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Posted to commits@commons.apache.org by tn...@apache.org on 2015/02/16 23:39:47 UTC
[17/82] [partial] [math] Update for next development iteration:
commons-math4
http://git-wip-us.apache.org/repos/asf/commons-math/blob/a7b4803f/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Rotation.java
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diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Rotation.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Rotation.java
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-/*
- * 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.geometry.euclidean.threed;
-
-import java.io.Serializable;
-
-import org.apache.commons.math3.exception.MathArithmeticException;
-import org.apache.commons.math3.exception.MathIllegalArgumentException;
-import org.apache.commons.math3.exception.util.LocalizedFormats;
-import org.apache.commons.math3.util.FastMath;
-import org.apache.commons.math3.util.MathArrays;
-
-/**
- * This class implements rotations in a three-dimensional space.
- *
- * <p>Rotations can be represented by several different mathematical
- * entities (matrices, axe and angle, Cardan or Euler angles,
- * quaternions). This class presents an higher level abstraction, more
- * user-oriented and hiding this implementation details. Well, for the
- * curious, we use quaternions for the internal representation. The
- * user can build a rotation from any of these representations, and
- * any of these representations can be retrieved from a
- * <code>Rotation</code> instance (see the various constructors and
- * getters). In addition, a rotation can also be built implicitly
- * from a set of vectors and their image.</p>
- * <p>This implies that this class can be used to convert from one
- * representation to another one. For example, converting a rotation
- * matrix into a set of Cardan angles from can be done using the
- * following single line of code:</p>
- * <pre>
- * double[] angles = new Rotation(matrix, 1.0e-10).getAngles(RotationOrder.XYZ);
- * </pre>
- * <p>Focus is oriented on what a rotation <em>do</em> rather than on its
- * underlying representation. Once it has been built, and regardless of its
- * internal representation, a rotation is an <em>operator</em> which basically
- * transforms three dimensional {@link Vector3D vectors} into other three
- * dimensional {@link Vector3D vectors}. Depending on the application, the
- * meaning of these vectors may vary and the semantics of the rotation also.</p>
- * <p>For example in an spacecraft attitude simulation tool, users will often
- * consider the vectors are fixed (say the Earth direction for example) and the
- * frames change. The rotation transforms the coordinates of the vector in inertial
- * frame into the coordinates of the same vector in satellite frame. In this
- * case, the rotation implicitly defines the relation between the two frames.</p>
- * <p>Another example could be a telescope control application, where the rotation
- * would transform the sighting direction at rest into the desired observing
- * direction when the telescope is pointed towards an object of interest. In this
- * case the rotation transforms the direction at rest in a topocentric frame
- * into the sighting direction in the same topocentric frame. This implies in this
- * case the frame is fixed and the vector moves.</p>
- * <p>In many case, both approaches will be combined. In our telescope example,
- * we will probably also need to transform the observing direction in the topocentric
- * frame into the observing direction in inertial frame taking into account the observatory
- * location and the Earth rotation, which would essentially be an application of the
- * first approach.</p>
- *
- * <p>These examples show that a rotation is what the user wants it to be. This
- * class does not push the user towards one specific definition and hence does not
- * provide methods like <code>projectVectorIntoDestinationFrame</code> or
- * <code>computeTransformedDirection</code>. It provides simpler and more generic
- * methods: {@link #applyTo(Vector3D) applyTo(Vector3D)} and {@link
- * #applyInverseTo(Vector3D) applyInverseTo(Vector3D)}.</p>
- *
- * <p>Since a rotation is basically a vectorial operator, several rotations can be
- * composed together and the composite operation <code>r = r<sub>1</sub> o
- * r<sub>2</sub></code> (which means that for each vector <code>u</code>,
- * <code>r(u) = r<sub>1</sub>(r<sub>2</sub>(u))</code>) is also a rotation. Hence
- * we can consider that in addition to vectors, a rotation can be applied to other
- * rotations as well (or to itself). With our previous notations, we would say we
- * can apply <code>r<sub>1</sub></code> to <code>r<sub>2</sub></code> and the result
- * we get is <code>r = r<sub>1</sub> o r<sub>2</sub></code>. For this purpose, the
- * class provides the methods: {@link #applyTo(Rotation) applyTo(Rotation)} and
- * {@link #applyInverseTo(Rotation) applyInverseTo(Rotation)}.</p>
- *
- * <p>Rotations are guaranteed to be immutable objects.</p>
- *
- * @see Vector3D
- * @see RotationOrder
- * @since 1.2
- */
-
-public class Rotation implements Serializable {
-
- /** Identity rotation. */
- public static final Rotation IDENTITY = new Rotation(1.0, 0.0, 0.0, 0.0, false);
-
- /** Serializable version identifier */
- private static final long serialVersionUID = -2153622329907944313L;
-
- /** Scalar coordinate of the quaternion. */
- private final double q0;
-
- /** First coordinate of the vectorial part of the quaternion. */
- private final double q1;
-
- /** Second coordinate of the vectorial part of the quaternion. */
- private final double q2;
-
- /** Third coordinate of the vectorial part of the quaternion. */
- private final double q3;
-
- /** Build a rotation from the quaternion coordinates.
- * <p>A rotation can be built from a <em>normalized</em> quaternion,
- * i.e. a quaternion for which q<sub>0</sub><sup>2</sup> +
- * q<sub>1</sub><sup>2</sup> + q<sub>2</sub><sup>2</sup> +
- * q<sub>3</sub><sup>2</sup> = 1. If the quaternion is not normalized,
- * the constructor can normalize it in a preprocessing step.</p>
- * <p>Note that some conventions put the scalar part of the quaternion
- * as the 4<sup>th</sup> component and the vector part as the first three
- * components. This is <em>not</em> our convention. We put the scalar part
- * as the first component.</p>
- * @param q0 scalar part of the quaternion
- * @param q1 first coordinate of the vectorial part of the quaternion
- * @param q2 second coordinate of the vectorial part of the quaternion
- * @param q3 third coordinate of the vectorial part of the quaternion
- * @param needsNormalization if true, the coordinates are considered
- * not to be normalized, a normalization preprocessing step is performed
- * before using them
- */
- public Rotation(double q0, double q1, double q2, double q3,
- boolean needsNormalization) {
-
- if (needsNormalization) {
- // normalization preprocessing
- double inv = 1.0 / FastMath.sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
- q0 *= inv;
- q1 *= inv;
- q2 *= inv;
- q3 *= inv;
- }
-
- this.q0 = q0;
- this.q1 = q1;
- this.q2 = q2;
- this.q3 = q3;
-
- }
-
- /** Build a rotation from an axis and an angle.
- * <p>We use the convention that angles are oriented according to
- * the effect of the rotation on vectors around the axis. That means
- * that if (i, j, k) is a direct frame and if we first provide +k as
- * the axis and π/2 as the angle to this constructor, and then
- * {@link #applyTo(Vector3D) apply} the instance to +i, we will get
- * +j.</p>
- * <p>Another way to represent our convention is to say that a rotation
- * of angle θ about the unit vector (x, y, z) is the same as the
- * rotation build from quaternion components { cos(-θ/2),
- * x * sin(-θ/2), y * sin(-θ/2), z * sin(-θ/2) }.
- * Note the minus sign on the angle!</p>
- * <p>On the one hand this convention is consistent with a vectorial
- * perspective (moving vectors in fixed frames), on the other hand it
- * is different from conventions with a frame perspective (fixed vectors
- * viewed from different frames) like the ones used for example in spacecraft
- * attitude community or in the graphics community.</p>
- * @param axis axis around which to rotate
- * @param angle rotation angle.
- * @exception MathIllegalArgumentException if the axis norm is zero
- */
- public Rotation(Vector3D axis, double angle) throws MathIllegalArgumentException {
-
- double norm = axis.getNorm();
- if (norm == 0) {
- throw new MathIllegalArgumentException(LocalizedFormats.ZERO_NORM_FOR_ROTATION_AXIS);
- }
-
- double halfAngle = -0.5 * angle;
- double coeff = FastMath.sin(halfAngle) / norm;
-
- q0 = FastMath.cos (halfAngle);
- q1 = coeff * axis.getX();
- q2 = coeff * axis.getY();
- q3 = coeff * axis.getZ();
-
- }
-
- /** Build a rotation from a 3X3 matrix.
-
- * <p>Rotation matrices are orthogonal matrices, i.e. unit matrices
- * (which are matrices for which m.m<sup>T</sup> = I) with real
- * coefficients. The module of the determinant of unit matrices is
- * 1, among the orthogonal 3X3 matrices, only the ones having a
- * positive determinant (+1) are rotation matrices.</p>
-
- * <p>When a rotation is defined by a matrix with truncated values
- * (typically when it is extracted from a technical sheet where only
- * four to five significant digits are available), the matrix is not
- * orthogonal anymore. This constructor handles this case
- * transparently by using a copy of the given matrix and applying a
- * correction to the copy in order to perfect its orthogonality. If
- * the Frobenius norm of the correction needed is above the given
- * threshold, then the matrix is considered to be too far from a
- * true rotation matrix and an exception is thrown.<p>
-
- * @param m rotation matrix
- * @param threshold convergence threshold for the iterative
- * orthogonality correction (convergence is reached when the
- * difference between two steps of the Frobenius norm of the
- * correction is below this threshold)
-
- * @exception NotARotationMatrixException if the matrix is not a 3X3
- * matrix, or if it cannot be transformed into an orthogonal matrix
- * with the given threshold, or if the determinant of the resulting
- * orthogonal matrix is negative
-
- */
- public Rotation(double[][] m, double threshold)
- throws NotARotationMatrixException {
-
- // dimension check
- if ((m.length != 3) || (m[0].length != 3) ||
- (m[1].length != 3) || (m[2].length != 3)) {
- throw new NotARotationMatrixException(
- LocalizedFormats.ROTATION_MATRIX_DIMENSIONS,
- m.length, m[0].length);
- }
-
- // compute a "close" orthogonal matrix
- double[][] ort = orthogonalizeMatrix(m, threshold);
-
- // check the sign of the determinant
- double det = ort[0][0] * (ort[1][1] * ort[2][2] - ort[2][1] * ort[1][2]) -
- ort[1][0] * (ort[0][1] * ort[2][2] - ort[2][1] * ort[0][2]) +
- ort[2][0] * (ort[0][1] * ort[1][2] - ort[1][1] * ort[0][2]);
- if (det < 0.0) {
- throw new NotARotationMatrixException(
- LocalizedFormats.CLOSEST_ORTHOGONAL_MATRIX_HAS_NEGATIVE_DETERMINANT,
- det);
- }
-
- double[] quat = mat2quat(ort);
- q0 = quat[0];
- q1 = quat[1];
- q2 = quat[2];
- q3 = quat[3];
-
- }
-
- /** Build the rotation that transforms a pair of vector into another pair.
