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| Original file line number | Diff line number | Diff line change |
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| import numpy as np | ||
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| class CoordinateSystemConverter(): | ||
| """ | ||
| Coordinate System Converter class. | ||
| Args: | ||
| cs1_direction: list, The visual direction corresponding to the xyz axis, | ||
| can be: | ||
| ["left"/"right"/"up"/"down"/"forward"/"back"/ | ||
| "l"/"r"/"u"/"d"/"f"/"b"/ | ||
| "-left"/"-right"/"-up"/"-down"/"-forward"/"-back"/ | ||
| "-l"/"-r"/"-u"/"-d"/"-f"/"-b"] | ||
| cs2_direction: list, The visual direction corresponding to the xyz axis, | ||
| can be: | ||
| ["left"/"right"/"up"/"down"/"forward"/"back"/ | ||
| "l"/"r"/"u"/"d"/"f"/"b"/ | ||
| "-left"/"-right"/"-up"/"-down"/"-forward"/"-back"/ | ||
| "-l"/"-r"/"-u"/"-d"/"-f"/"-b"] | ||
| """ | ||
| def __init__(self, cs1_direction=["right", "up", "forward"], cs2_direction=["right", "up", "forward"]): | ||
| self.cs1_dir, self.cs1_axis, self.cs1_sign, self.cs1_system = self._preprocessing(cs1_direction) | ||
| self.cs2_dir, self.cs2_axis, self.cs2_sign, self.cs2_system = self._preprocessing(cs2_direction) | ||
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| self.cs1_to_cs2_map = [ | ||
| self.cs1_axis[self.cs2_dir[0]], | ||
| self.cs1_axis[self.cs2_dir[1]], | ||
| self.cs1_axis[self.cs2_dir[2]], | ||
| ] | ||
| self.cs1_to_cs2_sign = [ | ||
| self.cs1_sign[self.cs2_dir[0]] * self.cs2_sign[self.cs2_dir[0]], | ||
| self.cs1_sign[self.cs2_dir[1]] * self.cs2_sign[self.cs2_dir[1]], | ||
| self.cs1_sign[self.cs2_dir[2]] * self.cs2_sign[self.cs2_dir[2]], | ||
| ] | ||
| self.cs2_to_cs1_map = [ | ||
| self.cs2_axis[self.cs1_dir[0]], | ||
| self.cs2_axis[self.cs1_dir[1]], | ||
| self.cs2_axis[self.cs1_dir[2]], | ||
| ] | ||
| self.cs2_to_cs1_sign = [ | ||
| self.cs1_sign[self.cs1_dir[0]] * self.cs2_sign[self.cs1_dir[0]], | ||
| self.cs1_sign[self.cs1_dir[1]] * self.cs2_sign[self.cs1_dir[1]], | ||
| self.cs1_sign[self.cs1_dir[2]] * self.cs2_sign[self.cs1_dir[2]], | ||
| ] | ||
| self.cs1_left_or_right = self.cs1_sign['right'] * self.cs1_sign['up'] * self.cs1_sign['forward'] | ||
| self.cs2_left_or_right = self.cs2_sign['right'] * self.cs2_sign['up'] * self.cs2_sign['forward'] | ||
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| def _preprocessing(self, direction): | ||
| dir = ["", "", ""] | ||
| axis = {} | ||
| sign = {} | ||
| direction_in_left = [[], [], []] | ||
| for i in range(3): | ||
| if direction[i] in ["right", "r", "-l", "-left"]: | ||
| dir[i] = "right" | ||
| axis["right"] = i | ||
| sign["right"] = 1 | ||
| direction_in_left[i] = [1, 0, 0] | ||
| elif direction[i] in ["up", "u", "-d", "-down"]: | ||
| dir[i] = "up" | ||
| axis["up"] = i | ||
| sign["up"] = 1 | ||
| direction_in_left[i] = [0, 1, 0] | ||
| elif direction[i] in ["forward", "f", "-b", "-back"]: | ||
| dir[i] = "forward" | ||
| axis["forward"] = i | ||
| sign["forward"] = 1 | ||
| direction_in_left[i] = [0, 0, 1] | ||
| elif direction[i] in ["-right", "-r", "l", "left"]: | ||
| dir[i] = "right" | ||
| axis["right"] = i | ||
| sign["right"] = -1 | ||
| direction_in_left[i] = [-1, 0, 0] | ||
| elif direction[i] in ["-up", "-u", "d", "down"]: | ||
| dir[i] = "up" | ||
| axis["up"] = i | ||
| sign["up"] = -1 | ||
| direction_in_left[i] = [0, -1, 0] | ||
| elif direction[i] in ["-forward", "-f", "b", "back"]: | ||
