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commit d0aaa27873a9739ef8c180f39ccecf5b0f0cdd22
Author: Matt Juntunen <[email protected]>
AuthorDate: Fri Dec 21 23:23:22 2018 -0500

    GEOMETRY-31: renaming dotProduct to dot and crossProduct to cross
---
 .../org/apache/commons/geometry/core/Vector.java   |  4 +--
 .../commons/geometry/euclidean/oned/Vector1D.java  |  2 +-
 .../commons/geometry/euclidean/threed/Line.java    | 16 ++++-----
 .../euclidean/threed/OutlineExtractor.java         | 12 +++----
 .../commons/geometry/euclidean/threed/Plane.java   | 20 +++++------
 .../geometry/euclidean/threed/PolyhedronsSet.java  |  2 +-
 .../geometry/euclidean/threed/SubPlane.java        |  4 +--
 .../geometry/euclidean/threed/Vector3D.java        | 10 +++---
 .../threed/rotation/QuaternionRotation.java        | 40 ++++++++++-----------
 .../commons/geometry/euclidean/twod/Vector2D.java  |  8 ++---
 .../geometry/euclidean/oned/Vector1DTest.java      |  8 ++---
 .../geometry/euclidean/threed/LineTest.java        |  2 +-
 .../euclidean/threed/PolyhedronsSetTest.java       |  2 +-
 .../geometry/euclidean/threed/Vector3DTest.java    | 42 +++++++++++-----------
 .../threed/rotation/QuaternionRotationTest.java    | 14 ++++----
 .../geometry/euclidean/twod/Vector2DTest.java      | 30 ++++++++--------
 .../euclidean/twod/hull/AklToussaintHeuristic.java |  4 +--
 .../commons/geometry/spherical/twod/Circle.java    |  8 ++---
 .../spherical/twod/PropertiesComputer.java         |  4 +--
 .../spherical/twod/SphericalPolygonsSet.java       |  2 +-
 .../geometry/spherical/twod/CircleTest.java        |  8 ++---
 21 files changed, 121 insertions(+), 121 deletions(-)

diff --git 
a/commons-geometry-core/src/main/java/org/apache/commons/geometry/core/Vector.java
 
b/commons-geometry-core/src/main/java/org/apache/commons/geometry/core/Vector.java
index 1b7aea0..873e24e 100644
--- 
a/commons-geometry-core/src/main/java/org/apache/commons/geometry/core/Vector.java
+++ 
b/commons-geometry-core/src/main/java/org/apache/commons/geometry/core/Vector.java
@@ -124,9 +124,9 @@ public interface Vector<V extends Vector<V>> extends 
Spatial {
 
     /** Compute the dot-product of the instance and another vector.
      * @param v second vector
-     * @return the dot product this &middot; v
+     * @return the dot product (this &middot; v)
      */
-    double dotProduct(V v);
+    double dot(V v);
 
     /** Compute the angular separation between two vectors in radians.
      * @param v other vector
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/oned/Vector1D.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/oned/Vector1D.java
index 9d59e6b..6556ca0 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/oned/Vector1D.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/oned/Vector1D.java
@@ -188,7 +188,7 @@ public class Vector1D extends EuclideanVector<Vector1D> {
 
     /** {@inheritDoc} */
     @Override
-    public double dotProduct(Vector1D v) {
+    public double dot(Vector1D v) {
         return x * v.x;
     }
 
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Line.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Line.java
index f650215..2f036a3 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Line.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Line.java
@@ -76,7 +76,7 @@ public class Line implements Embedding<Vector3D, Vector1D> {
             throw new IllegalArgumentException("Points are equal");
         }
         this.direction = Vector3D.linearCombination(1.0 / Math.sqrt(norm2), 
delta);
-        this.zero = Vector3D.linearCombination(1.0, p1, -p1.dotProduct(delta) 
/ norm2, delta);
+        this.zero = Vector3D.linearCombination(1.0, p1, -p1.dot(delta) / 
norm2, delta);
     }
 
     /** Get the tolerance below which points are considered identical.
@@ -117,7 +117,7 @@ public class Line implements Embedding<Vector3D, Vector1D> {
      * @return abscissa of the point
      */
     public double getAbscissa(final Vector3D point) {
-        return point.subtract(zero).dotProduct(direction);
+        return point.subtract(zero).dot(direction);
     }
 
     /** Get one point from the line.
@@ -174,7 +174,7 @@ public class Line implements Embedding<Vector3D, Vector1D> {
      */
     public double distance(final Vector3D p) {
         final Vector3D d = p.subtract(zero);
-        final Vector3D n = Vector3D.linearCombination(1.0, d, 
-d.dotProduct(direction), direction);
+        final Vector3D n = Vector3D.linearCombination(1.0, d, 
-d.dot(direction), direction);
         return n.norm();
     }
 
@@ -184,7 +184,7 @@ public class Line implements Embedding<Vector3D, Vector1D> {
      */
     public double distance(final Line line) {
 
-        final Vector3D normal = direction.crossProduct(line.direction);
+        final Vector3D normal = direction.cross(line.direction);
         final double n = normal.norm();
         if (n < Precision.SAFE_MIN) {
             // lines are parallel
@@ -192,7 +192,7 @@ public class Line implements Embedding<Vector3D, Vector1D> {
         }
 
         // signed separation of the two parallel planes that contains the lines
-        final double offset = line.zero.subtract(zero).dotProduct(normal) / n;
+        final double offset = line.zero.subtract(zero).dot(normal) / n;
 
         return Math.abs(offset);
 
@@ -204,7 +204,7 @@ public class Line implements Embedding<Vector3D, Vector1D> {
      */
     public Vector3D closestPoint(final Line line) {
 