-
- * <p>Except for possible scale factors, if the instance were applied to
- * the pair (u<sub>1</sub>, u<sub>2</sub>) it will produce the pair
- * (v<sub>1</sub>, v<sub>2</sub>).</p>
-
- * <p>If the angular separation between u<sub>1</sub> and u<sub>2</sub> is
- * not the same as the angular separation between v<sub>1</sub> and
- * v<sub>2</sub>, then a corrected v'<sub>2</sub> will be used rather than
- * v<sub>2</sub>, the corrected vector will be in the (v<sub>1</sub>,
- * v<sub>2</sub>) plane.</p>
-
- * @param u1 first vector of the origin pair
- * @param u2 second vector of the origin pair
- * @param v1 desired image of u1 by the rotation
- * @param v2 desired image of u2 by the rotation
- * @exception MathArithmeticException if the norm of one of the vectors is zero,
- * or if one of the pair is degenerated (i.e. the vectors of the pair are colinear)
- */
- public Rotation(Vector3D u1, Vector3D u2, Vector3D v1, Vector3D v2)
- throws MathArithmeticException {
-
- // build orthonormalized base from u1, u2
- // this fails when vectors are null or colinear, which is forbidden to define a rotation
- final Vector3D u3 = u1.crossProduct(u2).normalize();
- u2 = u3.crossProduct(u1).normalize();
- u1 = u1.normalize();
-
- // build an orthonormalized base from v1, v2
- // this fails when vectors are null or colinear, which is forbidden to define a rotation
- final Vector3D v3 = v1.crossProduct(v2).normalize();
- v2 = v3.crossProduct(v1).normalize();
- v1 = v1.normalize();
-
- // buid a matrix transforming the first base into the second one
- final double[][] m = new double[][] {
- {
- MathArrays.linearCombination(u1.getX(), v1.getX(), u2.getX(), v2.getX(), u3.getX(), v3.getX()),
- MathArrays.linearCombination(u1.getY(), v1.getX(), u2.getY(), v2.getX(), u3.getY(), v3.getX()),
- MathArrays.linearCombination(u1.getZ(), v1.getX(), u2.getZ(), v2.getX(), u3.getZ(), v3.getX())
- },
- {
- MathArrays.linearCombination(u1.getX(), v1.getY(), u2.getX(), v2.getY(), u3.getX(), v3.getY()),
- MathArrays.linearCombination(u1.getY(), v1.getY(), u2.getY(), v2.getY(), u3.getY(), v3.getY()),
- MathArrays.linearCombination(u1.getZ(), v1.getY(), u2.getZ(), v2.getY(), u3.getZ(), v3.getY())
- },
- {
- MathArrays.linearCombination(u1.getX(), v1.getZ(), u2.getX(), v2.getZ(), u3.getX(), v3.getZ()),
- MathArrays.linearCombination(u1.getY(), v1.getZ(), u2.getY(), v2.getZ(), u3.getY(), v3.getZ()),
- MathArrays.linearCombination(u1.getZ(), v1.getZ(), u2.getZ(), v2.getZ(), u3.getZ(), v3.getZ())
- }
- };
-
- double[] quat = mat2quat(m);
- q0 = quat[0];
- q1 = quat[1];
- q2 = quat[2];
- q3 = quat[3];
-
- }
-
- /** Build one of the rotations that transform one vector into another one.
-
- * <p>Except for a possible scale factor, if the instance were
- * applied to the vector u it will produce the vector v. There is an
- * infinite number of such rotations, this constructor choose the
- * one with the smallest associated angle (i.e. the one whose axis
- * is orthogonal to the (u, v) plane). If u and v are colinear, an
- * arbitrary rotation axis is chosen.</p>
-
- * @param u origin vector
- * @param v desired image of u by the rotation
- * @exception MathArithmeticException if the norm of one of the vectors is zero
- */
- public Rotation(Vector3D u, Vector3D v) throws MathArithmeticException {
-
- double normProduct = u.getNorm() * v.getNorm();
- if (normProduct == 0) {
- throw new MathArithmeticException(LocalizedFormats.ZERO_NORM_FOR_ROTATION_DEFINING_VECTOR);
- }
-
- double dot = u.dotProduct(v);
-
- if (dot < ((2.0e-15 - 1.0) * normProduct)) {
- // special case u = -v: we select a PI angle rotation around
- // an arbitrary vector orthogonal to u
- Vector3D w = u.orthogonal();
- q0 = 0.0;
- q1 = -w.getX();
- q2 = -w.getY();
- q3 = -w.getZ();
- } else {
- // general case: (u, v) defines a plane, we select
- // the shortest possible rotation: axis orthogonal to this plane
- q0 = FastMath.sqrt(0.5 * (1.0 + dot / normProduct));
- double coeff = 1.0 / (2.0 * q0 * normProduct);
- Vector3D q = v.crossProduct(u);
- q1 = coeff * q.getX();
- q2 = coeff * q.getY();
- q3 = coeff * q.getZ();
- }
-
- }
-
- /** Build a rotation from three Cardan or Euler elementary rotations.
-
- * <p>Cardan rotations are three successive rotations around the
- * canonical axes X, Y and Z, each axis being used once. There are
- * 6 such sets of rotations (XYZ, XZY, YXZ, YZX, ZXY and ZYX). Euler
- * rotations are three successive rotations around the canonical
- * axes X, Y and Z, the first and last rotations being around the
- * same axis. There are 6 such sets of rotations (XYX, XZX, YXY,
- * YZY, ZXZ and ZYZ), the most popular one being ZXZ.</p>
- * <p>Beware that many people routinely use the term Euler angles even
- * for what really are Cardan angles (this confusion is especially
- * widespread in the aerospace business where Roll, Pitch and Yaw angles
- * are often wrongly tagged as Euler angles).</p>
-
- * @param order order of rotations to use
- * @param alpha1 angle of the first elementary rotation
- * @param alpha2 angle of the second elementary rotation
- * @param alpha3 angle of the third elementary rotation
- */
- public Rotation(RotationOrder order,
- double alpha1, double alpha2, double alpha3) {
- Rotation r1 = new Rotation(order.getA1(), alpha1);
- Rotation r2 = new Rotation(order.getA2(), alpha2);
- Rotation r3 = new Rotation(order.getA3(), alpha3);
- Rotation composed = r1.applyTo(r2.applyTo(r3));
- q0 = composed.q0;
- q1 = composed.q1;
- q2 = composed.q2;
- q3 = composed.q3;
- }
-
- /** Convert an orthogonal rotation matrix to a quaternion.
- * @param ort orthogonal rotation matrix
- * @return quaternion corresponding to the matrix
- */
- private static double[] mat2quat(final double[][] ort) {
-
- final double[] quat = new double[4];
-
- // There are different ways to compute the quaternions elements
- // from the matrix. They all involve computing one element from
- // the diagonal of the matrix, and computing the three other ones
- // using a formula involving a division by the first element,
- // which unfortunately can be zero. Since the norm of the
- // quaternion is 1, we know at least one element has an absolute
- // value greater or equal to 0.5, so it is always possible to
- // select the right formula and avoid division by zero and even
- // numerical inaccuracy. Checking the elements in turn and using
- // the first one greater than 0.45 is safe (this leads to a simple
- // test since qi = 0.45 implies 4 qi^2 - 1 = -0.19)
- double s = ort[0][0] + ort[1][1] + ort[2][2];
- if (s > -0.19) {
- // compute q0 and deduce q1, q2 and q3
- quat[0] = 0.5 * FastMath.sqrt(s + 1.0);
- double inv = 0.25 / quat[0];
- quat[1] = inv * (ort[1][2] - ort[2][1]);
- quat[2] = inv * (ort[2][0] - ort[0][2]);
- quat[3] = inv * (ort[0][1] - ort[1][0]);
- } else {
- s = ort[0][0] - ort[1][1] - ort[2][2];
- if (s > -0.19) {
- // compute q1 and deduce q0, q2 and q3
- quat[1] = 0.5 * FastMath.sqrt(s + 1.0);
- double inv = 0.25 / quat[1];
- quat[0] = inv * (ort[1][2] - ort[2][1]);
- quat[2] = inv * (ort[0][1] + ort[1][0]);
- quat[3] = inv * (ort[0][2] + ort[2][0]);
- } else {
- s = ort[1][1] - ort[0][0] - ort[2][2];
- if (s > -0.19) {
- // compute q2 and deduce q0, q1 and q3
- quat[2] = 0.5 * FastMath.sqrt(s + 1.0);
- double inv = 0.25 / quat[2];
- quat[0] = inv * (ort[2][0] - ort[0][2]);
- quat[1] = inv * (ort[0][1] + ort[1][0]);
- quat[3] = inv * (ort[2][1] + ort[1][2]);
- } else {
- // compute q3 and deduce q0, q1 and q2
- s = ort[2][2] - ort[0][0] - ort[1][1];
- quat[3] = 0.5 * FastMath.sqrt(s + 1.0);
- double inv = 0.25 / quat[3];
- quat[0] = inv * (ort[0][1] - ort[1][0]);
- quat[1] = inv * (ort[0][2] + ort[2][0]);
- quat[2] = inv * (ort[2][1] + ort[1][2]);
- }
- }
- }
-
- return quat;
-
- }
-
- /** Revert a rotation.
- * Build a rotation which reverse the effect of another
- * rotation. This means that if r(u) = v, then r.revert(v) = u. The
- * instance is not changed.
- * @return a new rotation whose effect is the reverse of the effect
- * of the instance
- */
- public Rotation revert() {
- return new Rotation(-q0, q1, q2, q3, false);
- }
-
- /** Get the scalar coordinate of the quaternion.
- * @return scalar coordinate of the quaternion
- */
- public double getQ0() {
- return q0;
- }
-
- /** Get the first coordinate of the vectorial part of the quaternion.
- * @return first coordinate of the vectorial part of the quaternion
- */
- public double getQ1() {
- return q1;
- }
-
- /** Get the second coordinate of the vectorial part of the quaternion.