| dir[i] = "forward" | ||
| axis["forward"] = i | ||
| sign["forward"] = -1 | ||
| direction_in_left[i] = [0, 0, -1] | ||
| else: | ||
| raise f"{direction[i]} is Unrecognized axis" | ||
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| z = self._cross(direction_in_left[0], direction_in_left[1]) | ||
| if z == direction_in_left[2]: | ||
| system = 1 | ||
| else: | ||
| system = -1 | ||
| return dir, axis, sign, system | ||
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| def _cross(self, lhs: list, rhs: list) -> list: | ||
| return [lhs[1] * rhs[2] - lhs[2] * rhs[1], lhs[2] * rhs[0] - lhs[0] * rhs[2], lhs[0] * rhs[1] - lhs[1] * rhs[0]] | ||
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| def cs1_pos_to_cs2_pos(self, pos: list) -> list: | ||
| """ | ||
| Convert position form Coordinate System 1 to Coordinate System 2. | ||
| Args: | ||
| pos: List of length 3, position of Coordinate System 1. | ||
| Return: | ||
| list: List of length 3, position of Coordinate System 2. | ||
| """ | ||
| x = pos[self.cs1_to_cs2_map[0]] * self.cs1_to_cs2_sign[0] | ||
| y = pos[self.cs1_to_cs2_map[1]] * self.cs1_to_cs2_sign[1] | ||
| z = pos[self.cs1_to_cs2_map[2]] * self.cs1_to_cs2_sign[2] | ||
| return [x, y, z] | ||
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| def cs2_pos_to_cs1_pos(self, pos: list) -> list: | ||
| """ | ||
| Convert position form Coordinate System 2 to Coordinate System 1. | ||
| Args: | ||
| pos: List of length 3, position of Coordinate System 2. | ||
| Return: | ||
| list: List of length 3, position of Coordinate System 1. | ||
| """ | ||
| x = pos[self.cs2_to_cs1_map[0]] * self.cs2_to_cs1_sign[0] | ||
| y = pos[self.cs2_to_cs1_map[1]] * self.cs2_to_cs1_sign[1] | ||
| z = pos[self.cs2_to_cs1_map[2]] * self.cs2_to_cs1_sign[2] | ||
| return [x, y, z] | ||
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| def cs1_quat_to_cs2_quat(self, quat: list) -> list: | ||
| """ | ||
| Convert quaternion form Coordinate System 1 to Coordinate System 2. | ||
| Args: | ||
| quat: List of length 3, quaternion of Coordinate System 1. | ||
| Return: | ||
| list: List of length 3, quaternion of Coordinate System 2. | ||
| """ | ||
| x = quat[self.cs1_to_cs2_map[0]] * self.cs1_to_cs2_sign[0] | ||
| y = quat[self.cs1_to_cs2_map[1]] * self.cs1_to_cs2_sign[1] | ||
| z = quat[self.cs1_to_cs2_map[2]] * self.cs1_to_cs2_sign[2] | ||
| w = quat[3] * self.cs1_system * self.cs2_system | ||
| return [x, y, z, w] | ||
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| def cs2_quat_to_cs1_quat(self, quat: list) -> list: | ||
| """ | ||
| Convert quaternion form Coordinate System 2 to Coordinate System 1. | ||
| Args: | ||
| quat: List of length 4, quaternion[x,y,z,w] of Coordinate System 2. | ||
| Return: | ||
| list: List of length 4, quaternion[x,y,z,w] of Coordinate System 1. | ||
| """ | ||
| x = quat[self.cs2_to_cs1_map[0]] * self.cs2_to_cs1_sign[0] | ||
| y = quat[self.cs2_to_cs1_map[1]] * self.cs2_to_cs1_sign[1] | ||
| z = quat[self.cs2_to_cs1_map[2]] * self.cs2_to_cs1_sign[2] | ||
| w = quat[3] * self.cs1_system * self.cs2_system | ||
| return [x, y, z, w] | ||
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| def cs1_scale_to_cs2_scale(self, scale: list) -> list: | ||
| """ | ||
| Convert scale form Coordinate System 1 to Coordinate System 2. | ||
| Args: | ||
| scale: List of length 3, scale of Coordinate System 1. | ||
| Return: | ||
