort of obfuscates the more interesting diameter errors we expect to see. + +<img src="img/rotor_sideby.jpg" width="700"> + +Peering into the ID (where most of the actual error of interest is) we can see some hotspots, but might want to artificially scale length to see this better. + +<img src="img/rotor_both.jpg" width="700"> + +## Feature Walkthrough + +I haven't yet converted the script into a real addon, so calling these different functions is a matter of commenting out function calls and manually changing their arguments. In order of operation we have: + +- It isn't a function, but I start by finding the center of mass of both meshes and aligning each mesh such that it's at the origin. +- __principal_axis_align()__ will find the principal axis of both meshes, and then orient the scanned mesh such that its principal axis is aligned with that of the original CAD mesh. This is a good first step for taking measurements, and can be the only alignment step necessary if the part is radially symmetric +- __scale_model()__ will report the % difference in size of the width (x), height (y), and depth (z) of each model. If an optional "x", "y", or "z" argument is passed it will scale the entire mesh uniformly to ensure equality of the axis passed. If not specified it will just print the % difference to the terminal. +- __icp_step()__ iteratively best fits the scanned mesh using the [Iterative Closest Point](https://en.wikipedia.org/wiki/Iterative_closest_point) algorithm. You can specify the number of steps to take as well as the error to minimize to. +- __calculate_error()__ and __assign_color__ operate sequentially to find the nearest vertex neighbor and assign a color shader accordingly. I should update this to look for a point on the closest normal surface, but if the scan mesh is sufficiently dense this error is pretty small. + + +## Features to add + +- Right now you have to just know to order your mesh objects as "scanned" then "original" (naming doesn't matter just order), so need to add a selection GUI. +- At the time of writing I am leaving all of the absolute position deviation in a numpy array (they actually also get written to a .csv in the csv output folder), and the color values are normalized and applied to a vertex's R (in RGB) color shader. I would like to add more color depth here, as well as a scale bar relating color back to mm, this shouldn't take more than a day to add (although I am not sure of the best way to go about a scalebar object). +- A really great feature would be to be able to create a snapshot of a section view slice of the model, which overlays the bounds of the cross-section of the slice over the bounds of the original model. I think this would be the most compelling way to get metrology data (particularly for diamond rotors), as it preserves global context while letting you zoom in on local detail in a clear way. +- Blender has some great brush tools for selecting vertices, so it would be very cool to be able to select a subset of mesh points to use for ICP for models with asymmetry in their error. +- For scans of sample that have undergone large deformations (tensile tester, etc) it would be neat to look into un-squishing a mesh and then creating a link between points on the scanned (squished) model and their corresponding points on the original CAD. 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principal_axis_align(meshes): + ''' + Rotate the scanned mesh to align its principal axis with the original mesh's principal axis + This presently is done off of vertices, but should ideally be done off of faces + ''' + # convert all of our meshes to numpy arrays + scanned_points = np.array([meshes[0].matrix_world @ v.co for v in meshes[0].data.vertices]) + original_points = np.array([meshes[1].matrix_world @ v.co for v in meshes[1].data.vertices]) + + def find_principal_axis(points): + ''' + A sub function for finding the principal axis + Returns a unit vector representing the principal axis of the given points (numpy array) + ''' + # Find the covariance matrix + cov = np.cov(points.T) + # Find the eigenvalues and eigenvectors of the covariance matrix + eigvals, eigvecs = np.linalg.eig(cov) + # Find the index of the largest eigenvalue + max_eigval_index = np.argmax(eigvals) + # Find the corresponding eigenvector + max_eigvec = eigvecs[:, max_eigval_index] + # Convert to a unit vector (check if this is done automatically) + return max_eigvec / np.linalg.norm(max_eigvec) + + # Find the principal axis of the