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| from typing import Tuple | |
| import numpy as np | |
| XYZ = Tuple[np.ndarray, np.ndarray, np.ndarray] | |
| """ | |
| The normalized XYZ components of a normal map. Z is guaranteed to be >= 0. | |
| """ | |
| def normalize_normals(x: np.ndarray, y: np.ndarray) -> XYZ: | |
| # The square of the length of X and Y | |
| l_sq = np.square(x) + np.square(y) | |
| # If the length of X and Y is >1, then make it 1 | |
| l = np.sqrt(np.maximum(l_sq, 1)) | |
| x /= l | |
| y /= l | |
| l_sq = np.minimum(l_sq, 1, out=l_sq) | |
| # Compute Z | |
| z = np.sqrt(1 - l_sq) | |
| return x, y, z | |
| def gr_to_xyz(n: np.ndarray) -> XYZ: | |
| """ | |
| Takes a BGR or BGRA image and converts it into XYZ normal components only by looking at the R and G channels. | |
| """ | |
| x = n[:, :, 2] * 2 - 1 | |
| y = n[:, :, 1] * 2 - 1 | |
| return normalize_normals(x, y) | |
| def xyz_to_bgr(xyz: XYZ) -> np.ndarray: | |
| """ | |
| Converts the given XYZ components into an BGR image. | |
| """ | |
| x, y, z = xyz | |
| r = (x + 1) * 0.5 | |
| g = (y + 1) * 0.5 | |
| b = z | |
| return np.dstack((b, g, r)) | |
| def octahedral_gr_to_xyz(n: np.ndarray) -> XYZ: | |
| """ | |
| Takes a BGR or BGRA image of octahedral (RTX Remix) normals and converts it into XYZ normal components only by looking at the R and G channels. | |
| """ | |
| r = n[:, :, 2] * 2 - 1 | |
| g = n[:, :, 1] * 2 - 1 | |
| x: np.ndarray = (r + g) / 2 | |
| y: np.ndarray = r - x | |
| z: np.ndarray = 1 - np.abs(x) - np.abs(y) | |
| length = np.sqrt(np.square(x) + np.square(y) + np.square(z)) | |
| x /= length | |
| y /= length | |
| z /= length # type: ignore | |
| return x, y, z | |
| def xyz_to_octahedral_bgr(xyz: XYZ) -> np.ndarray: | |
| """ | |
| Converts the given XYZ components into an BGR image with normals using octahedral (RTX Remix) encoding. | |
| For more information about octahedral normals, see: | |
| https://knarkowicz.wordpress.com/2014/04/16/octahedron-normal-vector-encoding/ | |
| https://jcgt.org/published/0003/02/01/ | |
| """ | |
| x, y, z = xyz | |
| absolute = np.abs(x) + np.abs(y) + np.abs(z) | |
| x /= absolute | |
| y /= absolute | |
| # This is a trick used in RTX Remix to more efficiently encode normals. | |
| # Octahedral normals are defined for the whole range of values (so all possible unit vectors). | |
| # However, we know that we are working with hemispheric normal maps (z>=0) | |
| # and can use this knowledge to remap xy values to assume all possible values in [-1..1]x[-1..1]. | |
| r = x + y | |
| g = x - y | |
| r = (r + 1) * 0.5 | |
| g = (g + 1) * 0.5 | |
| b = np.zeros(x.shape, dtype=np.float32) | |
| return np.dstack((b, g, r)) | |