- * @return second coordinate of the vectorial part of the quaternion
- */
- public double getQ2() {
- return q2;
- }
-
- /** Get the third coordinate of the vectorial part of the quaternion.
- * @return third coordinate of the vectorial part of the quaternion
- */
- public double getQ3() {
- return q3;
- }
-
- /** Get the normalized axis of the rotation.
- * @return normalized axis of the rotation
- * @see #Rotation(Vector3D, double)
- */
- public Vector3D getAxis() {
- double squaredSine = q1 * q1 + q2 * q2 + q3 * q3;
- if (squaredSine == 0) {
- return new Vector3D(1, 0, 0);
- } else if (q0 < 0) {
- double inverse = 1 / FastMath.sqrt(squaredSine);
- return new Vector3D(q1 * inverse, q2 * inverse, q3 * inverse);
- }
- double inverse = -1 / FastMath.sqrt(squaredSine);
- return new Vector3D(q1 * inverse, q2 * inverse, q3 * inverse);
- }
-
- /** Get the angle of the rotation.
- * @return angle of the rotation (between 0 and π)
- * @see #Rotation(Vector3D, double)
- */
- public double getAngle() {
- if ((q0 < -0.1) || (q0 > 0.1)) {
- return 2 * FastMath.asin(FastMath.sqrt(q1 * q1 + q2 * q2 + q3 * q3));
- } else if (q0 < 0) {
- return 2 * FastMath.acos(-q0);
- }
- return 2 * FastMath.acos(q0);
- }
-
- /** Get the Cardan or Euler angles corresponding to the instance.
-
- * <p>The equations show that each rotation can be defined by two
- * different values of the Cardan or Euler angles set. For example
- * if Cardan angles are used, the rotation defined by the angles
- * a<sub>1</sub>, a<sub>2</sub> and a<sub>3</sub> is the same as
- * the rotation defined by the angles π + a<sub>1</sub>, π
- * - a<sub>2</sub> and π + a<sub>3</sub>. This method implements
- * the following arbitrary choices:</p>
- * <ul>
- * <li>for Cardan angles, the chosen set is the one for which the
- * second angle is between -π/2 and π/2 (i.e its cosine is
- * positive),</li>
- * <li>for Euler angles, the chosen set is the one for which the
- * second angle is between 0 and π (i.e its sine is positive).</li>
- * </ul>
-
- * <p>Cardan and Euler angle have a very disappointing drawback: all
- * of them have singularities. This means that if the instance is
- * too close to the singularities corresponding to the given
- * rotation order, it will be impossible to retrieve the angles. For
- * Cardan angles, this is often called gimbal lock. There is
- * <em>nothing</em> to do to prevent this, it is an intrinsic problem
- * with Cardan and Euler representation (but not a problem with the
- * rotation itself, which is perfectly well defined). For Cardan
- * angles, singularities occur when the second angle is close to
- * -π/2 or +π/2, for Euler angle singularities occur when the
- * second angle is close to 0 or π, this implies that the identity
- * rotation is always singular for Euler angles!</p>
-
- * @param order rotation order to use
- * @return an array of three angles, in the order specified by the set
- * @exception CardanEulerSingularityException if the rotation is
- * singular with respect to the angles set specified
- */
- public double[] getAngles(RotationOrder order)
- throws CardanEulerSingularityException {
-
- if (order == RotationOrder.XYZ) {
-
- // r (Vector3D.plusK) coordinates are :
- // sin (theta), -cos (theta) sin (phi), cos (theta) cos (phi)
- // (-r) (Vector3D.plusI) coordinates are :
- // cos (psi) cos (theta), -sin (psi) cos (theta), sin (theta)
- // and we can choose to have theta in the interval [-PI/2 ; +PI/2]
- Vector3D v1 = applyTo(Vector3D.PLUS_K);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_I);
- if ((v2.getZ() < -0.9999999999) || (v2.getZ() > 0.9999999999)) {
- throw new CardanEulerSingularityException(true);
- }
- return new double[] {
- FastMath.atan2(-(v1.getY()), v1.getZ()),
- FastMath.asin(v2.getZ()),
- FastMath.atan2(-(v2.getY()), v2.getX())
- };
-
- } else if (order == RotationOrder.XZY) {
-
- // r (Vector3D.plusJ) coordinates are :
- // -sin (psi), cos (psi) cos (phi), cos (psi) sin (phi)
- // (-r) (Vector3D.plusI) coordinates are :
- // cos (theta) cos (psi), -sin (psi), sin (theta) cos (psi)
- // and we can choose to have psi in the interval [-PI/2 ; +PI/2]
- Vector3D v1 = applyTo(Vector3D.PLUS_J);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_I);
- if ((v2.getY() < -0.9999999999) || (v2.getY() > 0.9999999999)) {
- throw new CardanEulerSingularityException(true);
- }
- return new double[] {
- FastMath.atan2(v1.getZ(), v1.getY()),
- -FastMath.asin(v2.getY()),
- FastMath.atan2(v2.getZ(), v2.getX())
- };
-
- } else if (order == RotationOrder.YXZ) {
-
- // r (Vector3D.plusK) coordinates are :
- // cos (phi) sin (theta), -sin (phi), cos (phi) cos (theta)
- // (-r) (Vector3D.plusJ) coordinates are :
- // sin (psi) cos (phi), cos (psi) cos (phi), -sin (phi)
- // and we can choose to have phi in the interval [-PI/2 ; +PI/2]
- Vector3D v1 = applyTo(Vector3D.PLUS_K);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_J);
- if ((v2.getZ() < -0.9999999999) || (v2.getZ() > 0.9999999999)) {
- throw new CardanEulerSingularityException(true);
- }
- return new double[] {
- FastMath.atan2(v1.getX(), v1.getZ()),
- -FastMath.asin(v2.getZ()),
- FastMath.atan2(v2.getX(), v2.getY())
- };
-
- } else if (order == RotationOrder.YZX) {
-
- // r (Vector3D.plusI) coordinates are :
- // cos (psi) cos (theta), sin (psi), -cos (psi) sin (theta)
- // (-r) (Vector3D.plusJ) coordinates are :
- // sin (psi), cos (phi) cos (psi), -sin (phi) cos (psi)
- // and we can choose to have psi in the interval [-PI/2 ; +PI/2]
- Vector3D v1 = applyTo(Vector3D.PLUS_I);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_J);
- if ((v2.getX() < -0.9999999999) || (v2.getX() > 0.9999999999)) {
- throw new CardanEulerSingularityException(true);
- }
- return new double[] {
- FastMath.atan2(-(v1.getZ()), v1.getX()),
- FastMath.asin(v2.getX()),
- FastMath.atan2(-(v2.getZ()), v2.getY())
- };
-
- } else if (order == RotationOrder.ZXY) {
-
- // r (Vector3D.plusJ) coordinates are :
- // -cos (phi) sin (psi), cos (phi) cos (psi), sin (phi)
- // (-r) (Vector3D.plusK) coordinates are :
- // -sin (theta) cos (phi), sin (phi), cos (theta) cos (phi)
- // and we can choose to have phi in the interval [-PI/2 ; +PI/2]
- Vector3D v1 = applyTo(Vector3D.PLUS_J);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_K);
- if ((v2.getY() < -0.9999999999) || (v2.getY() > 0.9999999999)) {
- throw new CardanEulerSingularityException(true);
- }
- return new double[] {
- FastMath.atan2(-(v1.getX()), v1.getY()),
- FastMath.asin(v2.getY()),
- FastMath.atan2(-(v2.getX()), v2.getZ())
- };
-
- } else if (order == RotationOrder.ZYX) {
-
- // r (Vector3D.plusI) coordinates are :
- // cos (theta) cos (psi), cos (theta) sin (psi), -sin (theta)
- // (-r) (Vector3D.plusK) coordinates are :
- // -sin (theta), sin (phi) cos (theta), cos (phi) cos (theta)
- // and we can choose to have theta in the interval [-PI/2 ; +PI/2]
- Vector3D v1 = applyTo(Vector3D.PLUS_I);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_K);
- if ((v2.getX() < -0.9999999999) || (v2.getX() > 0.9999999999)) {
- throw new CardanEulerSingularityException(true);
- }
- return new double[] {
- FastMath.atan2(v1.getY(), v1.getX()),
- -FastMath.asin(v2.getX()),
- FastMath.atan2(v2.getY(), v2.getZ())
- };
-
- } else if (order == RotationOrder.XYX) {
-
- // r (Vector3D.plusI) coordinates are :
- // cos (theta), sin (phi1) sin (theta), -cos (phi1) sin (theta)
- // (-r) (Vector3D.plusI) coordinates are :
- // cos (theta), sin (theta) sin (phi2), sin (theta) cos (phi2)
- // and we can choose to have theta in the interval [0 ; PI]
- Vector3D v1 = applyTo(Vector3D.PLUS_I);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_I);
- if ((v2.getX() < -0.9999999999) || (v2.getX() > 0.9999999999)) {
- throw new CardanEulerSingularityException(false);
- }
- return new double[] {
- FastMath.atan2(v1.getY(), -v1.getZ()),
- FastMath.acos(v2.getX()),
- FastMath.atan2(v2.getY(), v2.getZ())
- };
-
- } else if (order == RotationOrder.XZX) {
-
- // r (Vector3D.plusI) coordinates are :
- // cos (psi), cos (phi1) sin (psi), sin (phi1) sin (psi)
- // (-r) (Vector3D.plusI) coordinates are :
