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With inspiration from other libraries

There is a newer version: 2.12.15

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package org.apache.commons.math3.analysis.interpolation;

import org.apache.commons.math3.analysis.TrivariateFunction;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.NoDataException;
import org.apache.commons.math3.exception.NonMonotonicSequenceException;
import org.apache.commons.math3.exception.NumberIsTooSmallException;

/**
 * Interface representing a trivariate real interpolating function where the
 * sample points must be specified on a regular grid.
 *
 * @since 2.2
 */
public interface TrivariateGridInterpolator {
    /**
     * Compute an interpolating function for the dataset.
     *
     * @param xval All the x-coordinates of the interpolation points, sorted
     * in increasing order.
     * @param yval All the y-coordinates of the interpolation points, sorted
     * in increasing order.
     * @param zval All the z-coordinates of the interpolation points, sorted
     * in increasing order.
     * @param fval the values of the interpolation points on all the grid knots:
     * {@code fval[i][j][k] = f(xval[i], yval[j], zval[k])}.
     * @return a function that interpolates the data set.
     * @throws NoDataException if any of the arrays has zero length.
     * @throws DimensionMismatchException if the array lengths are inconsistent.
     * @throws NonMonotonicSequenceException if arrays are not sorted
     * @throws NumberIsTooSmallException if the number of points is too small for
     * the order of the interpolation
     */
    TrivariateFunction interpolate(double[] xval, double[] yval, double[] zval,
                                   double[][][] fval)
        throws NoDataException, NumberIsTooSmallException,
               DimensionMismatchException, NonMonotonicSequenceException;
}