diff --git a/src/height_map/data/processed_depth_vals.json b/src/height_map/data/processed_depth_vals.json new file mode 100644 index 00000000..5a76ae7b --- /dev/null +++ b/src/height_map/data/processed_depth_vals.json @@ -0,0 +1 @@ +{"(0, 0)": 3.0419847992928095, "(0, 1)": 3.0314442529599184, "(0, 2)": 3.0209037066270277, "(0, 3)": 3.0103631602941365, "(0, 4)": 2.999822613961246, "(0, 5)": 2.9892820676283547, "(0, 6)": 2.978741521295464, "(0, 7)": 2.968200974962573, "(0, 8)": 2.957660428629682, "(0, 9)": 2.947119882296791, "(0, 10)": 2.9365793359639003, "(0, 11)": 2.926038789631009, "(0, 12)": 2.9154982432981185, "(0, 13)": 2.9049576969652273, "(0, 14)": 2.8944171506323366, "(0, 15)": 2.8838766042994455, "(0, 16)": 2.873336057966555, "(0, 17)": 2.8627955116336636, "(0, 18)": 2.852254965300773, "(0, 19)": 2.841714418967882, "(0, 20)": 2.8311738726349907, "(0, 21)": 2.8206333263021, "(0, 22)": 2.8100927799692093, "(0, 23)": 2.799552233636318, "(0, 24)": 2.789011687303427, "(0, 25)": 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62)": 2.3070403125866865, + "(163, 126)": 1.718118404588721, + "(23, 26)": 3.131430868556314, + "(307, 141)": 1.6611965133929207, + "(272, 21)": 3.360240344678669, + "(178, 45)": 2.6141423643394215, + "(104, 83)": 2.203718762968717, + "(144, 25)": 3.06674576233676, + "(142, 74)": 2.196073332793764, + "(7, 2)": 3.131430868556314, + "(207, 106)": 1.9246336737030707 +} \ No newline at end of file diff --git a/src/height_map/height_map.py b/src/height_map/height_map.py new file mode 100644 index 00000000..cbba0ed2 --- /dev/null +++ b/src/height_map/height_map.py @@ -0,0 +1,97 @@ +import json +import os +from typing import Dict, Tuple + +import numpy as np +import matplotlib.pyplot as plt + +HEIGHT: int = 180 +WIDTH: int = 330 +RAW_DEPTH_VALS_PATH: str = ( + f"{os.path.dirname(os.path.abspath(__file__))}/data/raw_depth_vals.json" +) +PROCESSED_DEPTH_VALS_PATH: str = ( + f"{os.path.dirname(os.path.abspath(__file__))}/data/processed_depth_vals.json" +) + + +def load_depth_vals(depth_vals_path: str) -> Dict[str, float]: + with open(depth_vals_path) as f: + depth_vals = json.load(f) + return depth_vals + + +def process_raw_depth_vals(raw_depth_vals: Dict[str, float]) -> np.ndarray: + depth_vals = np.zeros((HEIGHT, WIDTH), dtype=float) + points = np.zeros((HEIGHT * WIDTH, 3), dtype=float) + for y in range(HEIGHT): + for x in range(WIDTH): + depth = raw_depth_vals[str((x, y))] + depth_vals[y, x] = depth + points[y * WIDTH + x] = x, y, depth + return points + + +def least_squares(raw_depth_vals_path: str, drawit: bool = True) -> np.ndarray: + """Generate the parameters for the planar approximation using least squares. + From https://math.stackexchange.com/questions/99299/best-fitting-plane-given-a-set-of-points. + + I preserved the mathematical logic and the plotting implementation from the + given reference. + """ + raw_depth_vals = load_depth_vals(raw_depth_vals_path) + points = process_raw_depth_vals(raw_depth_vals) + + # Do fit + b = points[:, 2].T + A = np.block([points[:, 0:2], np.ones_like(points[:, 0:1])]) + + # Manual solution + fit = np.linalg.inv(A.T @ A) @ A.T @ b + errors = b - A @ fit + residual = np.linalg.norm(errors) + + print("solution: %f x + %f y + %f = z" % (fit[0], fit[1], fit[2])) + print("errors: \n", errors) + print("residual:", residual) + + if drawit: + xs, ys, zs = points[:, 0], points[:, 1], points[:, 2] + + # Plot raw data + plt.figure() + ax = plt.subplot(111, projection="3d") + ax.scatter(xs, ys, zs, color="b") + + # Plot plane + xlim = ax.get_xlim() + ylim = ax.get_ylim() + x_grid, y_grid = np.meshgrid( + np.arange(xlim[0], xlim[1]), np.arange(ylim[0], ylim[1]) + ) + z_grid = fit[0] * x_grid + fit[1] * y_grid + fit[2] + ax.plot_wireframe(x_grid, y_grid, z_grid, color="k") + + ax.set_xlabel("x") + ax.set_ylabel("y") + ax.set_zlabel("z") + plt.show() + return fit + + +def generate_processed_depth_vals( + raw_depth_vals_path: str, processed_depth_vals_path: str +): + a, b, c = least_squares(raw_depth_vals_path) + + processed_depth_vals: Dict[Tuple[int, int], float] = { + f"({x}, {y})": a * x + b * y + c for x in range(WIDTH) for y in range(HEIGHT) + } + with open(processed_depth_vals_path, "w") as f: + json.dump(processed_depth_vals, f) + + least_squares(processed_depth_vals_path) + + +if __name__ == "__main__": + generate_processed_depth_vals(RAW_DEPTH_VALS_PATH, PROCESSED_DEPTH_VALS_PATH)