-        final double cos = direction.dotProduct(line.direction);
+        final double cos = direction.dot(line.direction);
         final double n = 1 - cos * cos;
         if (n < Precision.EPSILON) {
             // the lines are parallel
@@ -212,8 +212,8 @@ public class Line implements Embedding<Vector3D, Vector1D> {
         }
 
         final Vector3D delta0 = line.zero.subtract(zero);
-        final double a        = delta0.dotProduct(direction);
-        final double b        = delta0.dotProduct(line.direction);
+        final double a        = delta0.dot(direction);
+        final double b        = delta0.dot(line.direction);
 
         return Vector3D.linearCombination(1, zero, (a - b * cos) / n, 
direction);
 
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/OutlineExtractor.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/OutlineExtractor.java
index 0fd8448..3ea8376 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/OutlineExtractor.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/OutlineExtractor.java
@@ -49,7 +49,7 @@ public class OutlineExtractor {
     public OutlineExtractor(final Vector3D u, final Vector3D v) {
         this.u = u;
         this.v = v;
-        this.w = u.crossProduct(v);
+        this.w = u.cross(v);
     }
 
     /** Extract the outline of a polyhedrons set.
@@ -168,7 +168,7 @@ public class OutlineExtractor {
                 (AbstractSubHyperplane<Vector3D, Vector2D>) facet;
             final Plane plane    = (Plane) facet.getHyperplane();
 
-            final double scal = plane.getNormal().dotProduct(w);
+            final double scal = plane.getNormal().dot(w);
             if (Math.abs(scal) > 1.0e-3) {
                 Vector2D[][] vertices =
                     ((PolygonsSet) 
absFacet.getRemainingRegion()).getVertices();
@@ -205,13 +205,13 @@ public class OutlineExtractor {
                     int previous         = closed ? (loop.length - 1) : 1;
                     Vector3D previous3D  = plane.toSpace(loop[previous]);
                     int current          = (previous + 1) % loop.length;
-                    Vector2D pPoint       = 
Vector2D.of(previous3D.dotProduct(u),
-                                                         
previous3D.dotProduct(v));
+                    Vector2D pPoint       = Vector2D.of(previous3D.dot(u),
+                                                         previous3D.dot(v));
                     while (current < loop.length) {
 
                         final Vector3D current3D = 
plane.toSpace(loop[current]);
-                        final Vector2D  cPoint    = 
Vector2D.of(current3D.dotProduct(u),
-                                                                 
current3D.dotProduct(v));
+                        final Vector2D  cPoint    = 
Vector2D.of(current3D.dot(u),
+                                                                 
current3D.dot(v));
                         final org.apache.commons.geometry.euclidean.twod.Line 
line =
                             new 
org.apache.commons.geometry.euclidean.twod.Line(pPoint, cPoint, tolerance);
                         SubHyperplane<Vector2D> edge = line.wholeHyperplane();
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Plane.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Plane.java
index 963b76d..b1f2955 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Plane.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Plane.java
@@ -70,7 +70,7 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
         throws IllegalArgumentException {
         setNormal(normal);
         this.tolerance = tolerance;
-        this.originOffset = -p.dotProduct(w);
+        this.originOffset = -p.dot(w);
         setFrame();
     }
 
@@ -85,7 +85,7 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
      */
     public Plane(final Vector3D p1, final Vector3D p2, final Vector3D p3, 
final double tolerance)
         throws IllegalArgumentException {
-        this(p1, p2.subtract(p1).crossProduct(p3.subtract(p1)), tolerance);
+        this(p1, p2.subtract(p1).cross(p3.subtract(p1)), tolerance);
     }
 
     /** Copy constructor.
@@ -121,7 +121,7 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
      */
     public void reset(final Vector3D p, final Vector3D normal) {
         setNormal(normal);
-        originOffset = -p.dotProduct(w);
+        originOffset = -p.dot(w);
         setFrame();
     }
 
@@ -154,7 +154,7 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
     private void setFrame() {
         origin = Vector3D.linearCombination(-originOffset, w);
         u = w.orthogonal();
-        v = w.crossProduct(u);
+        v = w.cross(u);
     }
 
     /** Get the origin point of the plane frame.
@@ -242,7 +242,7 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
     @Override
     public Vector2D toSubSpace(final Vector3D point) {
         Vector3D vec = point;
-        return Vector2D.of(vec.dotProduct(u), vec.dotProduct(v));
+        return Vector2D.of(vec.dot(u), vec.dot(v));
     }
 
     /** Transform an in-plane point into a 3D space point.
@@ -323,12 +323,12 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
      */
     public Vector3D intersection(final Line line) {
         final Vector3D direction = line.getDirection();
-        final double   dot       = w.dotProduct(direction);
+        final double   dot       = w.dot(direction);
         if (Math.abs(dot) < 1.0e-10) {
             return null;
         }
         final Vector3D point = line.toSpace(Vector1D.ZERO);
-        final double   k     = -(originOffset + w.dotProduct(point)) / dot;
+        final double   k     = -(originOffset + w.dot(point)) / dot;
         return Vector3D.linearCombination(1.0, point, k, direction);
     }
 
@@ -338,7 +338,7 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
      * other plane (really a {@link Line Line} instance)
      */
     public Line intersection(final Plane other) {
-        final Vector3D direction = w.crossProduct(other.w);
+        final Vector3D direction = w.cross(other.w);
         if (direction.norm() < tolerance) {
             return null;
         }
@@ -437,7 +437,7 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
      */
     @Override
     public double getOffset(final Vector3D point) {
-        return point.dotProduct(w) + originOffset;
+        return point.dot(w) + originOffset;
     }
 
     /** Check if the instance has the same orientation as another hyperplane.
@@ -447,7 +447,7 @@ public class Plane implements Hyperplane<Vector3D>, 
Embedding<Vector3D, Vector2D
      */
     @Override
     public boolean sameOrientationAs(final Hyperplane<Vector3D> other) {
-        return (((Plane) other).w).dotProduct(w) > 0.0;
+        return (((Plane) other).w).dot(w) > 0.0;
     }
 
