ENH: Add multi-dimensional drag coefficient support (Cd as function of M, Re, α)

.pylintrc

@@ -229,6 +229,7 @@ good-names=FlightPhases,
            center_of_mass_without_motor_to_CDM,
            motor_center_of_dry_mass_to_CDM,
            generic_motor_cesaroni_M1520,
+           Re, # Reynolds number
 
 # Good variable names regexes, separated by a comma. If names match any regex,
 # they will always be accepted

rocketpy/mathutils/function.py

@@ -22,6 +22,7 @@
     LinearNDInterpolator,
     NearestNDInterpolator,
     RBFInterpolator,
+    RegularGridInterpolator,
 )
 
 from rocketpy.plots.plot_helpers import show_or_save_plot
@@ -43,6 +44,7 @@
     "spline": 3,
     "shepard": 4,
     "rbf": 5,
+    "linear_grid": 6,
 }
 EXTRAPOLATION_TYPES = {"zero": 0, "natural": 1, "constant": 2}
 
@@ -449,6 +451,41 @@ def rbf_interpolation(x, x_min, x_max, x_data, y_data, coeffs):  # pylint: disab
 
             self._interpolation_func = rbf_interpolation
 
+        elif interpolation == 6:  # linear_grid (RegularGridInterpolator)
+            # For grid interpolation, the actual interpolator is stored separately
+            # This function is a placeholder that should not be called directly
+            # since __get_value_opt_grid is used instead
+            if hasattr(self, "_grid_interpolator"):
+
+                def grid_interpolation(x, x_min, x_max, x_data, y_data, coeffs):  # pylint: disable=unused-argument
+                    return self._grid_interpolator(x)
+
+                self._interpolation_func = grid_interpolation
+            else:
+                # Fallback to shepard if grid interpolator not available
+                warnings.warn(
+                    "Grid interpolator not found, falling back to shepard interpolation"
+                )
+
+                def shepard_fallback(x, x_min, x_max, x_data, y_data, _):
+                    # pylint: disable=unused-argument
+                    arg_qty, arg_dim = x.shape
+                    result = np.empty(arg_qty)
+                    x = x.reshape((arg_qty, 1, arg_dim))
+                    sub_matrix = x_data - x
+                    distances_squared = np.sum(sub_matrix**2, axis=2)
+                    zero_distances = np.where(distances_squared == 0)
+                    valid_indexes = np.ones(arg_qty, dtype=bool)
+                    valid_indexes[zero_distances[0]] = False
+                    weights = distances_squared[valid_indexes] ** (-1.5)
+                    numerator_sum = np.sum(y_data * weights, axis=1)
+                    denominator_sum = np.sum(weights, axis=1)
+                    result[valid_indexes] = numerator_sum / denominator_sum
+                    result[~valid_indexes] = y_data[zero_distances[1]]
+                    return result
+
+                self._interpolation_func = shepard_fallback
+
         else:
             raise ValueError(f"Interpolation {interpolation} method not recognized.")
 
@@ -635,6 +672,66 @@ def __get_value_opt_nd(self, *args):
 
         return result
 
+    def __get_value_opt_grid(self, *args):  # pylint: disable=unused-private-member
+        """Evaluate the Function using RegularGridInterpolator for structured grids.
+
+        This method is dynamically assigned in from_grid() class method.
+
+        Parameters
+        ----------
+        args : tuple
+            Values where the Function is to be evaluated. Must match the number
+            of dimensions of the grid.
+
+        Returns
+        -------
+        result : scalar or ndarray
+            Value of the Function at the specified points.
+        """
+        # Check if we have the grid interpolator
+        if not hasattr(self, "_grid_interpolator"):
+            raise RuntimeError(
+                "Grid interpolator not initialized. Use from_grid() to create "
+                "a Function with grid interpolation."
+            )
+
+        # Convert args to appropriate format for RegularGridInterpolator
+        # RegularGridInterpolator expects points as (N, ndim) array
+        if len(args) != self.__dom_dim__:
+            raise ValueError(
+                f"Expected {self.__dom_dim__} arguments but got {len(args)}"
+            )
+
+        # Handle single point evaluation
+        point = np.array(args).reshape(1, -1)
+
+        # Handle extrapolation based on the extrapolation setting
+        if self.__extrapolation__ == "constant":
+            # Clamp point to grid boundaries for constant extrapolation
+            for i, axis in enumerate(self._grid_axes):
+                point[0, i] = np.clip(point[0, i], axis[0], axis[-1])
+            result = self._grid_interpolator(point)
+        elif self.__extrapolation__ == "zero":
+            # Check if point is outside bounds
+            outside_bounds = False
+            for i, axis in enumerate(self._grid_axes):
+                if point[0, i] < axis[0] or point[0, i] > axis[-1]:
+                    outside_bounds = True
+                    break
+            if outside_bounds:
+                result = np.array([0.0])
+            else:
+                result = self._grid_interpolator(point)
+        else:
+            # Natural or other extrapolation - use interpolator directly
+            result = self._grid_interpolator(point)
+
+        # Return scalar for single evaluation
+        if result.size == 1:
+            return float(result[0])
+
+        return result
+
     def __determine_1d_domain_bounds(self, lower, upper):
         """Determine domain bounds for 1-D function discretization.
 