scanned and orginal meshes + scanned_principal_axis = find_principal_axis(scanned_points) + original_principal_axis = find_principal_axis(original_points) + + # Now we can calculate the rotation matrix by applying the Rodrigues rotation formula + # https://mathworld.wolfram.com/RodriguesRotationFormula.html + # Find the angle between the principal axis of the scanned object and the principal axis of the original object + angle = np.arccos(np.dot(scanned_principal_axis, original_principal_axis)) + # Find the axis of rotation between the two principal axes by taking the cross product + axis = np.cross(scanned_principal_axis, original_principal_axis) + x, y, z = axis # unpack the axis of rotation + c = np.cos(angle) # cos(angle) + s = np.sin(angle) # sin(angle) + t = 1 - c # cos complement + rotation_matrix = np.array([ + [t*x*x + c, t*x*y - z*s, t*x*z + y*s], + [t*x*y + z*s, t*y*y + c, t*y*z - x*s], + [t*x*z - y*s, t*y*z + x*s, t*z*z + c] + ]) + + # Here we directly change the coords of each vertex in the actual scanned mesh by applying the rotation matrix (this was easier than applying it as an actual blender rotation) + for v in meshes[0].data.vertices: + v.co = rotation_matrix @ v.co + + +def scale_model(meshes, target_axis='none'): + ''' + After the scanned and original meshes are aligned, find the percent difference between the width, height, and depth of the two meshes + Then scale the scanned mesh by that percent difference + Takes an optional target_axis parameter to specify which axis to scale the scanned mesh by + ''' + # Create a numpy array of the vertices of the selected object in absolute coordinates + scanned_points = np.array([meshes[1].matrix_world @ v.co for v in meshes[0].data.vertices]) + original_points = np.array([meshes[0].matrix_world @ v.co for v in meshes[1].data.vertices]) + scanned_size, scanned_dim = scanned_points.shape + original_size, orignal_dim = original_points.shape + + # Find the width, height, and depth of the scanned and original meshes + scanned_width = np.max(scanned_points[:, 0]) - np.min(scanned_points[:, 0]) + scanned_height = np.max(scanned_points[:, 1]) - np.min(scanned_points[:, 1]) + scanned_depth = np.max(scanned_points[:, 2]) - np.min(scanned_points[:, 2]) + original_width = np.max(original_points[:, 0]) - np.min(original_points[:, 0]) + original_height = np.max(original_points[:, 1]) - np.min(original_points[:, 1]) + original_depth = np.max(original_points[:, 2]) - np.min(original_points[:, 2]) + print(f'X difference (mm): {scanned_width - original_width}') + print(f'Y difference (mm): {scanned_height - original_height}') + print(f'Z difference (mm): {scanned_depth - original_depth}') + # Find the percent difference between the scanned and original meshes + width_percent = scanned_width / original_width + height_percent = scanned_height / original_height + depth_percent = scanned_depth / original_depth + print(f'X percent: {width_percent*100}') + print(f'Y percent: {height_percent*100}') + print(f'Z percent: {depth_percent*100}') + + # Scale the scanned mesh uniformly by the specified target_axis + scale_factor = 1 + if target_axis == 'X' or target_axis == 'x': + scale_factor = width_percent + elif target_axis == 'Y' or target_axis == 'y': + scale_factor = height_percent + elif target_axis == 'Z' or target_axis == 'z': + scale_factor = depth_percent + + # Scale the scanned mesh by the percent difference + for v in meshes[1].data.vertices: + v.co *= scale_factor + + +def icp_step(meshes, max_iterations, tolerance=0.01): + ''' + Run Iterative Closest Point (ICP) to translate and rotate the scanned (first) mesh to align with the original (second) mesh + https://www.ipb.uni-bonn.de/html/teaching/msr2-2020/sse2-03-icp.pdf + Immediately converts to numpy arrays and performs all calculations in absolute coordinates + ''' + # Create a numpy array of the vertices of the selected object in absolute coordinates + scanned_points = np.array([meshes[1].matrix_world @ v.co for v in meshes[0].data.vertices]) + original_points = np.array([meshes[0].matrix_world @ v.co for v in meshes[1].data.vertices]) + scanned_size, scanned_dim = scanned_points.shape + original_size, orignal_dim = original_points.shape + + transformation = np.identity(scanned_dim) + translation_final = np.zeros(scanned_dim) + rotations_final = np.identity(scanned_dim) + + for i in range(max_iterations): + # Find the nearest neighbors between the scanned and original points + tree = KDTree(original_points) + distances, indices = tree.query(scanned_points) + + # Compute the transformation matrix using singular value decomposition + scanned_mean = np.mean(scanned_points, axis=0) + original_mean = np.mean(original_points[indices], axis=0) + centered_scanned = scanned_points - scanned_mean # subtract the mean from each point + centered_original = original_points[indices] - original_mean + + covariance_matrix = np.dot(centered_scanned.T, centered_original) + u, _, vh = np.linalg.svd(covariance_matrix) + rotation = np.dot(u, vh) + translation = original_mean - np.dot(rotation, scanned_mean) + + # Update the transformation matrix (and our translation and rotations) + transformation = np.dot(rotation, transformation) + transformation[:, -1] += translation + translation_final += translation + rotations_final = np.dot(rotation, rotations_final) + + # Apply the transformation to the source points, just dot with the rotation matrix and add the translation vector + transformed_source = np.dot(scanned_points, rotation) + translation + scanned_points = transformed_source + + # Check the convergence criteria + # Here I should really be taking into account the actual vector connecting points such that direction is accounted for + error = np.mean(distances) + if error < tolerance: + break + + # For each vertex in the actual scanned mesh object, move it to the corresponding vertex in the new_points array + for i, v in enumerate(meshes[0].data.vertices): + v.co = scanned_points[i] + + +def calculate_error(meshes): + ''' + Find the distance between each point on the original mesh and the closest face on the scanned mesh + ''' + # Create a numpy array of the vertices of both objects in absolute coordinates + scanned_points = np.array([meshes[1].matrix_world @ v.co for v in meshes[0].data.vertices]) + original_points = np.array([meshes[0].matrix_world @ v.co for v in meshes[1].data.vertices]) + + # Find the distance between all points on the original mesh and the closest face on the scanned mesh + tree = KDTree(scanned_points) + distances, indices = tree.query(original_points) + + # Initialize our distance array + errors = np.zeros(len(original_points)) + + # now find the closest point on the target mesh to each point on the source mesh + for i, point in enumerate(original_points): + # find the closest point on the scanned mesh to each point on the original mesh + errors[i] = distances[i] + + name = bpy.context.object.name + outputFile = bpy.path.abspath("//csv_export\\" + name + ".csv") + # save errors to a csv in the local directory + np.savetxt(outputFile, errors, delimiter=",") + + return errors + + +def assign_colors(meshes, errors): + ''' + Assign colors to each face of the original mesh based on the error at each vertex + https://medium.com/@bldevries/using-python-and-custom-data-to-vertex-color-your-blender-model-4fd0d69134a3 + ''' + # We want to color the original mesh + original_points = meshes[1] + + # delete all previous vertex color layers + for i in range(len(original_points.data.vertex_colors)): + original_points.data.vertex_colors.remove(original_points.data.vertex_colors[0]) + + # Find the max and min errors + max_error = np.max(errors) + min_error = np.min(errors) + print(f'Max error: {max_error}') + + # Normalize the errors + errors_norm = (errors - min_error) / (max_error - min_error) + + # Create a new vertex color layer + color_layer = original_points.data.vertex_colors.new(name="Color Errors") + + # We assign some amount of red based on error_norm + # Because each vertex has a value for each face it's connected to, we need to iterate through each vertex as well + for poly in original_points.data.polygons: + for vert_i_poly, vert_i_mesh in zip(poly.loop_indices, poly.vertices): + # Assign the color to the vertex + color_layer.data[vert_i_poly].color = (errors_norm[vert_i_mesh], 0, 0, 1) + + +def slice_rotors(meshes, slice_location_percent, slice_axis = 'y', slice_width = 0.1): + ''' + Produces 2D cross section segment of all the points that fall within the bounds created by + dividing the scanned and original meshes into vertical sliced number of divisions, + ''' + # Create a numpy array of the vertices of both objects in absolute coordinates + scanned_points = np.array([meshes[1].matrix_world @ v.co for v in meshes[0].data.vertices]) + original_points = np.array([meshes[0].matrix_world @ v.co for v in meshes[1].data.vertices]) + + # Find the min and max of the scanned mesh along the y-axis + scanned_min = np.min(scanned_points[:,1]) + scanned_max = np.max(scanned_points[:,1]) + # Same for original mesh + original_min = np.min(original_points[:,1]) + original_max = np.max(original_points[:,1]) + # Take the larger of the two minima and the smaller of the two maxima + min_y = np.max([scanned_min, original_min]) + max_y = np.min([scanned_max, original_max]) + + # Find the y-value of the slice + slice_y = min_y + (max_y - min_y) * slice_location_percent + + # Create an array to hold the points that fall within the slice + scanned_sliced_points = [] + original_sliced_points = [] + + # Find the points that fall within the scanned slice + for point in scanned_points: + if point[1] >= slice_y - slice_width/2 and point[1] <= slice_y + slice_width/2: + scanned_sliced_points.append(point) + # Same for original slice + for point in original_points: + if point[1] >= slice_y - slice_width/2 and point[1] <= slice_y + slice_width/2: + original_sliced_points.append(point) + # Quickly convert to numpy arrays + scanned_sliced_points = np.array(scanned_sliced_points) + original_sliced_points = np.array(original_sliced_points) + + # get the max and min x and z values of the scanned points + scanned_x_min = np.min(scanned_sliced_points[:,0]) + scanned_x_max = np.max(scanned_sliced_points[:,0]) + box_bound = (scanned_x_max - scanned_x_min)*1.25 + # Add a cube to the scene to represent the slice width + bpy.ops.mesh.primitive_cube_add(size=1, enter_editmode=False, align='WORLD', location=(0, slice_y, 0), scale=(box_bound, slice_width, box_bound)) + # Get the cube object + cube = bpy.context.object + # Set the cube to be wireframe + cube.display_type = 'WIRE' + + # set the image resolution in pixels + plt.gcf().set_size_inches(1080/100, 1080/100) + plt.scatter(original_sliced_points[:,0], original_sliced_points[:,2], s=0.1, c='red', label='Original') + plt.scatter(scanned_sliced_points[:,0], scanned_sliced_points[:,2], s=0.1, c='blue', label='Scanned', alpha=0.5) + plt.xlim(scanned_x_min*1.1, scanned_x_max*1.1) + plt.ylim(scanned_x_min*1.1, scanned_x_max*1.1) + plt.gca().set_aspect('equal', adjustable='box') # Set axes to be equal scale + # save the plot + name = 'slice_' + str(slice_location_percent) + outputFile = bpy.path.abspath("//csv_export\\" + name + ".png") + plt.savefig(outputFile) + + +def main(): + # For each mesh, set the origin to the center of mass and move it to the global origin + meshes = [] + for so in bpy.data.objects: + # if the object is not the camera, or the lamp + if so.type != 'CAMERA' and so.type != 'LAMP': + # Set the mesh origin to its center of mass and move it to the global origin + bpy.ops.object.select_all(action='DESELECT') + so.select_set(True) + # Set the center of mass to be the mesh's origin + bpy.ops.object.origin_set(type='ORIGIN_CENTER_OF_VOLUME') + so.location = [0,0,0] + # permanently apply the transformation + bpy.ops.object.transform_apply(location=True, rotation=True, scale=True) + # Add the mesh to the list of meshes + meshes.append(so) + ''' Align the principal axis of each mesh with the z axis ''' + #principal_axis_align(meshes) + + ''' Scale the meshes if there's a scaling issue) ''' +# scale_model(meshes) +# scale_model(meshes, 'y') + + ''' Perform ICP to finish the alignment for non-radially symmetric parts ''' +# icp_step(meshes, 5) + + '''Calculate the error between the two meshes. The assign colors to the original mesh based on the error at each point ''' +# errors = calculate_error(meshes) +# assign_colors(meshes, errors) + + ''' Slice the meshes into 2D cross sections ''' + slice_rotors(meshes, 0.5, 'y', 650 * 0.005) + +if __name__ == "__main__": + main() \ No newline at end of file diff --git a/final/numpy_stl_experiment.py b/final/numpy_stl_experiment.py deleted file mode 100644 index ea2045c..0000000 --- a/final/numpy_stl_experiment.py +++ /dev/null @@ -1,34 +0,0 @@ -import os -import numpy as np -from stl import mesh -import matplotlib.pyplot as plt -from mpl_toolkits import mplot3d - -def load_stl_files(): - stl_files = [file for file in os.listdir() if file.endswith('.stl')] - meshes = [] - for file in stl_files: - meshes.append(mesh.Mesh.from_file(file)) - return meshes - -def main(): - # Load STL files - meshes = load_stl_files() - - # Create a 3D plot - figure = plt.figure() - axes = mplot3d.Axes3D(figure) - - # Plot the meshes - for mesh_data in 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visualization of the shape -visualizer = steputils.Visualizer() - -# Display the visualization -visualizer.display(shape) \ No newline at end of file -- GitLab