 }
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/PolyhedronsSet.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/PolyhedronsSet.java
index fd7ded9..58269fe 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/PolyhedronsSet.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/PolyhedronsSet.java
@@ -450,7 +450,7 @@ public class PolyhedronsSet extends 
AbstractRegion<Vector3D, Vector2D> {
 
                 // the volume here is actually 3x the actual pyramid volume; 
we'll apply
                 // the final scaling all at once at the end
-                double scaledVolume = area * 
facetBarycenter.dotProduct(plane.getNormal());
+                double scaledVolume = area * 
facetBarycenter.dot(plane.getNormal());
                 if (reversed) {
                     scaledVolume = -scaledVolume;
                 }
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/SubPlane.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/SubPlane.java
index eece004..485f514 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/SubPlane.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/SubPlane.java
@@ -74,8 +74,8 @@ public class SubPlane extends AbstractSubHyperplane<Vector3D, 
Vector2D> {
         // the hyperplanes do intersect
         Vector2D p = thisPlane.toSubSpace(inter.toSpace(Vector1D.ZERO));
         Vector2D q = thisPlane.toSubSpace(inter.toSpace(Vector1D.ONE));
-        Vector3D crossP = 
inter.getDirection().crossProduct(thisPlane.getNormal());
-        if (crossP.dotProduct(otherPlane.getNormal()) < 0) {
+        Vector3D crossP = inter.getDirection().cross(thisPlane.getNormal());
+        if (crossP.dot(otherPlane.getNormal()) < 0) {
             final Vector2D tmp = p;
             p           = q;
             q           = tmp;
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Vector3D.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Vector3D.java
index 4ff6dff..b59793a 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Vector3D.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/Vector3D.java
@@ -271,7 +271,7 @@ public class Vector3D extends 
MultiDimensionalEuclideanVector<Vector3D> {
      * @see LinearCombination#value(double, double, double, double, double, 
double)
      */
     @Override
-    public double dotProduct(Vector3D v) {
+    public double dot(Vector3D v) {
         return LinearCombination.value(x, v.x, y, v.y, z, v.z);
     }
 
@@ -286,11 +286,11 @@ public class Vector3D extends 
MultiDimensionalEuclideanVector<Vector3D> {
     public double angle(Vector3D v) {
         double normProduct = getCheckedNorm() * v.getCheckedNorm();
 
-        double dot = dotProduct(v);
+        double dot = dot(v);
         double threshold = normProduct * 0.99;
         if ((dot < -threshold) || (dot > threshold)) {
             // the vectors are almost aligned, compute using the sine
-            Vector3D cross = crossProduct(v);
+            Vector3D cross = cross(v);
             if (dot >= 0) {
                 return Math.asin(cross.norm() / normProduct);
             }
@@ -354,7 +354,7 @@ public class Vector3D extends 
MultiDimensionalEuclideanVector<Vector3D> {
      * @param v other vector
      * @return the cross product this ^ v as a new Vector3D
      */
-    public Vector3D crossProduct(final Vector3D v) {
+    public Vector3D cross(final Vector3D v) {
         return new Vector3D(LinearCombination.value(y, v.z, -z, v.y),
                             LinearCombination.value(z, v.x, -x, v.z),
                             LinearCombination.value(x, v.y, -y, v.x));
@@ -439,7 +439,7 @@ public class Vector3D extends 
MultiDimensionalEuclideanVector<Vector3D> {
      * @throws IllegalNormException if {@code base} has a zero, NaN, or 
infinite norm
      */
     private Vector3D getComponent(Vector3D base, boolean reject, 
DoubleFunction3N<Vector3D> factory) {
-        final double aDotB = dotProduct(base);
+        final double aDotB = dot(base);
 
         // We need to check the norm value here to ensure that it's legal. 
However, we don't
         // want to incur the cost or floating point error of getting the 
actual norm and then
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/rotation/QuaternionRotation.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/rotation/QuaternionRotation.java
index f9f51c2..957ff56 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/rotation/QuaternionRotation.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/threed/rotation/QuaternionRotation.java
@@ -384,15 +384,15 @@ public final class QuaternionRotation implements 
Rotation3D, Serializable {
         final Vector3D vec3 = apply(axis3);
         final Vector3D invVec1 = inverse().apply(axis1);
 
-        final double angle2Sin = vec3.dotProduct(axis2.crossProduct(axis3));
+        final double angle2Sin = vec3.dot(axis2.cross(axis3));
 
         if (angle2Sin < -AXIS_ANGLE_SINGULARITY_THRESHOLD ||
                 angle2Sin > AXIS_ANGLE_SINGULARITY_THRESHOLD) {
 
             final Vector3D vec2 = apply(axis2);
 
-            final double angle1TanY = 
vec2.dotProduct(axis1.crossProduct(axis2));
-            final double angle1TanX = vec2.dotProduct(axis2);
+            final double angle1TanY = vec2.dot(axis1.cross(axis2));
+            final double angle1TanX = vec2.dot(axis2);
 
             final double angle2 = angle2Sin > AXIS_ANGLE_SINGULARITY_THRESHOLD 
? Geometry.HALF_PI : Geometry.MINUS_HALF_PI;
 
@@ -403,13 +403,13 @@ public final class QuaternionRotation implements 
Rotation3D, Serializable {
             };
         }
 
-        final Vector3D  crossAxis13 = axis1.crossProduct(axis3);
+        final Vector3D  crossAxis13 = axis1.cross(axis3);
 
-        final double angle1TanY = vec3.dotProduct(crossAxis13);
-        final double angle1TanX = vec3.dotProduct(axis3);
+        final double angle1TanY = vec3.dot(crossAxis13);
+        final double angle1TanX = vec3.dot(axis3);
 
-        final double angle3TanY = invVec1.dotProduct(crossAxis13);
-        final double angle3TanX = invVec1.dotProduct(axis1);
+        final double angle3TanY = invVec1.dot(crossAxis13);
+        final double angle3TanX = invVec1.dot(axis1);
 
         return new double[] {
             Math.atan2(angle1TanY, angle1TanX),
@@ -445,20 +445,20 @@ public final class QuaternionRotation implements 
Rotation3D, Serializable {
         // Use the same overall approach as with the Tait-Bryan angles: get 
the first two angles by looking
         // at the transformed rotation axes and the third by using the inverse.
 
