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1   /*
2    * Licensed to the Apache Software Foundation (ASF) under one or more
3    * contributor license agreements.  See the NOTICE file distributed with
4    * this work for additional information regarding copyright ownership.
5    * The ASF licenses this file to You under the Apache License, Version 2.0
6    * (the "License"); you may not use this file except in compliance with
7    * the License.  You may obtain a copy of the License at
8    *
9    *      http://www.apache.org/licenses/LICENSE-2.0
10   *
11   * Unless required by applicable law or agreed to in writing, software
12   * distributed under the License is distributed on an "AS IS" BASIS,
13   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14   * See the License for the specific language governing permissions and
15   * limitations under the License.
16   */
17  package org.apache.commons.geometry.euclidean.twod;
18  
19  import java.text.MessageFormat;
20  
21  import org.apache.commons.geometry.euclidean.oned.Interval;
22  import org.apache.commons.numbers.core.Precision;
23  
24  /** Class containing factory methods for constructing {@link Line} and {@link LineSubset} instances.
25   */
26  public final class Lines {
27  
28      /** Utility class; no instantiation. */
29      private Lines() {
30      }
31  
32      /** Create a line from two points lying on the line. The line points in the direction
33       * from {@code p1} to {@code p2}.
34       * @param p1 first point
35       * @param p2 second point
36       * @param precision precision context used to compare floating point values
37       * @return new line containing {@code p1} and {@code p2} and pointing in the direction
38       *      from {@code p1} to {@code p2}
39       * @throws IllegalArgumentException If the vector between {@code p1} and {@code p2} has zero length,
40       *      as evaluated by the given precision context
41       */
42      public static Line fromPoints(final Vector2D p1, final Vector2D p2, final Precision.DoubleEquivalence precision) {
43          return fromPointAndDirection(p1, p1.vectorTo(p2), precision);
44      }
45  
46      /** Create a line from a point and direction.
47       * @param pt point belonging to the line
48       * @param dir the direction of the line
49       * @param precision precision context used to compare floating point values
50       * @return new line containing {@code pt} and pointing in direction {@code dir}
51       * @throws IllegalArgumentException If {@code dir} has zero length, as evaluated by the
52       *      given precision context
53       */
54      public static Line fromPointAndDirection(final Vector2D pt, final Vector2D dir,
55              final Precision.DoubleEquivalence precision) {
56          if (dir.isZero(precision)) {
57              throw new IllegalArgumentException("Line direction cannot be zero");
58          }
59  
60          final Vector2D.Unit normalizedDir = dir.normalize();
61          final double originOffset = normalizedDir.signedArea(pt);
62  
63          return new Line(normalizedDir, originOffset, precision);
64      }
65  
66      /** Create a line from a point lying on the line and an angle relative to the abscissa (x) axis. Note that the
67       * line does not need to intersect the x-axis; the given angle is simply relative to it.
68       * @param pt point belonging to the line
69       * @param angle angle of the line with respect to abscissa (x) axis, in radians
70       * @param precision precision context used to compare floating point values
71       * @return new line containing {@code pt} and forming the given angle with the
72       *      abscissa (x) axis.
73       */
74      public static Line fromPointAndAngle(final Vector2D pt, final double angle,
75              final Precision.DoubleEquivalence precision) {
76          final Vector2D.Unit dir = Vector2D.Unit.from(Math.cos(angle), Math.sin(angle));
77          return fromPointAndDirection(pt, dir, precision);
78      }
79  
80      /** Construct a ray from a start point and a direction.
81       * @param startPoint ray start point
82       * @param direction ray direction
83       * @param precision precision context used for floating point comparisons
84       * @return a new ray instance with the given start point and direction
85       * @throws IllegalArgumentException If {@code direction} has zero length, as evaluated by the
86       *      given precision context
87       * @see #fromPointAndDirection(Vector2D, Vector2D, Precision.DoubleEquivalence)
88       */
89      public static Ray rayFromPointAndDirection(final Vector2D startPoint, final Vector2D direction,
90              final Precision.DoubleEquivalence precision) {
91          final Line line = Lines.fromPointAndDirection(startPoint, direction, precision);
92  
93          return new Ray(line, startPoint);
94      }
95  
96      /** Construct a ray starting at the given point and continuing to infinity in the direction
97       * of {@code line}. The given point is projected onto the line.