- // cos (psi), -sin (psi) cos (phi2), sin (psi) sin (phi2)
- // and we can choose to have psi in the interval [0 ; PI]
- Vector3D v1 = applyTo(Vector3D.PLUS_I);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_I);
- if ((v2.getX() < -0.9999999999) || (v2.getX() > 0.9999999999)) {
- throw new CardanEulerSingularityException(false);
- }
- return new double[] {
- FastMath.atan2(v1.getZ(), v1.getY()),
- FastMath.acos(v2.getX()),
- FastMath.atan2(v2.getZ(), -v2.getY())
- };
-
- } else if (order == RotationOrder.YXY) {
-
- // r (Vector3D.plusJ) coordinates are :
- // sin (theta1) sin (phi), cos (phi), cos (theta1) sin (phi)
- // (-r) (Vector3D.plusJ) coordinates are :
- // sin (phi) sin (theta2), cos (phi), -sin (phi) cos (theta2)
- // and we can choose to have phi in the interval [0 ; PI]
- Vector3D v1 = applyTo(Vector3D.PLUS_J);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_J);
- if ((v2.getY() < -0.9999999999) || (v2.getY() > 0.9999999999)) {
- throw new CardanEulerSingularityException(false);
- }
- return new double[] {
- FastMath.atan2(v1.getX(), v1.getZ()),
- FastMath.acos(v2.getY()),
- FastMath.atan2(v2.getX(), -v2.getZ())
- };
-
- } else if (order == RotationOrder.YZY) {
-
- // r (Vector3D.plusJ) coordinates are :
- // -cos (theta1) sin (psi), cos (psi), sin (theta1) sin (psi)
- // (-r) (Vector3D.plusJ) coordinates are :
- // sin (psi) cos (theta2), cos (psi), sin (psi) sin (theta2)
- // and we can choose to have psi in the interval [0 ; PI]
- Vector3D v1 = applyTo(Vector3D.PLUS_J);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_J);
- if ((v2.getY() < -0.9999999999) || (v2.getY() > 0.9999999999)) {
- throw new CardanEulerSingularityException(false);
- }
- return new double[] {
- FastMath.atan2(v1.getZ(), -v1.getX()),
- FastMath.acos(v2.getY()),
- FastMath.atan2(v2.getZ(), v2.getX())
- };
-
- } else if (order == RotationOrder.ZXZ) {
-
- // r (Vector3D.plusK) coordinates are :
- // sin (psi1) sin (phi), -cos (psi1) sin (phi), cos (phi)
- // (-r) (Vector3D.plusK) coordinates are :
- // sin (phi) sin (psi2), sin (phi) cos (psi2), cos (phi)
- // and we can choose to have phi in the interval [0 ; PI]
- Vector3D v1 = applyTo(Vector3D.PLUS_K);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_K);
- if ((v2.getZ() < -0.9999999999) || (v2.getZ() > 0.9999999999)) {
- throw new CardanEulerSingularityException(false);
- }
- return new double[] {
- FastMath.atan2(v1.getX(), -v1.getY()),
- FastMath.acos(v2.getZ()),
- FastMath.atan2(v2.getX(), v2.getY())
- };
-
- } else { // last possibility is ZYZ
-
- // r (Vector3D.plusK) coordinates are :
- // cos (psi1) sin (theta), sin (psi1) sin (theta), cos (theta)
- // (-r) (Vector3D.plusK) coordinates are :
- // -sin (theta) cos (psi2), sin (theta) sin (psi2), cos (theta)
- // and we can choose to have theta in the interval [0 ; PI]
- Vector3D v1 = applyTo(Vector3D.PLUS_K);
- Vector3D v2 = applyInverseTo(Vector3D.PLUS_K);
- if ((v2.getZ() < -0.9999999999) || (v2.getZ() > 0.9999999999)) {
- throw new CardanEulerSingularityException(false);
- }
- return new double[] {
- FastMath.atan2(v1.getY(), v1.getX()),
- FastMath.acos(v2.getZ()),
- FastMath.atan2(v2.getY(), -v2.getX())
- };
-
- }
-
- }
-
- /** Get the 3X3 matrix corresponding to the instance
- * @return the matrix corresponding to the instance
- */
- public double[][] getMatrix() {
-
- // products
- double q0q0 = q0 * q0;
- double q0q1 = q0 * q1;
- double q0q2 = q0 * q2;
- double q0q3 = q0 * q3;
- double q1q1 = q1 * q1;
- double q1q2 = q1 * q2;
- double q1q3 = q1 * q3;
- double q2q2 = q2 * q2;
- double q2q3 = q2 * q3;
- double q3q3 = q3 * q3;
-
- // create the matrix
- double[][] m = new double[3][];
- m[0] = new double[3];
- m[1] = new double[3];
- m[2] = new double[3];
-
- m [0][0] = 2.0 * (q0q0 + q1q1) - 1.0;
- m [1][0] = 2.0 * (q1q2 - q0q3);
- m [2][0] = 2.0 * (q1q3 + q0q2);
-
- m [0][1] = 2.0 * (q1q2 + q0q3);
- m [1][1] = 2.0 * (q0q0 + q2q2) - 1.0;
- m [2][1] = 2.0 * (q2q3 - q0q1);
-
- m [0][2] = 2.0 * (q1q3 - q0q2);
- m [1][2] = 2.0 * (q2q3 + q0q1);
- m [2][2] = 2.0 * (q0q0 + q3q3) - 1.0;
-
- return m;
-
- }
-
- /** Apply the rotation to a vector.
- * @param u vector to apply the rotation to
- * @return a new vector which is the image of u by the rotation
- */
- public Vector3D applyTo(Vector3D u) {
-
- double x = u.getX();
- double y = u.getY();
- double z = u.getZ();
-
- double s = q1 * x + q2 * y + q3 * z;
-
- return new Vector3D(2 * (q0 * (x * q0 - (q2 * z - q3 * y)) + s * q1) - x,
- 2 * (q0 * (y * q0 - (q3 * x - q1 * z)) + s * q2) - y,
- 2 * (q0 * (z * q0 - (q1 * y - q2 * x)) + s * q3) - z);
-
- }
-
- /** Apply the rotation to a vector stored in an array.
- * @param in an array with three items which stores vector to rotate
- * @param out an array with three items to put result to (it can be the same
- * array as in)
- */
- public void applyTo(final double[] in, final double[] out) {
-
- final double x = in[0];
- final double y = in[1];
- final double z = in[2];
-
- final double s = q1 * x + q2 * y + q3 * z;
-
- out[0] = 2 * (q0 * (x * q0 - (q2 * z - q3 * y)) + s * q1) - x;
- out[1] = 2 * (q0 * (y * q0 - (q3 * x - q1 * z)) + s * q2) - y;
- out[2] = 2 * (q0 * (z * q0 - (q1 * y - q2 * x)) + s * q3) - z;
-
- }
-
- /** Apply the inverse of the rotation to a vector.
- * @param u vector to apply the inverse of the rotation to
- * @return a new vector which such that u is its image by the rotation
- */
- public Vector3D applyInverseTo(Vector3D u) {
-
- double x = u.getX();
- double y = u.getY();
- double z = u.getZ();
-
- double s = q1 * x + q2 * y + q3 * z;
- double m0 = -q0;
-
- return new Vector3D(2 * (m0 * (x * m0 - (q2 * z - q3 * y)) + s * q1) - x,
- 2 * (m0 * (y * m0 - (q3 * x - q1 * z)) + s * q2) - y,
- 2 * (m0 * (z * m0 - (q1 * y - q2 * x)) + s * q3) - z);
-
- }
-
- /** Apply the inverse of the rotation to a vector stored in an array.
- * @param in an array with three items which stores vector to rotate
- * @param out an array with three items to put result to (it can be the same
- * array as in)
- */
- public void applyInverseTo(final double[] in, final double[] out) {
-
- final double x = in[0];
- final double y = in[1];
- final double z = in[2];
-
- final double s = q1 * x + q2 * y + q3 * z;
- final double m0 = -q0;
-
- out[0] = 2 * (m0 * (x * m0 - (q2 * z - q3 * y)) + s * q1) - x;
- out[1] = 2 * (m0 * (y * m0 - (q3 * x - q1 * z)) + s * q2) - y;
- out[2] = 2 * (m0 * (z * m0 - (q1 * y - q2 * x)) + s * q3) - z;
-
- }
-
- /** Apply the instance to another rotation.
- * Applying the instance to a rotation is computing the composition
- * in an order compliant with the following rule : let u be any
- * vector and v its image by r (i.e. r.applyTo(u) = v), let w be the image
- * of v by the instance (i.e. applyTo(v) = w), then w = comp.applyTo(u),
- * where comp = applyTo(r).
- * @param r rotation to apply the rotation to
- * @return a new rotation which is the composition of r by the instance
- */
- public Rotation applyTo(Rotation r) {
- return new Rotation(r.q0 * q0 - (r.q1 * q1 + r.q2 * q2 + r.q3 * q3),
- r.q1 * q0 + r.q0 * q1 + (r.q2 * q3 - r.q3 * q2),
- r.q2 * q0 + r.q0 * q2 + (r.q3 * q1 - r.q1 * q3),
- r.q3 * q0 + r.q0 * q3 + (r.q1 * q2 - r.q2 * q1),
- false);
- }
-
- /** Apply the inverse of the instance to another rotation.
- * Applying the inverse of the instance to a rotation is computing
- * the composition in an order compliant with the following rule :
- * let u be any vector and v its image by r (i.e. r.applyTo(u) = v),
- * let w be the inverse image of v by the instance
- * (i.e. applyInverseTo(v) = w), then w = comp.applyTo(u), where
- * comp = applyInverseTo(r).
- * @param r rotation to apply the rotation to
- * @return a new rotation which is the composition of r by the inverse
- * of the instance
- */
- public Rotation applyInverseTo(Rotation r) {
- return new Rotation(-r.q0 * q0 - (r.q1 * q1 + r.q2 * q2 + r.q3 * q3),
- -r.q1 * q0 + r.q0 * q1 + (r.q2 * q3 - r.q3 * q2),
- -r.q2 * q0 + r.q0 * q2 + (r.q3 * q1 - r.q1 * q3),
- -r.q3 * q0 + r.q0 * q3 + (r.q1 * q2 - r.q2 * q1),
- false);
- }
-
- /** Perfect orthogonality on a 3X3 matrix.