-        final Vector3D crossAxis = axis1.crossProduct(axis2);
+        final Vector3D crossAxis = axis1.cross(axis2);
 
         final Vector3D vec1 = apply(axis1);
         final Vector3D invVec1 = inverse().apply(axis1);
 
-        final double angle2Cos = vec1.dotProduct(axis1);
+        final double angle2Cos = vec1.dot(axis1);
 
         if (angle2Cos < -AXIS_ANGLE_SINGULARITY_THRESHOLD ||
                 angle2Cos > AXIS_ANGLE_SINGULARITY_THRESHOLD) {
 
             final Vector3D vec2 = apply(axis2);
 
-            final double angle1TanY = vec2.dotProduct(crossAxis);
-            final double angle1TanX = vec2.dotProduct(axis2);
+            final double angle1TanY = vec2.dot(crossAxis);
+            final double angle1TanX = vec2.dot(axis2);
 
             final double angle2 = angle2Cos > AXIS_ANGLE_SINGULARITY_THRESHOLD 
? Geometry.ZERO_PI : Geometry.PI;
 
@@ -469,11 +469,11 @@ public final class QuaternionRotation implements 
Rotation3D, Serializable {
             };
         }
 
-        final double angle1TanY = vec1.dotProduct(axis2);
-        final double angle1TanX = -vec1.dotProduct(crossAxis);
+        final double angle1TanY = vec1.dot(axis2);
+        final double angle1TanX = -vec1.dot(crossAxis);
 
-        final double angle3TanY = invVec1.dotProduct(axis2);
-        final double angle3TanX = invVec1.dotProduct(crossAxis);
+        final double angle3TanY = invVec1.dot(axis2);
+        final double angle3TanX = invVec1.dot(crossAxis);
 
         return new double[] {
             Math.atan2(angle1TanY, angle1TanX),
@@ -599,7 +599,7 @@ public final class QuaternionRotation implements 
Rotation3D, Serializable {
     public static QuaternionRotation createVectorRotation(final Vector3D u, 
final Vector3D v) {
 
         double normProduct  = Vectors.checkedNorm(u) * Vectors.checkedNorm(v);
-        double dot = u.dotProduct(v);
+        double dot = u.dot(v);
 
         if (dot < ANTIPARALLEL_DOT_THRESHOLD * normProduct) {
             // Special case where u1 = -u2:
@@ -634,7 +634,7 @@ public final class QuaternionRotation implements 
Rotation3D, Serializable {
         //
         // This can be simplified to the expression below.
         final double vectorialScaleFactor = 1.0 / (2.0 * w * normProduct);
-        final Vector3D axis = u.crossProduct(v);
+        final Vector3D axis = u.cross(v);
 
         return of(w,
                   vectorialScaleFactor * axis.getX(),
@@ -666,11 +666,11 @@ public final class QuaternionRotation implements 
Rotation3D, Serializable {
         // calculate orthonormalized bases
         final Vector3D a = u1.normalize();
         final Vector3D b = a.orthogonal(u2);
-        final Vector3D c = a.crossProduct(b);
+        final Vector3D c = a.cross(b);
 
         final Vector3D d = v1.normalize();
         final Vector3D e = d.orthogonal(v2);
-        final Vector3D f = d.crossProduct(e);
+        final Vector3D f = d.cross(e);
 
         // create an orthogonal rotation matrix representing the change of 
basis; this matrix will
         // be the multiplication of the matrix composed of the column vectors 
d, e, f and the
diff --git 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/twod/Vector2D.java
 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/twod/Vector2D.java
index 4949335..08b4f1f 100644
--- 
a/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/twod/Vector2D.java
+++ 
b/commons-geometry-euclidean/src/main/java/org/apache/commons/geometry/euclidean/twod/Vector2D.java
@@ -219,7 +219,7 @@ public class Vector2D extends 
MultiDimensionalEuclideanVector<Vector2D> {
 
     /** {@inheritDoc} */
     @Override
-    public double dotProduct(Vector2D v) {
+    public double dot(Vector2D v) {
         return LinearCombination.value(x, v.x, y, v.y);
     }
 
@@ -234,7 +234,7 @@ public class Vector2D extends 
MultiDimensionalEuclideanVector<Vector2D> {
     public double angle(Vector2D v) {
         double normProduct = getCheckedNorm() * v.getCheckedNorm();
 
-        double dot = dotProduct(v);
+        double dot = dot(v);
         double threshold = normProduct * 0.9999;
         if ((dot < -threshold) || (dot > threshold)) {
             // the vectors are almost aligned, compute using the sine
@@ -301,7 +301,7 @@ public class Vector2D extends 
MultiDimensionalEuclideanVector<Vector2D> {
      *
      * @see <a href="http://mathworld.wolfram.com/CrossProduct.html";>Cross 
product (Mathworld)</a>
      */
-    public double crossProduct(final Vector2D p1, final Vector2D p2) {
+    public double cross(final Vector2D p1, final Vector2D p2) {
         final double x1 = p2.x - p1.x;
         final double y1 = y - p1.y;
         final double x2 = x - p1.x;
@@ -389,7 +389,7 @@ public class Vector2D extends 
MultiDimensionalEuclideanVector<Vector2D> {
      * @throws IllegalNormException if {@code base} has a zero, NaN, or 
infinite norm
      */
     private Vector2D getComponent(Vector2D base, boolean reject, 
DoubleFunction2N<Vector2D> factory) {
-        final double aDotB = dotProduct(base);
+        final double aDotB = dot(base);
 
