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Lines 18-77
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*/ |
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*/ |
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public class Geometry |
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public class Geometry |
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{ |
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{ |
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/** |
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* Determines whether the two line segments formed by the given coordinates |
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* intersect. If one of the two line segments starts or ends on the other |
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* line, then they are considered to be intersecting. |
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* TODO: Decide whether co-linear overlapping line segments should be regarded |
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* as intersecting as well. |
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* |
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* @param ux |
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* x coordinate of starting point of line 1 |
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* @param uy |
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* y coordinate of starting point of line 1 |
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* @param vx |
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* x coordinate of ending point of line 1 |
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* @param vy |
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* y coordinate of ending point of line 1 |
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* @param sx |
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* x coordinate of the starting point of line 2 |
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* @param sy |
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* y coordinate of the starting point of line 2 |
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* @param tx |
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* x coordinate of the ending point of line 2 |
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* @param ty |
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* y coordinate of the ending point of line 2 |
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* @return <code>true</code> if the two line segments formed by the given |
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* coordinates cross |
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* @since 3.1 |
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*/ |
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public static boolean linesIntersect(int ux, int uy, int vx, int vy, |
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int sx, int sy, int tx, int ty) { |
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/* |
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* The following implementation is based on the line intersection |
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* algorithm published by Paul Bourke |
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* (http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/). |
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*/ |
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double den = (((double) ty - (double) sy) * ((double) vx - (double) ux)) |
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- (((double) tx - (double) sx) * ((double) vy - (double) uy)); |
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double numA = (((double) tx - (double) sx) * ((double) uy - (double) sy)) |
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- (((double) ty - (double) sy) * ((double) ux - (double) sx)); |
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double numB = (((double) vx - (double) ux) * ((double) uy - (double) sy)) |
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- (((double) vy - (double) uy) * ((double) ux - (double) sx)); |
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if (den == 0.0) { |
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if (numA == 0.0 && numB == 0.0) { |
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// co-linear |
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// TODO: decide whether co-linear overlapping line segments should be |
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// regarded as |
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// check if there is an overlap (sufficient to check x coordinates only) |
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if ((sx > vx && tx > vx) || (sx < ux && tx < ux)) { |
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// co-linear & non-overlapping |
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return false; |
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} |
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// co-linear & overlapping |
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return true; |
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} |
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// parallel |
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return false; |
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} |
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/** |
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double ua = numA / den; |
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* Determines whether the two line segments formed by the given coordinates intersect. If |
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double ub = numB / den; |
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* one of the two line segments starts or ends on the other line, then they are considered |
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* to be intersecting. |
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* |
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* @param ux x coordinate of starting point of line 1 |
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* @param uy y coordinate of starting point of line 1 |
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* @param vx x coordinate of ending point of line 1 |
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* @param vy y coordinate of endpoing point of line 1 |
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* @param sx x coordinate of the starting point of line 2 |
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* @param sy y coordinate of the starting point of line 2 |
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* @param tx x coordinate of the ending point of line 2 |
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* @param ty y coordinate of the ending point of line 2 |
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* @return <code>true</code> if the two line segments formed by the given coordinates |
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* cross |
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* @since 3.1 |
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*/ |
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public static boolean linesIntersect(int ux, int uy, int vx, int vy, |
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int sx, int sy, int tx, int ty) { |
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/* |
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* Given the segments: u-------v. s-------t. If s->t is inside the triangle u-v-s, |
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* then check whether the line u->u splits the line s->t. |
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*/ |
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/* Values are casted to long to avoid integer overflows */ |
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long usX = (long) ux - sx; |
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long usY = (long) uy - sy; |
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long vsX = (long) vx - sx; |
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long vsY = (long) vy - sy; |
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long stX = (long) sx - tx; |
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long stY = (long) sy - ty; |
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if (productSign(cross(vsX, vsY, stX, stY), cross(stX, stY, usX, usY)) >= 0) { |
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long vuX = (long) vx - ux; |
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long vuY = (long) vy - uy; |
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long utX = (long) ux - tx; |
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long utY = (long) uy - ty; |
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return productSign(cross(-usX, -usY, vuX, vuY), cross(vuX, vuY, utX, utY)) <= 0; |
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} |
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return false; |
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} |
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private static int productSign(long x, long y) { |
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if (x == 0 || y == 0) { |
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return 0; |
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} else if (x < 0 ^ y < 0) { |
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return -1; |
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} |
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return 1; |
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} |
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private static long cross(long x1, long y1, long x2, long y2) { |
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return x1 * y2 - x2 * y1; |
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} |
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if (ua >= 0.0 && ua <= 1.0 && ub >= 0.0 && ub <= 1.0) { |
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// intersecting |
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return true; |
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} |
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// non intersecting |
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return false; |
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} |
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/** |
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/** |
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* @see PointList#polylineContainsPoint(int, int, int) |
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* @see PointList#polylineContainsPoint(int, int, int) |
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* @since 3.5 |
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* @since 3.5 |