| list: List of length 3, scale of Coordinate System 2. | ||
| """ | ||
| x = scale[self.cs1_to_cs2_map[0]] | ||
| y = scale[self.cs1_to_cs2_map[1]] | ||
| z = scale[self.cs1_to_cs2_map[2]] | ||
| return [x, y, z] | ||
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| def cs2_scale_to_cs1_scale(self, scale: list) -> list: | ||
| """ | ||
| Convert scale form Coordinate System 2 to Coordinate System 1. | ||
| Args: | ||
| scale: List of length 3, scale of Coordinate System 2. | ||
| Return: | ||
| list: List of length 3, scale of Coordinate System 1. | ||
| """ | ||
| x = scale[self.cs2_to_cs1_map[0]] | ||
| y = scale[self.cs2_to_cs1_map[1]] | ||
| z = scale[self.cs2_to_cs1_map[2]] | ||
| return [x, y, z] | ||
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| def cs1_matrix_to_cs2_matrix(self, matrix) -> np.ndarray: | ||
| """ | ||
| Convert rotation matrix form Coordinate System 1 to Coordinate System 2. | ||
| Args: | ||
| matrix: list or np.ndarray shape[3,3], rotation matrix of Coordinate System 1. | ||
| Return: | ||
| np.ndarray: shape[3,3], rotation matrix of Coordinate System 2. | ||
| """ | ||
| quaternion = self.matrix_to_quat(matrix) | ||
| quaternion = self.cs1_quat_to_cs2_quat(quaternion) | ||
| return self.quat_to_matrix(quaternion) | ||
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| def cs2_matrix_to_cs1_matrix(self, matrix) -> np.ndarray: | ||
| """ | ||
| Convert rotation matrix form Coordinate System 2 to Coordinate System 1. | ||
| Args: | ||
| matrix: list or np.ndarray shape[3,3], rotation matrix of Coordinate System 2. | ||
| Return: | ||
| np.ndarray: shape[3,3], rotation matrix of Coordinate System 1. | ||
| """ | ||
| quaternion = self.matrix_to_quat(matrix) | ||
| quaternion = self.cs2_quat_to_cs1_quat(quaternion) | ||
| return self.quat_to_matrix(quaternion) | ||
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| def quat_to_matrix(self, quat=[0,0,0,1]) -> np.ndarray: | ||
| return np.array([ | ||
| [1 - 2 * (quat[1] ** 2 + quat[2] ** 2), 2 * (quat[0] * quat[1] - quat[2] * quat[3]), 2 * (quat[0] * quat[2] + quat[1] * quat[3])], | ||
| [2 * (quat[0] * quat[1] + quat[2] * quat[3]), 1 - 2 * (quat[0] ** 2 + quat[2] ** 2), 2 * (quat[1] * quat[2] - quat[0] * quat[3])], | ||
| [2 * (quat[0] * quat[2] - quat[1] * quat[3]), 2 * (quat[1] * quat[2] + quat[0] * quat[3]), 1 - 2 * (quat[0] ** 2 + quat[1] ** 2)] | ||
| ]) | ||
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| def matrix_to_quat(self, matrix) -> list: | ||
| m = np.array(matrix, dtype=float) | ||
| trace = np.trace(m) | ||
| if trace > 0: | ||
| s = 0.5 / np.sqrt(trace + 1.0) | ||
| w = 0.25 / s | ||
| x = (m[2, 1] - m[1, 2]) * s | ||
| y = (m[0, 2] - m[2, 0]) * s | ||
| z = (m[1, 0] - m[0, 1]) * s | ||
| elif m[0, 0] > m[1, 1] and m[0, 0] > m[2, 2]: | ||
| s = 2.0 * np.sqrt(1.0 + m[0, 0] - m[1, 1] - m[2, 2]) | ||
| w = (m[2, 1] - m[1, 2]) / s | ||
| x = 0.25 * s | ||
| y = (m[0, 1] + m[1, 0]) / s | ||
| z = (m[0, 2] + m[2, 0]) / s | ||
| elif m[1, 1] > m[2, 2]: | ||
| s = 2.0 * np.sqrt(1.0 + m[1, 1] - m[0, 0] - m[2, 2]) | ||
| w = (m[0, 2] - m[2, 0]) / s | ||
| x = (m[0, 1] + m[1, 0]) / s | ||
| y = 0.25 * s | ||
| z = (m[1, 2] + m[2, 1]) / s | ||
| else: | ||
| s = 2.0 * np.sqrt(1.0 + m[2, 2] - m[0, 0] - m[1, 1]) | ||
| w = (m[1, 0] - m[0, 1]) / s | ||
| x = (m[0, 2] + m[2, 0]) / s | ||
| y = (m[1, 2] + m[2, 1]) / s | ||
| z = 0.25 * s | ||
| return [x, y, z, w] |
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