         // We need to check the norm value here to ensure that it's legal. 
However, we don't
         // want to incur the cost or floating point error of getting the 
actual norm and then
diff --git 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/oned/Vector1DTest.java
 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/oned/Vector1DTest.java
index fda735c..8aa06b7 100644
--- 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/oned/Vector1DTest.java
+++ 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/oned/Vector1DTest.java
@@ -305,11 +305,11 @@ public class Vector1DTest {
         Vector1D v3 = Vector1D.of(3);
 
         // act/assert
-        Assert.assertEquals(-6.0, v1.dotProduct(v2), TEST_TOLERANCE);
-        Assert.assertEquals(-6.0, v2.dotProduct(v1), TEST_TOLERANCE);
+        Assert.assertEquals(-6.0, v1.dot(v2), TEST_TOLERANCE);
+        Assert.assertEquals(-6.0, v2.dot(v1), TEST_TOLERANCE);
 
-        Assert.assertEquals(6.0, v1.dotProduct(v3), TEST_TOLERANCE);
-        Assert.assertEquals(6.0, v3.dotProduct(v1), TEST_TOLERANCE);
+        Assert.assertEquals(6.0, v1.dot(v3), TEST_TOLERANCE);
+        Assert.assertEquals(6.0, v3.dot(v1), TEST_TOLERANCE);
     }
 
     @Test
diff --git 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/LineTest.java
 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/LineTest.java
index b0cd043..5779fbd 100644
--- 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/LineTest.java
+++ 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/LineTest.java
@@ -28,7 +28,7 @@ public class LineTest {
         Assert.assertTrue(l.contains(p1));
         Assert.assertTrue(l.contains(Vector3D.linearCombination(1.0, p1, 0.3, 
l.getDirection())));
         Vector3D u = l.getDirection().orthogonal();
-        Vector3D v = l.getDirection().crossProduct(u);
+        Vector3D v = l.getDirection().cross(u);
         for (double alpha = 0; alpha < 2 * Math.PI; alpha += 0.3) {
             Assert.assertTrue(! 
l.contains(p1.add(Vector3D.linearCombination(Math.cos(alpha), u,
                                                                
Math.sin(alpha), v))));
diff --git 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/PolyhedronsSetTest.java
 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/PolyhedronsSetTest.java
index 90d8b47..efc5a39 100644
--- 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/PolyhedronsSetTest.java
+++ 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/PolyhedronsSetTest.java
@@ -910,7 +910,7 @@ public class PolyhedronsSetTest {
             SubHyperplane<Vector3D> plane = polyset.firstIntersection(origin, 
line);
             if (plane != null) {
                 Vector3D intersectionPoint = 
((Plane)plane.getHyperplane()).intersection(line);
-                double dotProduct = 
direction.dotProduct(intersectionPoint.subtract(origin));
+                double dotProduct = 
direction.dot(intersectionPoint.subtract(origin));
                 Assert.assertTrue(dotProduct > 0);
             }
         }
diff --git 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/Vector3DTest.java
 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/Vector3DTest.java
index 6254ef4..c6243d5 100644
--- 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/Vector3DTest.java
+++ 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/Vector3DTest.java
@@ -365,10 +365,10 @@ public class Vector3DTest {
         Vector3D v4 = Vector3D.of(4.2, 0.1, -1.8);
 
         // act/assert
-        Assert.assertEquals(0.0, v1.dotProduct(v1.orthogonal()), EPS);
-        Assert.assertEquals(0.0, v2.dotProduct(v2.orthogonal()), EPS);
-        Assert.assertEquals(0.0, v3.dotProduct(v3.orthogonal()), EPS);
-        Assert.assertEquals(0.0, v4.dotProduct(v4.orthogonal()), EPS);
+        Assert.assertEquals(0.0, v1.dot(v1.orthogonal()), EPS);
+        Assert.assertEquals(0.0, v2.dot(v2.orthogonal()), EPS);
+        Assert.assertEquals(0.0, v3.dot(v3.orthogonal()), EPS);
+        Assert.assertEquals(0.0, v4.dot(v4.orthogonal()), EPS);
     }
 
     @Test
@@ -495,16 +495,16 @@ public class Vector3DTest {
     @Test
     public void testCrossProduct() {
         // act/assert
-        checkVector(Vector3D.PLUS_X.crossProduct(Vector3D.PLUS_Y), 0, 0, 1);
-        checkVector(Vector3D.PLUS_X.crossProduct(Vector3D.MINUS_Y), 0, 0, -1);
+        checkVector(Vector3D.PLUS_X.cross(Vector3D.PLUS_Y), 0, 0, 1);
+        checkVector(Vector3D.PLUS_X.cross(Vector3D.MINUS_Y), 0, 0, -1);
 
-        checkVector(Vector3D.MINUS_X.crossProduct(Vector3D.MINUS_Y), 0, 0, 1);
-        checkVector(Vector3D.MINUS_X.crossProduct(Vector3D.PLUS_Y), 0, 0, -1);
+        checkVector(Vector3D.MINUS_X.cross(Vector3D.MINUS_Y), 0, 0, 1);
+        checkVector(Vector3D.MINUS_X.cross(Vector3D.PLUS_Y), 0, 0, -1);
 
-        checkVector(Vector3D.of(2, 1, -4).crossProduct(Vector3D.of(3, 1, -1)), 
3, -10, -1);
+        checkVector(Vector3D.of(2, 1, -4).cross(Vector3D.of(3, 1, -1)), 3, 
-10, -1);
 
         double invSqrt6 = 1 / Math.sqrt(6);
-        checkVector(Vector3D.of(1, 1, 1).crossProduct(Vector3D.of(-1, 0, 
1)).normalize(), invSqrt6, - 2 * invSqrt6, invSqrt6);
+        checkVector(Vector3D.of(1, 1, 1).cross(Vector3D.of(-1, 0, 
1)).normalize(), invSqrt6, - 2 * invSqrt6, invSqrt6);
     }
 