- * @param m initial matrix (not exactly orthogonal)
- * @param threshold convergence threshold for the iterative
- * orthogonality correction (convergence is reached when the
- * difference between two steps of the Frobenius norm of the
- * correction is below this threshold)
- * @return an orthogonal matrix close to m
- * @exception NotARotationMatrixException if the matrix cannot be
- * orthogonalized with the given threshold after 10 iterations
- */
- private double[][] orthogonalizeMatrix(double[][] m, double threshold)
- throws NotARotationMatrixException {
- double[] m0 = m[0];
- double[] m1 = m[1];
- double[] m2 = m[2];
- double x00 = m0[0];
- double x01 = m0[1];
- double x02 = m0[2];
- double x10 = m1[0];
- double x11 = m1[1];
- double x12 = m1[2];
- double x20 = m2[0];
- double x21 = m2[1];
- double x22 = m2[2];
- double fn = 0;
- double fn1;
-
- double[][] o = new double[3][3];
- double[] o0 = o[0];
- double[] o1 = o[1];
- double[] o2 = o[2];
-
- // iterative correction: Xn+1 = Xn - 0.5 * (Xn.Mt.Xn - M)
- int i = 0;
- while (++i < 11) {
-
- // Mt.Xn
- double mx00 = m0[0] * x00 + m1[0] * x10 + m2[0] * x20;
- double mx10 = m0[1] * x00 + m1[1] * x10 + m2[1] * x20;
- double mx20 = m0[2] * x00 + m1[2] * x10 + m2[2] * x20;
- double mx01 = m0[0] * x01 + m1[0] * x11 + m2[0] * x21;
- double mx11 = m0[1] * x01 + m1[1] * x11 + m2[1] * x21;
- double mx21 = m0[2] * x01 + m1[2] * x11 + m2[2] * x21;
- double mx02 = m0[0] * x02 + m1[0] * x12 + m2[0] * x22;
- double mx12 = m0[1] * x02 + m1[1] * x12 + m2[1] * x22;
- double mx22 = m0[2] * x02 + m1[2] * x12 + m2[2] * x22;
-
- // Xn+1
- o0[0] = x00 - 0.5 * (x00 * mx00 + x01 * mx10 + x02 * mx20 - m0[0]);
- o0[1] = x01 - 0.5 * (x00 * mx01 + x01 * mx11 + x02 * mx21 - m0[1]);
- o0[2] = x02 - 0.5 * (x00 * mx02 + x01 * mx12 + x02 * mx22 - m0[2]);
- o1[0] = x10 - 0.5 * (x10 * mx00 + x11 * mx10 + x12 * mx20 - m1[0]);
- o1[1] = x11 - 0.5 * (x10 * mx01 + x11 * mx11 + x12 * mx21 - m1[1]);
- o1[2] = x12 - 0.5 * (x10 * mx02 + x11 * mx12 + x12 * mx22 - m1[2]);
- o2[0] = x20 - 0.5 * (x20 * mx00 + x21 * mx10 + x22 * mx20 - m2[0]);
- o2[1] = x21 - 0.5 * (x20 * mx01 + x21 * mx11 + x22 * mx21 - m2[1]);
- o2[2] = x22 - 0.5 * (x20 * mx02 + x21 * mx12 + x22 * mx22 - m2[2]);
-
- // correction on each elements
- double corr00 = o0[0] - m0[0];
- double corr01 = o0[1] - m0[1];
- double corr02 = o0[2] - m0[2];
- double corr10 = o1[0] - m1[0];
- double corr11 = o1[1] - m1[1];
- double corr12 = o1[2] - m1[2];
- double corr20 = o2[0] - m2[0];
- double corr21 = o2[1] - m2[1];
- double corr22 = o2[2] - m2[2];
-
- // Frobenius norm of the correction
- fn1 = corr00 * corr00 + corr01 * corr01 + corr02 * corr02 +
- corr10 * corr10 + corr11 * corr11 + corr12 * corr12 +
- corr20 * corr20 + corr21 * corr21 + corr22 * corr22;
-
- // convergence test
- if (FastMath.abs(fn1 - fn) <= threshold) {
- return o;
- }
-
- // prepare next iteration
- x00 = o0[0];
- x01 = o0[1];
- x02 = o0[2];
- x10 = o1[0];
- x11 = o1[1];
- x12 = o1[2];
- x20 = o2[0];
- x21 = o2[1];
- x22 = o2[2];
- fn = fn1;
-
- }
-
- // the algorithm did not converge after 10 iterations
- throw new NotARotationMatrixException(
- LocalizedFormats.UNABLE_TO_ORTHOGONOLIZE_MATRIX,
- i - 1);
- }
-
- /** Compute the <i>distance</i> between two rotations.
- * <p>The <i>distance</i> is intended here as a way to check if two
- * rotations are almost similar (i.e. they transform vectors the same way)
- * or very different. It is mathematically defined as the angle of
- * the rotation r that prepended to one of the rotations gives the other
- * one:</p>
- * <pre>
- * r<sub>1</sub>(r) = r<sub>2</sub>
- * </pre>
- * <p>This distance is an angle between 0 and π. Its value is the smallest
- * possible upper bound of the angle in radians between r<sub>1</sub>(v)
- * and r<sub>2</sub>(v) for all possible vectors v. This upper bound is
- * reached for some v. The distance is equal to 0 if and only if the two
- * rotations are identical.</p>
- * <p>Comparing two rotations should always be done using this value rather
- * than for example comparing the components of the quaternions. It is much
- * more stable, and has a geometric meaning. Also comparing quaternions
- * components is error prone since for example quaternions (0.36, 0.48, -0.48, -0.64)
- * and (-0.36, -0.48, 0.48, 0.64) represent exactly the same rotation despite
- * their components are different (they are exact opposites).</p>
- * @param r1 first rotation
- * @param r2 second rotation
- * @return <i>distance</i> between r1 and r2
- */
- public static double distance(Rotation r1, Rotation r2) {
- return r1.applyInverseTo(r2).getAngle();
- }
-
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/a7b4803f/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.java
deleted file mode 100644
index 03bc1c2..0000000
--- a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/RotationOrder.java
+++ /dev/null
@@ -1,174 +0,0 @@
-/*
- * 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.geometry.euclidean.threed;
-
-/**
- * This class is a utility representing a rotation order specification
- * for Cardan or Euler angles specification.
- *
- * This class cannot be instanciated by the user. He can only use one
- * of the twelve predefined supported orders as an argument to either
- * the {@link Rotation#Rotation(RotationOrder,double,double,double)}
- * constructor or the {@link Rotation#getAngles} method.
- *
- * @since 1.2
- */
-public final class RotationOrder {
-
- /** Set of Cardan angles.
- * this ordered set of rotations is around X, then around Y, then
- * around Z
- */
- public static final RotationOrder XYZ =
- new RotationOrder("XYZ", Vector3D.PLUS_I, Vector3D.PLUS_J, Vector3D.PLUS_K);
-
- /** Set of Cardan angles.
- * this ordered set of rotations is around X, then around Z, then
- * around Y
- */
- public static final RotationOrder XZY =
- new RotationOrder("XZY", Vector3D.PLUS_I, Vector3D.PLUS_K, Vector3D.PLUS_J);
-
- /** Set of Cardan angles.
- * this ordered set of rotations is around Y, then around X, then
- * around Z
- */
- public static final RotationOrder YXZ =
- new RotationOrder("YXZ", Vector3D.PLUS_J, Vector3D.PLUS_I, Vector3D.PLUS_K);
-
- /** Set of Cardan angles.
- * this ordered set of rotations is around Y, then around Z, then
- * around X
- */
- public static final RotationOrder YZX =
- new RotationOrder("YZX", Vector3D.PLUS_J, Vector3D.PLUS_K, Vector3D.PLUS_I);
-
- /** Set of Cardan angles.
- * this ordered set of rotations is around Z, then around X, then
- * around Y
- */
- public static final RotationOrder ZXY =
- new RotationOrder("ZXY", Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_J);
-
- /** Set of Cardan angles.
- * this ordered set of rotations is around Z, then around Y, then
- * around X
- */
- public static final RotationOrder ZYX =
- new RotationOrder("ZYX", Vector3D.PLUS_K, Vector3D.PLUS_J, Vector3D.PLUS_I);
-
- /** Set of Euler angles.
- * this ordered set of rotations is around X, then around Y, then
- * around X
- */
- public static final RotationOrder XYX =
- new RotationOrder("XYX", Vector3D.PLUS_I, Vector3D.PLUS_J, Vector3D.PLUS_I);
-
- /** Set of Euler angles.
- * this ordered set of rotations is around X, then around Z, then
- * around X
- */
- public static final RotationOrder XZX =
- new RotationOrder("XZX", Vector3D.PLUS_I, Vector3D.PLUS_K, Vector3D.PLUS_I);
-
- /** Set of Euler angles.
- * this ordered set of rotations is around Y, then around X, then
- * around Y
- */
- public static final RotationOrder YXY =
- new RotationOrder("YXY", Vector3D.PLUS_J, Vector3D.PLUS_I, Vector3D.PLUS_J);
-
- /** Set of Euler angles.
- * this ordered set of rotations is around Y, then around Z, then
- * around Y
- */
- public static final RotationOrder YZY =
- new RotationOrder("YZY", Vector3D.PLUS_J, Vector3D.PLUS_K, Vector3D.PLUS_J);
-
- /** Set of Euler angles.
- * this ordered set of rotations is around Z, then around X, then
- * around Z
- */
- public static final RotationOrder ZXZ =
- new RotationOrder("ZXZ", Vector3D.PLUS_K, Vector3D.PLUS_I, Vector3D.PLUS_K);
-
- /** Set of Euler angles.
- * this ordered set of rotations is around Z, then around Y, then
- * around Z
- */
- public static final RotationOrder ZYZ =
- new RotationOrder("ZYZ", Vector3D.PLUS_K, Vector3D.PLUS_J, Vector3D.PLUS_K);
-
- /** Name of the rotations order. */
- private final String name;
-
- /** Axis of the first rotation. */
- private final Vector3D a1;
-
- /** Axis of the second rotation. */
- private final Vector3D a2;
-
- /** Axis of the third rotation. */
- private final Vector3D a3;
-
- /** Private constructor.
- * This is a utility class that cannot be instantiated by the user,
- * so its only constructor is private.
- * @param name name of the rotation order
- * @param a1 axis of the first rotation
- * @param a2 axis of the second rotation
- * @param a3 axis of the third rotation
- */
- private RotationOrder(final String name,
- final Vector3D a1, final Vector3D a2, final Vector3D a3) {
- this.name = name;
- this.a1 = a1;
- this.a2 = a2;
- this.a3 = a3;
- }
-
- /** Get a string representation of the instance.
- * @return a string representation of the instance (in fact, its name)
- */
- @Override
- public String toString() {
- return name;
- }
-
- /** Get the axis of the first rotation.
- * @return axis of the first rotation
- */
- public Vector3D getA1() {
- return a1;
- }
-
- /** Get the axis of the second rotation.
- * @return axis of the second rotation
- */
- public Vector3D getA2() {
- return a2;
- }
-
- /** Get the axis of the second rotation.