@@ -3891,11 +3988,11 @@ def __validate_interpolation(self, interpolation):
         elif self.__dom_dim__ > 1:
             if interpolation is None:
                 interpolation = "shepard"
-            if interpolation.lower() not in ["shepard", "linear", "rbf"]:
+            if interpolation.lower() not in ["shepard", "linear", "rbf", "linear_grid"]:
                 warnings.warn(
                     (
                         "Interpolation method set to 'shepard'. The methods "
-                        "'linear', 'shepard' and 'rbf' are supported for "
+                        "'linear', 'shepard', 'rbf' and 'linear_grid' are supported for "
                         "multiple dimensions."
                     ),
                 )
@@ -3950,6 +4047,183 @@ def to_dict(self, **kwargs):  # pylint: disable=unused-argument
             "extrapolation": self.__extrapolation__,
         }
 
+    @classmethod
+    def from_grid(
+        cls,
+        grid_data,
+        axes,
+        inputs=None,
+        outputs=None,
+        interpolation="linear_grid",
+        extrapolation="constant",
+        **kwargs,
+    ):  # pylint: disable=too-many-statements #TODO: Refactor this method into smaller methods
+        """Creates a Function from N-dimensional grid data.
+
+        This method is designed for structured grid data, such as CFD simulation
+        results where values are computed on a regular grid. It uses
+        scipy.interpolate.RegularGridInterpolator for efficient interpolation.
+
+        Parameters
+        ----------
+        grid_data : ndarray
+            N-dimensional array containing the function values on the grid.
+            For example, for a 3D function Cd(M, Re, α), this would be a 3D array
+            where grid_data[i, j, k] = Cd(M[i], Re[j], α[k]).
+        axes : list of ndarray
+            List of 1D arrays defining the grid points along each axis.
+            Each array should be sorted in ascending order.
+            For example: [M_axis, Re_axis, alpha_axis].
+        inputs : list of str, optional
+            Names of the input variables. If None, generic names will be used.
+            For example: ['Mach', 'Reynolds', 'Alpha'].
+        outputs : str, optional
+            Name of the output variable. For example: 'Cd'.
+        interpolation : str, optional
+            Interpolation method. Default is 'linear_grid'.
+            Currently only 'linear_grid' is supported for grid data.
+        extrapolation : str, optional
+            Extrapolation behavior. Default is 'constant', which clamps to edge values.
+            'constant': Use nearest edge value for out-of-bounds points.
+            'zero': Return zero for out-of-bounds points.
+        **kwargs : dict, optional
+            Additional arguments passed to the Function constructor.
+
+        Returns
+        -------
+        Function
+            A Function object using RegularGridInterpolator for evaluation.
+
+        Notes
+        -----
+        - Grid data must be on a regular (structured) grid.
+        - For unstructured data, use the regular Function constructor with
+          scattered points.
+        - Extrapolation with 'constant' mode uses the nearest edge values,
+          which is appropriate for aerodynamic coefficients where extrapolation
+          beyond the data range should be avoided.
+
+        Examples
+        --------
+        >>> import numpy as np
+        >>> # Create 3D drag coefficient data
+        >>> mach = np.array([0.0, 0.5, 1.0, 1.5, 2.0])
+        >>> reynolds = np.array([1e5, 5e5, 1e6])
+        >>> alpha = np.array([0.0, 2.0, 4.0, 6.0])
+        >>> # Create a simple drag coefficient function
+        >>> M, Re, A = np.meshgrid(mach, reynolds, alpha, indexing='ij')
+        >>> cd_data = 0.3 + 0.1 * M + 1e-7 * Re + 0.01 * A
+        >>> # Create Function object
+        >>> cd_func = Function.from_grid(
+        ...     cd_data,
+        ...     [mach, reynolds, alpha],
+        ...     inputs=['Mach', 'Reynolds', 'Alpha'],
+        ...     outputs='Cd'
+        ... )
+        >>> # Evaluate at a point
+        >>> cd_func(1.2, 3e5, 3.0)
+        0.48000000000000004
+
+        """
+        # Validate inputs
+        if not isinstance(grid_data, np.ndarray):
+            grid_data = np.array(grid_data)
+
+        if not isinstance(axes, (list, tuple)):
+            raise ValueError("axes must be a list or tuple of 1D arrays")
+
+        # Ensure all axes are numpy arrays
+        axes = [
+            np.array(axis) if not isinstance(axis, np.ndarray) else axis
+            for axis in axes
+        ]
+
+        # Check dimensions match
+        if len(axes) != grid_data.ndim:
+            raise ValueError(
+                f"Number of axes ({len(axes)}) must match grid_data dimensions "