     @Test
@@ -530,7 +530,7 @@ public class Vector3DTest {
         Vector3D cNaive = Vector3D.of(u1.getY() * u2.getZ() - u1.getZ() * 
u2.getY(),
                                        u1.getZ() * u2.getX() - u1.getX() * 
u2.getZ(),
                                        u1.getX() * u2.getY() - u1.getY() * 
u2.getX());
-        Vector3D cAccurate = u1.crossProduct(u2);
+        Vector3D cAccurate = u1.cross(u2);
 
         // assert
         Assert.assertTrue(u3.distance(cNaive) > 2.9 * u3.norm());
@@ -553,7 +553,7 @@ public class Vector3DTest {
 
             // act
             Vector3D cNaive = Vector3D.of(uy * vz - uz * vy, uz * vx - ux * 
vz, ux * vy - uy * vx);
-            Vector3D cAccurate = Vector3D.of(ux, uy, 
uz).crossProduct(Vector3D.of(vx, vy, vz));
+            Vector3D cAccurate = Vector3D.of(ux, uy, uz).cross(Vector3D.of(vx, 
vy, vz));
 
             // assert
             Assert.assertEquals(0.0, cAccurate.distance(cNaive), 6.0e-15 * 
cAccurate.norm());
@@ -565,12 +565,12 @@ public class Vector3DTest {
         // act/assert
         Vector3D v1 = Vector3D.of(9070467121.0, 4535233560.0, 1);
         Vector3D v2 = Vector3D.of(9070467123.0, 4535233561.0, 1);
-        checkVector(v1.crossProduct(v2), -1, 2, 1);
+        checkVector(v1.cross(v2), -1, 2, 1);
 
         double scale    = Math.scalb(1.0, 100);
         Vector3D big1   = Vector3D.linearCombination(scale, v1);
         Vector3D small2 = Vector3D.linearCombination(1 / scale, v2);
-        checkVector(big1.crossProduct(small2), -1, 2, 1);
+        checkVector(big1.cross(small2), -1, 2, 1);
     }
 
     @Test
@@ -641,13 +641,13 @@ public class Vector3DTest {
         Vector3D v3 = Vector3D.of(7, 8, 9);
 
         // act/assert
-        Assert.assertEquals(14, v1.dotProduct(v1), EPS);
+        Assert.assertEquals(14, v1.dot(v1), EPS);
 
-        Assert.assertEquals(-32, v1.dotProduct(v2), EPS);
-        Assert.assertEquals(-32, v2.dotProduct(v1), EPS);
+        Assert.assertEquals(-32, v1.dot(v2), EPS);
+        Assert.assertEquals(-32, v2.dot(v1), EPS);
 
-        Assert.assertEquals(18, v1.dotProduct(v3), EPS);
-        Assert.assertEquals(18, v3.dotProduct(v1), EPS);
+        Assert.assertEquals(18, v1.dot(v3), EPS);
+        Assert.assertEquals(18, v3.dot(v1), EPS);
     }
 
     @Test
@@ -666,7 +666,7 @@ public class Vector3DTest {
 
         // act
         double sNaive = u1.getX() * u2.getX() + u1.getY() * u2.getY() + 
u1.getZ() * u2.getZ();
-        double sAccurate = u1.dotProduct(u2);
+        double sAccurate = u1.dot(u2);
 
         // assert
         Assert.assertEquals(0.0, sNaive, 1.0e-30);
@@ -689,7 +689,7 @@ public class Vector3DTest {
 
             // act
             double sNaive = ux * vx + uy * vy + uz * vz;
-            double sAccurate = Vector3D.of(ux, uy, 
uz).dotProduct(Vector3D.of(vx, vy, vz));
+            double sAccurate = Vector3D.of(ux, uy, uz).dot(Vector3D.of(vx, vy, 
vz));
 
             // assert
             Assert.assertEquals(sNaive, sAccurate, 2.5e-16 * sAccurate);
diff --git 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/rotation/QuaternionRotationTest.java
 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/rotation/QuaternionRotationTest.java
index 35175ea..0283700 100644
--- 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/rotation/QuaternionRotationTest.java
+++ 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/threed/rotation/QuaternionRotationTest.java
@@ -197,7 +197,7 @@ public class QuaternionRotationTest {
             Assert.assertTrue(angle <= Geometry.PI);
 
             double expected = 
PlaneAngleRadians.normalizeBetweenMinusPiAndPi(theta);
-            if (PLUS_DIAGONAL.dotProduct(rot.getAxis()) < 0) {
+            if (PLUS_DIAGONAL.dot(rot.getAxis()) < 0) {
                 // if the axis ended up being flipped, then negate the 
expected angle
                 expected *= -1;
             }
@@ -1116,8 +1116,8 @@ public class QuaternionRotationTest {
 
         // assert
         Vector3D axis = q.getAxis();
-        Assert.assertEquals(0.0, axis.dotProduct(u1), EPS);
-        Assert.assertEquals(0.0, axis.dotProduct(u2), EPS);
+        Assert.assertEquals(0.0, axis.dot(u1), EPS);
+        Assert.assertEquals(0.0, axis.dot(u2), EPS);
         Assert.assertEquals(Geometry.PI, q.getAngle(), EPS);
 
         EuclideanTestUtils.assertCoordinatesEqual(Vector3D.of(0, -2, 0), 
q.apply(u1), EPS);
@@ -1320,12 +1320,12 @@ public class QuaternionRotationTest {
             Assert.assertEquals(1.0, transformedY.norm(), EPS);
             Assert.assertEquals(1.0, transformedZ.norm(), EPS);
 
-            Assert.assertEquals(0.0, transformedX.dotProduct(transformedY), 
EPS);
-            Assert.assertEquals(0.0, transformedX.dotProduct(transformedZ), 
EPS);
-            Assert.assertEquals(0.0, transformedY.dotProduct(transformedZ), 
EPS);
+            Assert.assertEquals(0.0, transformedX.dot(transformedY), EPS);
+            Assert.assertEquals(0.0, transformedX.dot(transformedZ), EPS);
+            Assert.assertEquals(0.0, transformedY.dot(transformedZ), EPS);
 