98       * @param line line for the ray
99       * @param startPoint start point for the ray
100      * @return a new ray instance starting at the given point and continuing in the direction of
101      *      {@code line}
102      * @throws IllegalArgumentException if any coordinate in {@code startPoint} is NaN or infinite
103      */
104     public static Ray rayFromPoint(final Line line, final Vector2D startPoint) {
105         if (!startPoint.isFinite()) {
106             throw new IllegalArgumentException("Invalid ray start point: " + startPoint);
107         }
108         return new Ray(line, line.project(startPoint));
109     }
110 
111     /** Construct a ray starting at the given 1D location on {@code line} and continuing in the
112      * direction of the line to infinity.
113      * @param line line for the ray
114      * @param startLocation 1D location of the ray start point
115      * @return a new ray instance starting at the given 1D location and continuing to infinity
116      *      along {@code line}
117      * @throws IllegalArgumentException if {@code startLocation} is NaN or infinite
118      */
119     public static Ray rayFromLocation(final Line line, final double startLocation) {
120         if (!Double.isFinite(startLocation)) {
121             throw new IllegalArgumentException("Invalid ray start location: " + startLocation);
122         }
123         return new Ray(line, line.toSpace(startLocation));
124     }
125 
126     /** Construct a reverse ray from an end point and a line direction.
127      * @param endPoint instance end point
128      * @param lineDirection line direction
129      * @param precision precision context used for floating point comparisons
130      * @return a new instance with the given end point and line direction
131      * @throws IllegalArgumentException If {@code lineDirection} has zero length, as evaluated by the
132      *      given precision context
133      * @see #fromPointAndDirection(Vector2D, Vector2D, Precision.DoubleEquivalence)
134      */
135     public static ReverseRay reverseRayFromPointAndDirection(final Vector2D endPoint, final Vector2D lineDirection,
136             final Precision.DoubleEquivalence precision) {
137         final Line line = Lines.fromPointAndDirection(endPoint, lineDirection, precision);
138 
139         return new ReverseRay(line, endPoint);
140     }
141 
142     /** Construct a reverse ray starting at infinity and continuing in the direction of {@code line}
143      * to the given end point. The point is projected onto the line.
144      * @param line line for the instance
145      * @param endPoint end point for the instance
146      * @return a new instance starting at infinity and continuing along the line to {@code endPoint}
147      * @throws IllegalArgumentException if any coordinate in {@code endPoint} is NaN or infinite
148      */
149     public static ReverseRay reverseRayFromPoint(final Line line, final Vector2D endPoint) {
150         if (!endPoint.isFinite()) {
151             throw new IllegalArgumentException("Invalid reverse ray end point: " + endPoint);
152         }
153         return new ReverseRay(line, line.project(endPoint));
154     }
155 
156     /** Construct a reverse ray starting at infinity and continuing in the direction of {@code line}
157      * to the given 1D end location.
158      * @param line line for the instance
159      * @param endLocation 1D location of the instance end point
160      * @return a new instance starting infinity and continuing in the direction of {@code line}
161      *      to the given 1D end location
162      * @throws IllegalArgumentException if {@code endLocation} is NaN or infinite
163      */
164     public static ReverseRay reverseRayFromLocation(final Line line, final double endLocation) {
165         if (!Double.isFinite(endLocation)) {
166             throw new IllegalArgumentException("Invalid reverse ray end location: " + endLocation);
167         }
168 
169         return new ReverseRay(line, line.toSpace(endLocation));
170     }
171 
172     /** Construct a new line segment from two points. A new line is created for the segment and points in the
173      * direction from {@code startPoint} to {@code endPoint}.
174      * @param startPoint segment start point
175      * @param endPoint segment end point
176      * @param precision precision context to use for floating point comparisons
177      * @return a new line segment instance with the given start and end points
178      * @throws IllegalArgumentException If the vector between {@code startPoint} and {@code endPoint} has zero length,
179      *      as evaluated by the given precision context
180      */
181     public static Segment segmentFromPoints(final Vector2D startPoint, final Vector2D endPoint,
182             final Precision.DoubleEquivalence precision) {
183         final Line line = Lines.fromPoints(startPoint, endPoint, precision);
184 
185         // we know that the points lie on the line and are in increasing abscissa order
186         // since they were used to create the line
187         return new Segment(line, startPoint, endPoint);
188     }
189 
190     /** Construct a new line segment from a line and a pair of points. The returned segment represents
191      * all points on the line between the projected locations of {@code a} and {@code b}. The points may
192      * be given in any order.
