com.jme3.math.CurveAndSurfaceMath Maven / Gradle / Ivy

Go to download
Show more of this group Show more artifacts with this name
Show all versions of jme3-core Show documentation
jMonkeyEngine is a 3-D game engine for adventurous Java developers
The newest version!
/*
 * Copyright (c) 2009-2020 jMonkeyEngine
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 *
 * * Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 *
 * * Redistributions in binary form must reproduce the above copyright
 *   notice, this list of conditions and the following disclaimer in the
 *   documentation and/or other materials provided with the distribution.
 *
 * * Neither the name of 'jMonkeyEngine' nor the names of its contributors
 *   may be used to endorse or promote products derived from this software
 *   without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
 * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
 * LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */
package com.jme3.math;

import com.jme3.math.Spline.SplineType;
import java.util.List;

/**
 * This class offers methods to help with curves and surfaces calculations.
 *
 * @author Marcin Roguski (Kealthas)
 */
public class CurveAndSurfaceMath {
    private static final float KNOTS_MINIMUM_DELTA = 0.0001f;

    /**
     * A private constructor is defined to avoid instantiation of this class.
     */
    private CurveAndSurfaceMath() {
    }

    /**
     * This method interpolates the data for the nurbs curve.
     *
     * @param u   the u value
     * @param nurbSpline
     *            the nurbs spline definition
     * @param store
     *            the resulting point in 3D space
     */
    public static void interpolateNurbs(float u, Spline nurbSpline, Vector3f store) {
        if (nurbSpline.getType() != SplineType.Nurb) {
            throw new IllegalArgumentException("Given spline is not of a NURB type!");
        }
        List controlPoints = nurbSpline.getControlPoints();
        float[] weights = nurbSpline.getWeights();
        List knots = nurbSpline.getKnots();
        int controlPointAmount = controlPoints.size();
        store.set(Vector3f.ZERO);
        float delimiter = 0;
        for (int i = 0; i < controlPointAmount; ++i) {
            float val = weights[i] * CurveAndSurfaceMath.computeBaseFunctionValue(i, nurbSpline.getBasisFunctionDegree(), u, knots);
            store.addLocal(nurbSpline.getControlPoints().get(i)
                    .mult(val));
            delimiter += val;
        }
        store.divideLocal(delimiter);
    }

    /**
     * This method interpolates the data for the nurbs surface.
     *
     * @param u   the u value
     * @param v   the v value
     * @param controlPoints
     *            the nurbs' control points
     * @param knots
     *            the nurbs' knots
     * @param basisUFunctionDegree
     *            the degree of basis U function
     * @param basisVFunctionDegree
     *            the degree of basis V function
     * @param store
     *            the resulting point in 3D space
     */
    public static void interpolate(float u, float v, List> controlPoints, List[] knots,
            int basisUFunctionDegree, int basisVFunctionDegree, Vector3f store) {
        store.set(Vector3f.ZERO);
        float delimiter = 0;
        int vControlPointsAmount = controlPoints.size();
        int uControlPointsAmount = controlPoints.get(0).size();
        for (int i = 0; i < vControlPointsAmount; ++i) {
            for (int j = 0; j < uControlPointsAmount; ++j) {
                Vector4f controlPoint = controlPoints.get(i).get(j);
                float val = controlPoint.w
                        * CurveAndSurfaceMath.computeBaseFunctionValue(i, basisVFunctionDegree, v, knots[1])
                        * CurveAndSurfaceMath.computeBaseFunctionValue(j, basisUFunctionDegree, u, knots[0]);
                store.addLocal(controlPoint.x * val, controlPoint.y * val, controlPoint.z * val);
                delimiter += val;
            }
        }
        store.divideLocal(delimiter);
    }

    /**
     * This method prepares the knots to be used. If the knots represent
     * non-uniform B-splines (first and last knot values are being repeated) it
     * leads to NaN results during calculations. This method adds a small number
     * to each of such knots to avoid NaN's.
     *
     * @param knots
     *            the knots to be prepared to use
     * @param basisFunctionDegree
     *            the degree of basis function
     */
    // TODO: improve this; constant delta may lead to errors if the difference between tha last repeated
    // point and the following one is lower than it
    public static void prepareNurbsKnots(List knots, int basisFunctionDegree) {
        float delta = KNOTS_MINIMUM_DELTA;
        float prevValue = knots.get(0).floatValue();
        for (int i = 1; i < knots.size(); ++i) {
            float value = knots.get(i).floatValue();
            if (value <= prevValue) {
                value += delta;
                knots.set(i, Float.valueOf(value));
                delta += KNOTS_MINIMUM_DELTA;
            } else {
                delta = KNOTS_MINIMUM_DELTA;//reset the delta's value
            }

            prevValue = value;
        }
    }

    /**
     * This method computes the base function value for the NURB curve.
     *
     * @param i   the knot index
     * @param k   the base function degree
     * @param t   the knot value
     * @param knots
     *            the knots' values
     * @return the base function value
     */
    private static float computeBaseFunctionValue(int i, int k, float t, List knots) {
        if (k == 1) {
            return knots.get(i) <= t && t < knots.get(i + 1) ? 1.0f : 0.0f;
        } else {
            return (t - knots.get(i)) / (knots.get(i + k - 1) - knots.get(i))
                    * CurveAndSurfaceMath.computeBaseFunctionValue(i, k - 1, t, knots)
                    + (knots.get(i + k) - t) / (knots.get(i + k) - knots.get(i + 1))
                    * CurveAndSurfaceMath.computeBaseFunctionValue(i + 1, k - 1, t, knots);
        }
    }
}