- * @return axis of the second rotation
- */
- public Vector3D getA3() {
- return a3;
- }
-
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/a7b4803f/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Segment.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Segment.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Segment.java
deleted file mode 100644
index 200b462..0000000
--- a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/Segment.java
+++ /dev/null
@@ -1,66 +0,0 @@
-/*
- * 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.geometry.euclidean.threed;
-
-
-/** Simple container for a two-points segment.
- * @since 3.0
- */
-public class Segment {
-
- /** Start point of the segment. */
- private final Vector3D start;
-
- /** End point of the segments. */
- private final Vector3D end;
-
- /** Line containing the segment. */
- private final Line line;
-
- /** Build a segment.
- * @param start start point of the segment
- * @param end end point of the segment
- * @param line line containing the segment
- */
- public Segment(final Vector3D start, final Vector3D end, final Line line) {
- this.start = start;
- this.end = end;
- this.line = line;
- }
-
- /** Get the start point of the segment.
- * @return start point of the segment
- */
- public Vector3D getStart() {
- return start;
- }
-
- /** Get the end point of the segment.
- * @return end point of the segment
- */
- public Vector3D getEnd() {
- return end;
- }
-
- /** Get the line containing the segment.
- * @return line containing the segment
- */
- public Line getLine() {
- return line;
- }
-
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/a7b4803f/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SphereGenerator.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SphereGenerator.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SphereGenerator.java
deleted file mode 100644
index b553510..0000000
--- a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SphereGenerator.java
+++ /dev/null
@@ -1,152 +0,0 @@
-/*
- * 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.geometry.euclidean.threed;
-
-import java.util.Arrays;
-import java.util.List;
-
-import org.apache.commons.math3.fraction.BigFraction;
-import org.apache.commons.math3.geometry.enclosing.EnclosingBall;
-import org.apache.commons.math3.geometry.enclosing.SupportBallGenerator;
-import org.apache.commons.math3.geometry.euclidean.twod.DiskGenerator;
-import org.apache.commons.math3.geometry.euclidean.twod.Euclidean2D;
-import org.apache.commons.math3.geometry.euclidean.twod.Vector2D;
-import org.apache.commons.math3.util.FastMath;
-
-/** Class generating an enclosing ball from its support points.
- * @since 3.3
- */
-public class SphereGenerator implements SupportBallGenerator<Euclidean3D, Vector3D> {
-
- /** {@inheritDoc} */
- public EnclosingBall<Euclidean3D, Vector3D> ballOnSupport(final List<Vector3D> support) {
-
- if (support.size() < 1) {
- return new EnclosingBall<Euclidean3D, Vector3D>(Vector3D.ZERO, Double.NEGATIVE_INFINITY);
- } else {
- final Vector3D vA = support.get(0);
- if (support.size() < 2) {
- return new EnclosingBall<Euclidean3D, Vector3D>(vA, 0, vA);
- } else {
- final Vector3D vB = support.get(1);
- if (support.size() < 3) {
- return new EnclosingBall<Euclidean3D, Vector3D>(new Vector3D(0.5, vA, 0.5, vB),
- 0.5 * vA.distance(vB),
- vA, vB);
- } else {
- final Vector3D vC = support.get(2);
- if (support.size() < 4) {
-
- // delegate to 2D disk generator
- final Plane p = new Plane(vA, vB, vC,
- 1.0e-10 * (vA.getNorm1() + vB.getNorm1() + vC.getNorm1()));
- final EnclosingBall<Euclidean2D, Vector2D> disk =
- new DiskGenerator().ballOnSupport(Arrays.asList(p.toSubSpace(vA),
- p.toSubSpace(vB),
- p.toSubSpace(vC)));
-
- // convert back to 3D
- return new EnclosingBall<Euclidean3D, Vector3D>(p.toSpace(disk.getCenter()),
- disk.getRadius(), vA, vB, vC);
-
- } else {
- final Vector3D vD = support.get(3);
- // a sphere is 3D can be defined as:
- // (1) (x - x_0)^2 + (y - y_0)^2 + (z - z_0)^2 = r^2
- // which can be written:
- // (2) (x^2 + y^2 + z^2) - 2 x_0 x - 2 y_0 y - 2 z_0 z + (x_0^2 + y_0^2 + z_0^2 - r^2) = 0
- // or simply:
- // (3) (x^2 + y^2 + z^2) + a x + b y + c z + d = 0
- // with sphere center coordinates -a/2, -b/2, -c/2
- // If the sphere exists, a b, c and d are a non zero solution to
- // [ (x^2 + y^2 + z^2) x y z 1 ] [ 1 ] [ 0 ]
- // [ (xA^2 + yA^2 + zA^2) xA yA zA 1 ] [ a ] [ 0 ]
- // [ (xB^2 + yB^2 + zB^2) xB yB zB 1 ] * [ b ] = [ 0 ]
- // [ (xC^2 + yC^2 + zC^2) xC yC zC 1 ] [ c ] [ 0 ]
- // [ (xD^2 + yD^2 + zD^2) xD yD zD 1 ] [ d ] [ 0 ]
- // So the determinant of the matrix is zero. Computing this determinant
- // by expanding it using the minors m_ij of first row leads to
- // (4) m_11 (x^2 + y^2 + z^2) - m_12 x + m_13 y - m_14 z + m_15 = 0
- // So by identifying equations (2) and (4) we get the coordinates
- // of center as:
- // x_0 = +m_12 / (2 m_11)
- // y_0 = -m_13 / (2 m_11)
- // z_0 = +m_14 / (2 m_11)
- // Note that the minors m_11, m_12, m_13 and m_14 all have the last column
- // filled with 1.0, hence simplifying the computation
- final BigFraction[] c2 = new BigFraction[] {
- new BigFraction(vA.getX()), new BigFraction(vB.getX()),
- new BigFraction(vC.getX()), new BigFraction(vD.getX())
- };
- final BigFraction[] c3 = new BigFraction[] {
- new BigFraction(vA.getY()), new BigFraction(vB.getY()),
- new BigFraction(vC.getY()), new BigFraction(vD.getY())
- };
- final BigFraction[] c4 = new BigFraction[] {
- new BigFraction(vA.getZ()), new BigFraction(vB.getZ()),
- new BigFraction(vC.getZ()), new BigFraction(vD.getZ())
- };
- final BigFraction[] c1 = new BigFraction[] {
- c2[0].multiply(c2[0]).add(c3[0].multiply(c3[0])).add(c4[0].multiply(c4[0])),
- c2[1].multiply(c2[1]).add(c3[1].multiply(c3[1])).add(c4[1].multiply(c4[1])),
- c2[2].multiply(c2[2]).add(c3[2].multiply(c3[2])).add(c4[2].multiply(c4[2])),
- c2[3].multiply(c2[3]).add(c3[3].multiply(c3[3])).add(c4[3].multiply(c4[3]))
- };
- final BigFraction twoM11 = minor(c2, c3, c4).multiply(2);
- final BigFraction m12 = minor(c1, c3, c4);
- final BigFraction m13 = minor(c1, c2, c4);
- final BigFraction m14 = minor(c1, c2, c3);
- final BigFraction centerX = m12.divide(twoM11);
- final BigFraction centerY = m13.divide(twoM11).negate();
- final BigFraction centerZ = m14.divide(twoM11);
- final BigFraction dx = c2[0].subtract(centerX);
- final BigFraction dy = c3[0].subtract(centerY);
- final BigFraction dz = c4[0].subtract(centerZ);
- final BigFraction r2 = dx.multiply(dx).add(dy.multiply(dy)).add(dz.multiply(dz));
- return new EnclosingBall<Euclidean3D, Vector3D>(new Vector3D(centerX.doubleValue(),
- centerY.doubleValue(),
- centerZ.doubleValue()),
- FastMath.sqrt(r2.doubleValue()),
- vA, vB, vC, vD);
- }
- }
- }
- }
- }
-
- /** Compute a dimension 4 minor, when 4<sup>th</sup> column is known to be filled with 1.0.
- * @param c1 first column
- * @param c2 second column
- * @param c3 third column
- * @return value of the minor computed has an exact fraction
- */
- private BigFraction minor(final BigFraction[] c1, final BigFraction[] c2, final BigFraction[] c3) {
- return c2[0].multiply(c3[1]).multiply(c1[2].subtract(c1[3])).
- add(c2[0].multiply(c3[2]).multiply(c1[3].subtract(c1[1]))).
- add(c2[0].multiply(c3[3]).multiply(c1[1].subtract(c1[2]))).
- add(c2[1].multiply(c3[0]).multiply(c1[3].subtract(c1[2]))).
- add(c2[1].multiply(c3[2]).multiply(c1[0].subtract(c1[3]))).
- add(c2[1].multiply(c3[3]).multiply(c1[2].subtract(c1[0]))).
- add(c2[2].multiply(c3[0]).multiply(c1[1].subtract(c1[3]))).
- add(c2[2].multiply(c3[1]).multiply(c1[3].subtract(c1[0]))).
- add(c2[2].multiply(c3[3]).multiply(c1[0].subtract(c1[1]))).
- add(c2[3].multiply(c3[0]).multiply(c1[2].subtract(c1[1]))).
- add(c2[3].multiply(c3[1]).multiply(c1[0].subtract(c1[2]))).
- add(c2[3].multiply(c3[2]).multiply(c1[1].subtract(c1[0])));
- }
-
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/a7b4803f/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.java
deleted file mode 100644
index 23d818e..0000000
--- a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SphericalCoordinates.java
+++ /dev/null
@@ -1,395 +0,0 @@
-/*
- * 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.geometry.euclidean.threed;
-
-
-import java.io.Serializable;
-
-import org.apache.commons.math3.util.FastMath;
-
-/** This class provides conversions related to <a
- * href="http://mathworld.wolfram.com/SphericalCoordinates.html">spherical coordinates</a>.
- * <p>
- * The conventions used here are the mathematical ones, i.e. spherical coordinates are
- * related to Cartesian coordinates as follows:
- * </p>
- * <ul>
- * <li>x = r cos(θ) sin(Φ)</li>
- * <li>y = r sin(θ) sin(Φ)</li>
- * <li>z = r cos(Φ)</li>
- * </ul>
- * <ul>
- * <li>r = √(x<sup>2</sup>+y<sup>2</sup>+z<sup>2</sup>)</li>
- * <li>θ = atan2(y, x)</li>
- * <li>Φ = acos(z/r)</li>
- * </ul>
- * <p>
- * r is the radius, θ is the azimuthal angle in the x-y plane and Φ is the polar
- * (co-latitude) angle. These conventions are <em>different</em> from the conventions used
- * in physics (and in particular in spherical harmonics) where the meanings of θ and
- * Φ are reversed.