             EuclideanTestUtils.assertCoordinatesEqual(transformedZ.normalize(),
-                    
transformedX.normalize().crossProduct(transformedY.normalize()), EPS);
+                    transformedX.normalize().cross(transformedY.normalize()), 
EPS);
 
             Assert.assertEquals(1.0, q.getQuaternion().norm(), EPS);
         });
diff --git 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/twod/Vector2DTest.java
 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/twod/Vector2DTest.java
index e106537..5a4c268 100644
--- 
a/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/twod/Vector2DTest.java
+++ 
b/commons-geometry-euclidean/src/test/java/org/apache/commons/geometry/euclidean/twod/Vector2DTest.java
@@ -360,20 +360,20 @@ public class Vector2DTest {
         Vector2D v3 = Vector2D.of(-1, 0);
 
         // act/assert
-        Assert.assertEquals(2, v1.dotProduct(v1), EPS);
-        Assert.assertEquals(41, v2.dotProduct(v2), EPS);
-        Assert.assertEquals(1, v3.dotProduct(v3), EPS);
+        Assert.assertEquals(2, v1.dot(v1), EPS);
+        Assert.assertEquals(41, v2.dot(v2), EPS);
+        Assert.assertEquals(1, v3.dot(v3), EPS);
 
-        Assert.assertEquals(9, v1.dotProduct(v2), EPS);
-        Assert.assertEquals(9, v2.dotProduct(v1), EPS);
+        Assert.assertEquals(9, v1.dot(v2), EPS);
+        Assert.assertEquals(9, v2.dot(v1), EPS);
 
-        Assert.assertEquals(-1, v1.dotProduct(v3), EPS);
-        Assert.assertEquals(-1, v3.dotProduct(v1), EPS);
+        Assert.assertEquals(-1, v1.dot(v3), EPS);
+        Assert.assertEquals(-1, v3.dot(v1), EPS);
 
-        Assert.assertEquals(1, Vector2D.PLUS_X.dotProduct(Vector2D.PLUS_X), 
EPS);
-        Assert.assertEquals(0, Vector2D.PLUS_X.dotProduct(Vector2D.PLUS_Y), 
EPS);
-        Assert.assertEquals(-1, Vector2D.PLUS_X.dotProduct(Vector2D.MINUS_X), 
EPS);
-        Assert.assertEquals(0, Vector2D.PLUS_X.dotProduct(Vector2D.MINUS_Y), 
EPS);
+        Assert.assertEquals(1, Vector2D.PLUS_X.dot(Vector2D.PLUS_X), EPS);
+        Assert.assertEquals(0, Vector2D.PLUS_X.dot(Vector2D.PLUS_Y), EPS);
+        Assert.assertEquals(-1, Vector2D.PLUS_X.dot(Vector2D.MINUS_X), EPS);
+        Assert.assertEquals(0, Vector2D.PLUS_X.dot(Vector2D.MINUS_Y), EPS);
     }
 
     @Test
@@ -406,7 +406,7 @@ public class Vector2DTest {
 
             // assert
             Assert.assertEquals(1.0, ortho.norm(), EPS);
-            Assert.assertEquals(0.0, v.dotProduct(ortho), EPS);
+            Assert.assertEquals(0.0, v.dot(ortho), EPS);
         }
     }
 
@@ -523,9 +523,9 @@ public class Vector2DTest {
         Vector2D p5 = Vector2D.of(2, 1);
 
         // act/assert
-        Assert.assertEquals(0.0, p3.crossProduct(p1, p2), EPS);
-        Assert.assertEquals(1.0, p4.crossProduct(p1, p2), EPS);
-        Assert.assertEquals(-1.0, p5.crossProduct(p1, p2), EPS);
+        Assert.assertEquals(0.0, p3.cross(p1, p2), EPS);
+        Assert.assertEquals(1.0, p4.cross(p1, p2), EPS);
+        Assert.assertEquals(-1.0, p5.cross(p1, p2), EPS);
     }
 
     @Test
diff --git 
a/commons-geometry-hull/src/main/java/org/apache/commons/geometry/euclidean/twod/hull/AklToussaintHeuristic.java
 
b/commons-geometry-hull/src/main/java/org/apache/commons/geometry/euclidean/twod/hull/AklToussaintHeuristic.java
index 4616553..af3c034 100644
--- 
a/commons-geometry-hull/src/main/java/org/apache/commons/geometry/euclidean/twod/hull/AklToussaintHeuristic.java
+++ 
b/commons-geometry-hull/src/main/java/org/apache/commons/geometry/euclidean/twod/hull/AklToussaintHeuristic.java
@@ -129,7 +129,7 @@ public final class AklToussaintHeuristic {
         }
 
         // get the location of the point relative to the first two vertices
-        final double last = v0.crossProduct(v1, v2);
+        final double last = v0.cross(v1, v2);
         final int size = quadrilateralPoints.size();
         // loop through the rest of the vertices
         for (int i = 1; i < size; i++) {
@@ -143,7 +143,7 @@ public final class AklToussaintHeuristic {
             // do side of line test: multiply the last location with this 
location
             // if they are the same sign then the operation will yield a 
positive result
             // -x * -y = +xy, x * y = +xy, -x * y = -xy, x * -y = -xy
-            if (last * v0.crossProduct(v1, v2) < 0) {
+            if (last * v0.cross(v1, v2) < 0) {
                 return false;
             }
         }
diff --git 
a/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/Circle.java
 
b/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/Circle.java
index 564a69b..9d3c932 100644
--- 
a/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/Circle.java
+++ 
b/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/Circle.java
@@ -68,7 +68,7 @@ public class Circle implements Hyperplane<S2Point>, 
Embedding<S2Point, S1Point>
      * @param tolerance tolerance below which close sub-arcs are merged 
together
      */
     public Circle(final S2Point first, final S2Point second, final double 
tolerance) {
-        reset(first.getVector().crossProduct(second.getVector()));
+        reset(first.getVector().cross(second.getVector()));
         this.tolerance = tolerance;
     }
 