+                f"({grid_data.ndim})"
+            )
+
+        # Check each axis matches corresponding grid dimension
+        for i, axis in enumerate(axes):
+            if len(axis) != grid_data.shape[i]:
+                raise ValueError(
+                    f"Axis {i} has {len(axis)} points but grid dimension {i} "
+                    f"has {grid_data.shape[i]} points"
+                )
+
+        # Set default inputs if not provided
+        if inputs is None:
+            inputs = [f"x{i}" for i in range(len(axes))]
+        elif len(inputs) != len(axes):
+            raise ValueError(
+                f"Number of inputs ({len(inputs)}) must match number of axes ({len(axes)})"
+            )
+
+        # Create a new Function instance
+        func = cls.__new__(cls)
+
+        # Store grid-specific data first
+        func._grid_axes = axes
+        func._grid_data = grid_data
+
+        # Create RegularGridInterpolator
+        # We handle extrapolation manually in __get_value_opt_grid,
+        # so we set bounds_error=False and let it extrapolate linearly
+        # (which we'll override when needed)
+        func._grid_interpolator = RegularGridInterpolator(
+            axes,
+            grid_data,
+            method="linear",
+            bounds_error=False,
+            fill_value=None,  # Linear extrapolation (will be overridden by manual handling)
+        )
+
+        # Create placeholder domain and image for compatibility
+        # This flattens the grid for any code expecting these attributes
+        mesh = np.meshgrid(*axes, indexing="ij")
+        domain_points = np.column_stack([m.ravel() for m in mesh])
+        func._domain = domain_points
+        func._image = grid_data.ravel()
+
+        # Set source as flattened data array (for compatibility with serialization, etc.)
+        func.source = np.column_stack([domain_points, func._image])
+
+        # Initialize basic attributes
+        func.__inputs__ = inputs
+        func.__outputs__ = outputs if outputs is not None else "f"
+        func.__interpolation__ = interpolation
+        func.__extrapolation__ = extrapolation
+        func.title = kwargs.get("title", None)
+        func.__img_dim__ = 1
+        func.__cropped_domain__ = (None, None)
+        func._source_type = SourceType.ARRAY
+        func.__dom_dim__ = len(axes)
+
+        # Set basic array attributes for compatibility
+        func.x_array = axes[0]
+        func.x_initial, func.x_final = axes[0][0], axes[0][-1]
+        func.y_array = func._image[: len(axes[0])]  # Placeholder
+        func.y_initial, func.y_final = func._image[0], func._image[-1]
+        if len(axes) > 2:
+            func.z_array = axes[2]
+            func.z_initial, func.z_final = axes[2][0], axes[2][-1]
+
+        # Set get_value_opt to use grid interpolation
+        func.get_value_opt = func.__get_value_opt_grid
+
+        # Set interpolation and extrapolation functions
+        func.__set_interpolation_func()
+        func.__set_extrapolation_func()
+
+        # Set inputs and outputs properly
+        func.set_inputs(inputs)
+        func.set_outputs(outputs)
+        func.set_title(func.title)
+
+        return func
+
     @classmethod
     def from_dict(cls, func_dict):
         """Creates a Function instance from a dictionary.

rocketpy/rocket/rocket.py

@@ -341,20 +341,28 @@ def __init__(  # pylint: disable=too-many-statements
         )
 
         # Define aerodynamic drag coefficients
-        self.power_off_drag = Function(
-            power_off_drag,
-            "Mach Number",
-            "Drag Coefficient with Power Off",
-            "linear",
-            "constant",
-        )
-        self.power_on_drag = Function(
-            power_on_drag,
-            "Mach Number",
-            "Drag Coefficient with Power On",
-            "linear",
-            "constant",
-        )
+        # If already a Function, use it directly (preserves multi-dimensional drag)
+        if isinstance(power_off_drag, Function):
+            self.power_off_drag = power_off_drag
+        else:
+            self.power_off_drag = Function(
+                power_off_drag,
+                "Mach Number",
+                "Drag Coefficient with Power Off",
+                "linear",
+                "constant",
+            )
+
+        if isinstance(power_on_drag, Function):
+            self.power_on_drag = power_on_drag
+        else:
+            self.power_on_drag = Function(
+                power_on_drag,
+                "Mach Number",
+                "Drag Coefficient with Power On",
+                "linear",
+                "constant",
+            )
 
         # Create a, possibly, temporary empty motor
         # self.motors = Components()  # currently unused, only 1 motor is supported