- * </p>
- * <p>
- * This class provides conversion of coordinates and also of gradient and Hessian
- * between spherical and Cartesian coordinates.
- * </p>
- * @since 3.2
- */
-public class SphericalCoordinates implements Serializable {
-
- /** Serializable UID. */
- private static final long serialVersionUID = 20130206L;
-
- /** Cartesian coordinates. */
- private final Vector3D v;
-
- /** Radius. */
- private final double r;
-
- /** Azimuthal angle in the x-y plane θ. */
- private final double theta;
-
- /** Polar angle (co-latitude) Φ. */
- private final double phi;
-
- /** Jacobian of (r, θ &Phi). */
- private double[][] jacobian;
-
- /** Hessian of radius. */
- private double[][] rHessian;
-
- /** Hessian of azimuthal angle in the x-y plane θ. */
- private double[][] thetaHessian;
-
- /** Hessian of polar (co-latitude) angle Φ. */
- private double[][] phiHessian;
-
- /** Build a spherical coordinates transformer from Cartesian coordinates.
- * @param v Cartesian coordinates
- */
- public SphericalCoordinates(final Vector3D v) {
-
- // Cartesian coordinates
- this.v = v;
-
- // remaining spherical coordinates
- this.r = v.getNorm();
- this.theta = v.getAlpha();
- this.phi = FastMath.acos(v.getZ() / r);
-
- }
-
- /** Build a spherical coordinates transformer from spherical coordinates.
- * @param r radius
- * @param theta azimuthal angle in x-y plane
- * @param phi polar (co-latitude) angle
- */
- public SphericalCoordinates(final double r, final double theta, final double phi) {
-
- final double cosTheta = FastMath.cos(theta);
- final double sinTheta = FastMath.sin(theta);
- final double cosPhi = FastMath.cos(phi);
- final double sinPhi = FastMath.sin(phi);
-
- // spherical coordinates
- this.r = r;
- this.theta = theta;
- this.phi = phi;
-
- // Cartesian coordinates
- this.v = new Vector3D(r * cosTheta * sinPhi,
- r * sinTheta * sinPhi,
- r * cosPhi);
-
- }
-
- /** Get the Cartesian coordinates.
- * @return Cartesian coordinates
- */
- public Vector3D getCartesian() {
- return v;
- }
-
- /** Get the radius.
- * @return radius r
- * @see #getTheta()
- * @see #getPhi()
- */
- public double getR() {
- return r;
- }
-
- /** Get the azimuthal angle in x-y plane.
- * @return azimuthal angle in x-y plane θ
- * @see #getR()
- * @see #getPhi()
- */
- public double getTheta() {
- return theta;
- }
-
- /** Get the polar (co-latitude) angle.
- * @return polar (co-latitude) angle Φ
- * @see #getR()
- * @see #getTheta()
- */
- public double getPhi() {
- return phi;
- }
-
- /** Convert a gradient with respect to spherical coordinates into a gradient
- * with respect to Cartesian coordinates.
- * @param sGradient gradient with respect to spherical coordinates
- * {df/dr, df/dθ, df/dΦ}
- * @return gradient with respect to Cartesian coordinates
- * {df/dx, df/dy, df/dz}
- */
- public double[] toCartesianGradient(final double[] sGradient) {
-
- // lazy evaluation of Jacobian
- computeJacobian();
-
- // compose derivatives as gradient^T . J
- // the expressions have been simplified since we know jacobian[1][2] = dTheta/dZ = 0
- return new double[] {
- sGradient[0] * jacobian[0][0] + sGradient[1] * jacobian[1][0] + sGradient[2] * jacobian[2][0],
- sGradient[0] * jacobian[0][1] + sGradient[1] * jacobian[1][1] + sGradient[2] * jacobian[2][1],
- sGradient[0] * jacobian[0][2] + sGradient[2] * jacobian[2][2]
- };
-
- }
-
- /** Convert a Hessian with respect to spherical coordinates into a Hessian
- * with respect to Cartesian coordinates.
- * <p>
- * As Hessian are always symmetric, we use only the lower left part of the provided
- * spherical Hessian, so the upper part may not be initialized. However, we still
- * do fill up the complete array we create, with guaranteed symmetry.
- * </p>
- * @param sHessian Hessian with respect to spherical coordinates
- * {{d<sup>2</sup>f/dr<sup>2</sup>, d<sup>2</sup>f/drdθ, d<sup>2</sup>f/drdΦ},
- * {d<sup>2</sup>f/drdθ, d<sup>2</sup>f/dθ<sup>2</sup>, d<sup>2</sup>f/dθdΦ},
- * {d<sup>2</sup>f/drdΦ, d<sup>2</sup>f/dθdΦ, d<sup>2</sup>f/dΦ<sup>2</sup>}
- * @param sGradient gradient with respect to spherical coordinates
- * {df/dr, df/dθ, df/dΦ}
- * @return Hessian with respect to Cartesian coordinates
- * {{d<sup>2</sup>f/dx<sup>2</sup>, d<sup>2</sup>f/dxdy, d<sup>2</sup>f/dxdz},
- * {d<sup>2</sup>f/dxdy, d<sup>2</sup>f/dy<sup>2</sup>, d<sup>2</sup>f/dydz},
- * {d<sup>2</sup>f/dxdz, d<sup>2</sup>f/dydz, d<sup>2</sup>f/dz<sup>2</sup>}}
- */
- public double[][] toCartesianHessian(final double[][] sHessian, final double[] sGradient) {
-
- computeJacobian();
- computeHessians();
-
- // compose derivative as J^T . H_f . J + df/dr H_r + df/dtheta H_theta + df/dphi H_phi
- // the expressions have been simplified since we know jacobian[1][2] = dTheta/dZ = 0
- // and H_theta is only a 2x2 matrix as it does not depend on z
- final double[][] hj = new double[3][3];
- final double[][] cHessian = new double[3][3];
-
- // compute H_f . J
- // beware we use ONLY the lower-left part of sHessian
- hj[0][0] = sHessian[0][0] * jacobian[0][0] + sHessian[1][0] * jacobian[1][0] + sHessian[2][0] * jacobian[2][0];
- hj[0][1] = sHessian[0][0] * jacobian[0][1] + sHessian[1][0] * jacobian[1][1] + sHessian[2][0] * jacobian[2][1];
- hj[0][2] = sHessian[0][0] * jacobian[0][2] + sHessian[2][0] * jacobian[2][2];
- hj[1][0] = sHessian[1][0] * jacobian[0][0] + sHessian[1][1] * jacobian[1][0] + sHessian[2][1] * jacobian[2][0];
- hj[1][1] = sHessian[1][0] * jacobian[0][1] + sHessian[1][1] * jacobian[1][1] + sHessian[2][1] * jacobian[2][1];
- // don't compute hj[1][2] as it is not used below
- hj[2][0] = sHessian[2][0] * jacobian[0][0] + sHessian[2][1] * jacobian[1][0] + sHessian[2][2] * jacobian[2][0];
- hj[2][1] = sHessian[2][0] * jacobian[0][1] + sHessian[2][1] * jacobian[1][1] + sHessian[2][2] * jacobian[2][1];
- hj[2][2] = sHessian[2][0] * jacobian[0][2] + sHessian[2][2] * jacobian[2][2];
-
- // compute lower-left part of J^T . H_f . J
- cHessian[0][0] = jacobian[0][0] * hj[0][0] + jacobian[1][0] * hj[1][0] + jacobian[2][0] * hj[2][0];
- cHessian[1][0] = jacobian[0][1] * hj[0][0] + jacobian[1][1] * hj[1][0] + jacobian[2][1] * hj[2][0];
- cHessian[2][0] = jacobian[0][2] * hj[0][0] + jacobian[2][2] * hj[2][0];
- cHessian[1][1] = jacobian[0][1] * hj[0][1] + jacobian[1][1] * hj[1][1] + jacobian[2][1] * hj[2][1];
- cHessian[2][1] = jacobian[0][2] * hj[0][1] + jacobian[2][2] * hj[2][1];
- cHessian[2][2] = jacobian[0][2] * hj[0][2] + jacobian[2][2] * hj[2][2];
-
- // add gradient contribution
- cHessian[0][0] += sGradient[0] * rHessian[0][0] + sGradient[1] * thetaHessian[0][0] + sGradient[2] * phiHessian[0][0];
- cHessian[1][0] += sGradient[0] * rHessian[1][0] + sGradient[1] * thetaHessian[1][0] + sGradient[2] * phiHessian[1][0];
- cHessian[2][0] += sGradient[0] * rHessian[2][0] + sGradient[2] * phiHessian[2][0];
- cHessian[1][1] += sGradient[0] * rHessian[1][1] + sGradient[1] * thetaHessian[1][1] + sGradient[2] * phiHessian[1][1];
- cHessian[2][1] += sGradient[0] * rHessian[2][1] + sGradient[2] * phiHessian[2][1];
- cHessian[2][2] += sGradient[0] * rHessian[2][2] + sGradient[2] * phiHessian[2][2];
-
- // ensure symmetry
- cHessian[0][1] = cHessian[1][0];
- cHessian[0][2] = cHessian[2][0];
- cHessian[1][2] = cHessian[2][1];
-
- return cHessian;
-
- }
-
- /** Lazy evaluation of (r, θ, φ) Jacobian.
- */
- private void computeJacobian() {
- if (jacobian == null) {
-
- // intermediate variables
- final double x = v.getX();
- final double y = v.getY();
- final double z = v.getZ();
- final double rho2 = x * x + y * y;
- final double rho = FastMath.sqrt(rho2);
- final double r2 = rho2 + z * z;
-
- jacobian = new double[3][3];
-
- // row representing the gradient of r
- jacobian[0][0] = x / r;
- jacobian[0][1] = y / r;
- jacobian[0][2] = z / r;
-
- // row representing the gradient of theta
- jacobian[1][0] = -y / rho2;
- jacobian[1][1] = x / rho2;
- // jacobian[1][2] is already set to 0 at allocation time
-
- // row representing the gradient of phi
- jacobian[2][0] = x * z / (rho * r2);
- jacobian[2][1] = y * z / (rho * r2);
- jacobian[2][2] = -rho / r2;
-
- }
- }
-
- /** Lazy evaluation of Hessians.