193      * @param line line forming the base of the segment
194      * @param a first point
195      * @param b second point
196      * @return a new line segment representing the points between the projected locations of {@code a}
197      *      and {@code b} on the given line
198      * @throws IllegalArgumentException if either point contains NaN or infinite coordinate values
199      */
200     public static Segment segmentFromPoints(final Line line, final Vector2D a, final Vector2D b) {
201         return segmentFromLocations(line, line.abscissa(a), line.abscissa(b));
202     }
203 
204     /** Construct a new line segment from a pair of 1D locations on a line. The returned line
205      * segment consists of all points between the two locations, regardless of the order the
206      * arguments are given.
207      * @param line line forming the base of the segment
208      * @param a first 1D location on the line
209      * @param b second 1D location on the line
210      * @return a new line segment representing the points between {@code a} and {@code b} on
211      *      the given line
212      * @throws IllegalArgumentException if either of the locations is NaN or infinite
213      */
214     public static Segment segmentFromLocations(final Line line, final double a, final double b) {
215 
216         if (Double.isFinite(a) && Double.isFinite(b)) {
217             final double min = Math.min(a, b);
218             final double max = Math.max(a, b);
219 
220             return new Segment(line, line.toSpace(min), line.toSpace(max));
221         }
222 
223         throw new IllegalArgumentException(
224                 MessageFormat.format("Invalid line segment locations: {0}, {1}",
225                         Double.toString(a), Double.toString(b)));
226     }
227 
228     /** Create a {@link LineConvexSubset} spanning the entire line. In other words, the returned
229      * subset is infinite and contains all points on the given line.
230      * @param line the line to span
231      * @return a convex subset spanning the entire line
232      */
233     public static LineConvexSubset span(final Line line) {
234         return new LineSpanningSubset(line);
235     }
236 
237     /** Create a line subset from a line and a 1D interval on the line. The returned subset
238      * uses the precision context from the line and not any precision contexts referenced by the interval.
239      * @param line the line containing the subset
240      * @param interval 1D interval on the line
241      * @return a convex subset defined by the given line and interval
242      */
243     public static LineConvexSubset subsetFromInterval(final Line line, final Interval interval) {
244         return subsetFromInterval(line, interval.getMin(), interval.getMax());
245     }
246 
247     /** Create a line subset from a line and a 1D interval on the line. The double values may be given in any
248      * order and support the use of infinite values. For example, the call
249      * {@code Lines.subsetFromInterval(line, Double.POSITIVE_INFINITY, Double.NEGATIVE_INFINITY)} will return
250      * an instance representing the full span of the line.
251      * @param line the line containing the subset
252      * @param a first 1D location on the line
253      * @param b second 1D location on the line
254      * @return a line subset defined by the given line and interval
255      * @throws IllegalArgumentException if either double value is NaN or both are infinite with the same sign
256      *      (eg, both positive infinity or both negative infinity)
257      */
258     public static LineConvexSubset subsetFromInterval(final Line line, final double a, final double b) {
259         final double min = Math.min(a, b);
260         final double max = Math.max(a, b);
261 
262         final boolean hasMin = Double.isFinite(min);
263         final boolean hasMax = Double.isFinite(max);
264 
265         if (hasMin) {
266             if (hasMax) {
267                 // has both
268                 return new Segment(line, line.toSpace(min), line.toSpace(max));
269             }
270             // min only
271             return new Ray(line, line.toSpace(min));
272         } else if (hasMax) {
273             // max only
274             return new ReverseRay(line, line.toSpace(max));
275         } else if (Double.isInfinite(min) && Double.isInfinite(max) && Double.compare(min, max) < 0) {
276             return new LineSpanningSubset(line);
277         }
278 
279         throw new IllegalArgumentException(MessageFormat.format(
280                 "Invalid line subset interval: {0}, {1}", Double.toString(a), Double.toString(b)));
281     }
282 
283     /** Validate that the actual line is equivalent to the expected line, throwing an exception if not.
284      * @param expected the expected line
285      * @param actual the actual line
286      * @throws IllegalArgumentException if the actual line is not equivalent to the expected line
287      */
288     static void validateLinesEquivalent(final Line expected, final Line actual) {
289         if (!expected.eq(actual, expected.getPrecision())) {
290             throw new IllegalArgumentException("Arguments do not represent the same line. Expected " +
291                     expected + " but was " + actual + ".");
292         }
293     }
294 }