@@ -109,7 +109,7 @@ public class Circle implements Hyperplane<S2Point>, 
Embedding<S2Point, S1Point>
     public void reset(final Vector3D newPole) {
         this.pole = newPole.normalize();
         this.x    = newPole.orthogonal();
-        this.y    = newPole.crossProduct(x).normalize();
+        this.y    = newPole.cross(x).normalize();
     }
 
     /** Revert the instance.
@@ -160,7 +160,7 @@ public class Circle implements Hyperplane<S2Point>, 
Embedding<S2Point, S1Point>
      * @see #toSubSpace(Point)
      */
     public double getPhase(final Vector3D direction) {
-        return Math.PI + Math.atan2(-direction.dotProduct(y), 
-direction.dotProduct(x));
+        return Math.PI + Math.atan2(-direction.dot(y), -direction.dot(x));
     }
 
     /** {@inheritDoc}
@@ -275,7 +275,7 @@ public class Circle implements Hyperplane<S2Point>, 
Embedding<S2Point, S1Point>
     @Override
     public boolean sameOrientationAs(final Hyperplane<S2Point> other) {
         final Circle otherC = (Circle) other;
-        return pole.dotProduct(otherC.pole) >= 0.0;
+        return pole.dot(otherC.pole) >= 0.0;
     }
 
     /** Get a {@link org.apache.commons.geometry.core.partitioning.Transform
diff --git 
a/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/PropertiesComputer.java
 
b/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/PropertiesComputer.java
index 2781da4..0bd4dca 100644
--- 
a/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/PropertiesComputer.java
+++ 
b/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/PropertiesComputer.java
@@ -110,8 +110,8 @@ class PropertiesComputer implements BSPTreeVisitor<S2Point> 
{
             final Vector3D previousPole = e.getCircle().getPole();
             final Vector3D nextPole     = 
e.getEnd().getOutgoing().getCircle().getPole();
             final Vector3D point        = e.getEnd().getLocation().getVector();
-            double alpha = 
Math.atan2(nextPole.dotProduct(point.crossProduct(previousPole)),
-                                          - nextPole.dotProduct(previousPole));
+            double alpha = Math.atan2(nextPole.dot(point.cross(previousPole)),
+                                          - nextPole.dot(previousPole));
             if (alpha < 0) {
                 alpha += Geometry.TWO_PI;
             }
diff --git 
a/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/SphericalPolygonsSet.java
 
b/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/SphericalPolygonsSet.java
index 9f09d77..647e448 100644
--- 
a/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/SphericalPolygonsSet.java
+++ 
b/commons-geometry-spherical/src/main/java/org/apache/commons/geometry/spherical/twod/SphericalPolygonsSet.java
@@ -157,7 +157,7 @@ public class SphericalPolygonsSet extends 
AbstractRegion<S2Point, S1Point> {
     private static S2Point[] createRegularPolygonVertices(final Vector3D 
center, final Vector3D meridian,
                                                           final double 
outsideRadius, final int n) {
         final S2Point[] array = new S2Point[n];
-        final QuaternionRotation r0 = 
QuaternionRotation.fromAxisAngle(center.crossProduct(meridian),
+        final QuaternionRotation r0 = 
QuaternionRotation.fromAxisAngle(center.cross(meridian),
                                          outsideRadius);
         array[0] = S2Point.ofVector(r0.apply(center));
 
diff --git 
a/commons-geometry-spherical/src/test/java/org/apache/commons/geometry/spherical/twod/CircleTest.java
 
b/commons-geometry-spherical/src/test/java/org/apache/commons/geometry/spherical/twod/CircleTest.java
index 6fa4464..de3de2b 100644
--- 
a/commons-geometry-spherical/src/test/java/org/apache/commons/geometry/spherical/twod/CircleTest.java
+++ 
b/commons-geometry-spherical/src/test/java/org/apache/commons/geometry/spherical/twod/CircleTest.java
@@ -53,7 +53,7 @@ public class CircleTest {
         Assert.assertEquals(0.5 * Math.PI, 
circle.getXAxis().angle(circle.getPole()), 1.0e-10);
         Assert.assertEquals(0.5 * Math.PI, 
circle.getPole().angle(circle.getYAxis()), 1.0e-10);
         Assert.assertEquals(0.0,
-                            
circle.getPole().distance(circle.getXAxis().crossProduct(circle.getYAxis())),
+                            
circle.getPole().distance(circle.getXAxis().cross(circle.getYAxis())),
                             1.0e-10);
     }
 
@@ -67,7 +67,7 @@ public class CircleTest {
         Assert.assertEquals(0.5 * Math.PI, 
reversed.getXAxis().angle(reversed.getPole()), 1.0e-10);
         Assert.assertEquals(0.5 * Math.PI, 
reversed.getPole().angle(reversed.getYAxis()), 1.0e-10);
         Assert.assertEquals(0.0,
-                            
reversed.getPole().distance(reversed.getXAxis().crossProduct(reversed.getYAxis())),
+                            
reversed.getPole().distance(reversed.getXAxis().cross(reversed.getYAxis())),
                             1.0e-10);
 
         Assert.assertEquals(0, circle.getXAxis().angle(reversed.getXAxis()), 
1.0e-10);
@@ -84,8 +84,8 @@ public class CircleTest {
         Vector3D p = Vector3D.of(1, 2, -4);
         Vector3D samePhase = circle.getPointAt(circle.getPhase(p));
         Assert.assertEquals(0.0,
-                            circle.getPole().crossProduct(p).angle(
-                                           
circle.getPole().crossProduct(samePhase)),
+                            circle.getPole().cross(p).angle(
+                                           circle.getPole().cross(samePhase)),
                             1.0e-10);
         Assert.assertEquals(0.5 * Math.PI, circle.getPole().angle(samePhase), 
1.0e-10);
         Assert.assertEquals(circle.getPhase(p), circle.getPhase(samePhase), 
1.0e-10);

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