- */
- private void computeHessians() {
-
- if (rHessian == null) {
-
- // intermediate variables
- final double x = v.getX();
- final double y = v.getY();
- final double z = v.getZ();
- final double x2 = x * x;
- final double y2 = y * y;
- final double z2 = z * z;
- final double rho2 = x2 + y2;
- final double rho = FastMath.sqrt(rho2);
- final double r2 = rho2 + z2;
- final double xOr = x / r;
- final double yOr = y / r;
- final double zOr = z / r;
- final double xOrho2 = x / rho2;
- final double yOrho2 = y / rho2;
- final double xOr3 = xOr / r2;
- final double yOr3 = yOr / r2;
- final double zOr3 = zOr / r2;
-
- // lower-left part of Hessian of r
- rHessian = new double[3][3];
- rHessian[0][0] = y * yOr3 + z * zOr3;
- rHessian[1][0] = -x * yOr3;
- rHessian[2][0] = -z * xOr3;
- rHessian[1][1] = x * xOr3 + z * zOr3;
- rHessian[2][1] = -y * zOr3;
- rHessian[2][2] = x * xOr3 + y * yOr3;
-
- // upper-right part is symmetric
- rHessian[0][1] = rHessian[1][0];
- rHessian[0][2] = rHessian[2][0];
- rHessian[1][2] = rHessian[2][1];
-
- // lower-left part of Hessian of azimuthal angle theta
- thetaHessian = new double[2][2];
- thetaHessian[0][0] = 2 * xOrho2 * yOrho2;
- thetaHessian[1][0] = yOrho2 * yOrho2 - xOrho2 * xOrho2;
- thetaHessian[1][1] = -2 * xOrho2 * yOrho2;
-
- // upper-right part is symmetric
- thetaHessian[0][1] = thetaHessian[1][0];
-
- // lower-left part of Hessian of polar (co-latitude) angle phi
- final double rhor2 = rho * r2;
- final double rho2r2 = rho * rhor2;
- final double rhor4 = rhor2 * r2;
- final double rho3r4 = rhor4 * rho2;
- final double r2P2rho2 = 3 * rho2 + z2;
- phiHessian = new double[3][3];
- phiHessian[0][0] = z * (rho2r2 - x2 * r2P2rho2) / rho3r4;
- phiHessian[1][0] = -x * y * z * r2P2rho2 / rho3r4;
- phiHessian[2][0] = x * (rho2 - z2) / rhor4;
- phiHessian[1][1] = z * (rho2r2 - y2 * r2P2rho2) / rho3r4;
- phiHessian[2][1] = y * (rho2 - z2) / rhor4;
- phiHessian[2][2] = 2 * rho * zOr3 / r;
-
- // upper-right part is symmetric
- phiHessian[0][1] = phiHessian[1][0];
- phiHessian[0][2] = phiHessian[2][0];
- phiHessian[1][2] = phiHessian[2][1];
-
- }
-
- }
-
- /**
- * Replace the instance with a data transfer object for serialization.
- * @return data transfer object that will be serialized
- */
- private Object writeReplace() {
- return new DataTransferObject(v.getX(), v.getY(), v.getZ());
- }
-
- /** Internal class used only for serialization. */
- private static class DataTransferObject implements Serializable {
-
- /** Serializable UID. */
- private static final long serialVersionUID = 20130206L;
-
- /** Abscissa.
- * @serial
- */
- private final double x;
-
- /** Ordinate.
- * @serial
- */
- private final double y;
-
- /** Height.
- * @serial
- */
- private final double z;
-
- /** Simple constructor.
- * @param x abscissa
- * @param y ordinate
- * @param z height
- */
- public DataTransferObject(final double x, final double y, final double z) {
- this.x = x;
- this.y = y;
- this.z = z;
- }
-
- /** Replace the deserialized data transfer object with a {@link SphericalCoordinates}.
- * @return replacement {@link SphericalCoordinates}
- */
- private Object readResolve() {
- return new SphericalCoordinates(new Vector3D(x, y, z));
- }
-
- }
-
-}
http://git-wip-us.apache.org/repos/asf/commons-math/blob/a7b4803f/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SubLine.java
----------------------------------------------------------------------
diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SubLine.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SubLine.java
deleted file mode 100644
index 2ac917f..0000000
--- a/src/main/java/org/apache/commons/math3/geometry/euclidean/threed/SubLine.java
+++ /dev/null
@@ -1,165 +0,0 @@
-/*
- * 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.geometry.euclidean.threed;
-
-import java.util.ArrayList;
-import java.util.List;
-
-import org.apache.commons.math3.exception.MathIllegalArgumentException;
-import org.apache.commons.math3.geometry.Point;
-import org.apache.commons.math3.geometry.euclidean.oned.Euclidean1D;
-import org.apache.commons.math3.geometry.euclidean.oned.Interval;
-import org.apache.commons.math3.geometry.euclidean.oned.IntervalsSet;
-import org.apache.commons.math3.geometry.euclidean.oned.Vector1D;
-import org.apache.commons.math3.geometry.partitioning.Region.Location;
-
-/** This class represents a subset of a {@link Line}.
- * @since 3.0
- */
-public class SubLine {
-
- /** Default value for tolerance. */
- private static final double DEFAULT_TOLERANCE = 1.0e-10;
-
- /** Underlying line. */
- private final Line line;
-
- /** Remaining region of the hyperplane. */
- private final IntervalsSet remainingRegion;
-
- /** Simple constructor.
- * @param line underlying line
- * @param remainingRegion remaining region of the line
- */
- public SubLine(final Line line, final IntervalsSet remainingRegion) {
- this.line = line;
- this.remainingRegion = remainingRegion;
- }
-
- /** Create a sub-line from two endpoints.
- * @param start start point
- * @param end end point
- * @param tolerance tolerance below which points are considered identical
- * @exception MathIllegalArgumentException if the points are equal
- * @since 3.3
- */
- public SubLine(final Vector3D start, final Vector3D end, final double tolerance)
- throws MathIllegalArgumentException {
- this(new Line(start, end, tolerance), buildIntervalSet(start, end, tolerance));
- }
-
- /** Create a sub-line from two endpoints.
- * @param start start point
- * @param end end point
- * @exception MathIllegalArgumentException if the points are equal
- * @deprecated as of 3.3, replaced with {@link #SubLine(Vector3D, Vector3D, double)}
- */
- public SubLine(final Vector3D start, final Vector3D end)
- throws MathIllegalArgumentException {
- this(start, end, DEFAULT_TOLERANCE);
- }
-
- /** Create a sub-line from a segment.
- * @param segment single segment forming the sub-line
- * @exception MathIllegalArgumentException if the segment endpoints are equal
- */
- public SubLine(final Segment segment) throws MathIllegalArgumentException {
- this(segment.getLine(),
- buildIntervalSet(segment.getStart(), segment.getEnd(), segment.getLine().getTolerance()));
- }
-
- /** Get the endpoints of the sub-line.
- * <p>
- * A subline may be any arbitrary number of disjoints segments, so the endpoints
- * are provided as a list of endpoint pairs. Each element of the list represents
- * one segment, and each segment contains a start point at index 0 and an end point
- * at index 1. If the sub-line is unbounded in the negative infinity direction,
- * the start point of the first segment will have infinite coordinates. If the
- * sub-line is unbounded in the positive infinity direction, the end point of the
- * last segment will have infinite coordinates. So a sub-line covering the whole
- * line will contain just one row and both elements of this row will have infinite
- * coordinates. If the sub-line is empty, the returned list will contain 0 segments.
- * </p>
- * @return list of segments endpoints
- */
- public List<Segment> getSegments() {
-
- final List<Interval> list = remainingRegion.asList();
- final List<Segment> segments = new ArrayList<Segment>(list.size());
-
- for (final Interval interval : list) {
- final Vector3D start = line.toSpace((Point<Euclidean1D>) new Vector1D(interval.getInf()));
- final Vector3D end = line.toSpace((Point<Euclidean1D>) new Vector1D(interval.getSup()));
- segments.add(new Segment(start, end, line));
- }
-
- return segments;
-
- }
-
- /** Get the intersection of the instance and another sub-line.
- * <p>
- * This method is related to the {@link Line#intersection(Line)
- * intersection} method in the {@link Line Line} class, but in addition
- * to compute the point along infinite lines, it also checks the point
- * lies on both sub-line ranges.
- * </p>
- * @param subLine other sub-line which may intersect instance
- * @param includeEndPoints if true, endpoints are considered to belong to
- * instance (i.e. they are closed sets) and may be returned, otherwise endpoints
- * are considered to not belong to instance (i.e. they are open sets) and intersection
- * occurring on endpoints lead to null being returned
- * @return the intersection point if there is one, null if the sub-lines don't intersect
- */
- public Vector3D intersection(final SubLine subLine, final boolean includeEndPoints) {
-
- // compute the intersection on infinite line
- Vector3D v1D = line.intersection(subLine.line);
- if (v1D == null) {
- return null;
- }
-
- // check location of point with respect to first sub-line
- Location loc1 = remainingRegion.checkPoint((Point<Euclidean1D>) line.toSubSpace((Point<Euclidean3D>) v1D));
-
- // check location of point with respect to second sub-line
- Location loc2 = subLine.remainingRegion.checkPoint((Point<Euclidean1D>) subLine.line.toSubSpace((Point<Euclidean3D>) v1D));
-
- if (includeEndPoints) {
- return ((loc1 != Location.OUTSIDE) && (loc2 != Location.OUTSIDE)) ? v1D : null;
- } else {
- return ((loc1 == Location.INSIDE) && (loc2 == Location.INSIDE)) ? v1D : null;
- }
-
- }
-
- /** Build an interval set from two points.
- * @param start start point
- * @param end end point
- * @return an interval set
- * @param tolerance tolerance below which points are considered identical
- * @exception MathIllegalArgumentException if the points are equal
- */
- private static IntervalsSet buildIntervalSet(final Vector3D start, final Vector3D end, final double tolerance)
- throws MathIllegalArgumentException {
- final Line line = new Line(start, end, tolerance);
- return new IntervalsSet(line.toSubSpace((Point<Euclidean3D>) start).getX(),
- line.toSubSpace((Point<Euclidean3D>) end).getX(),
- tolerance);
- }
-
-}