|
Lines 18-77
Link Here
|
| 18 |
*/ |
18 |
*/ |
| 19 |
public class Geometry |
19 |
public class Geometry |
| 20 |
{ |
20 |
{ |
|
|
21 |
/** |
| 22 |
* Determines whether the two line segments formed by the given coordinates |
| 23 |
* intersect. If one of the two line segments starts or ends on the other |
| 24 |
* line, then they are considered to be intersecting. |
| 25 |
* TODO: Decide whether co-linear overlapping line segments should be regarded |
| 26 |
* as intersecting as well. |
| 27 |
* |
| 28 |
* @param ux |
| 29 |
* x coordinate of starting point of line 1 |
| 30 |
* @param uy |
| 31 |
* y coordinate of starting point of line 1 |
| 32 |
* @param vx |
| 33 |
* x coordinate of ending point of line 1 |
| 34 |
* @param vy |
| 35 |
* y coordinate of ending point of line 1 |
| 36 |
* @param sx |
| 37 |
* x coordinate of the starting point of line 2 |
| 38 |
* @param sy |
| 39 |
* y coordinate of the starting point of line 2 |
| 40 |
* @param tx |
| 41 |
* x coordinate of the ending point of line 2 |
| 42 |
* @param ty |
| 43 |
* y coordinate of the ending point of line 2 |
| 44 |
* @return <code>true</code> if the two line segments formed by the given |
| 45 |
* coordinates cross |
| 46 |
* @since 3.1 |
| 47 |
*/ |
| 48 |
public static boolean linesIntersect(int ux, int uy, int vx, int vy, |
| 49 |
int sx, int sy, int tx, int ty) { |
| 50 |
/* |
| 51 |
* The following implementation is based on the line intersection |
| 52 |
* algorithm published by Paul Bourke |
| 53 |
* (http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/). |
| 54 |
*/ |
| 55 |
long den = (((long) ty - (long) sy) * ((long) vx - (long) ux)) |
| 56 |
- (((long) tx - (long) sx) * ((long) vy - (long) uy)); |
| 57 |
|
| 58 |
long numA = (((long) tx - (long) sx) * ((long) uy - (long) sy)) |
| 59 |
- (((long) ty - (long) sy) * ((long) ux - (long) sx)); |
| 60 |
|
| 61 |
long numB = (((long) vx - (long) ux) * ((long) uy - (long) sy)) |
| 62 |
- (((long) vy - (long) uy) * ((long) ux - (long) sx)); |
| 63 |
|
| 64 |
if (den == 0) { |
| 65 |
if (numA == 0 && numB == 0) { |
| 66 |
// co-linear |
| 67 |
// TODO: decide whether co-linear overlapping segments should be regarded |
| 68 |
// as overlapping |
| 69 |
// check if there is an overlap (sufficient to check x coordinates only) |
| 70 |
if ((sx > vx && tx > vx) || (sx < ux && tx < ux)) { |
| 71 |
// co-linear & non-overlapping |
| 72 |
return false; |
| 73 |
} |
| 74 |
// co-linear & overlapping |
| 75 |
return true; |
| 76 |
} |
| 77 |
// parallel |
| 78 |
return false; |
| 79 |
} |
| 21 |
|
80 |
|
| 22 |
/** |
81 |
long ua = numA / den; |
| 23 |
* Determines whether the two line segments formed by the given coordinates intersect. If |
82 |
long ub = numB / den; |
| 24 |
* one of the two line segments starts or ends on the other line, then they are considered |
|
|
| 25 |
* to be intersecting. |
| 26 |
* |
| 27 |
* @param ux x coordinate of starting point of line 1 |
| 28 |
* @param uy y coordinate of starting point of line 1 |
| 29 |
* @param vx x coordinate of ending point of line 1 |
| 30 |
* @param vy y coordinate of endpoing point of line 1 |
| 31 |
* @param sx x coordinate of the starting point of line 2 |
| 32 |
* @param sy y coordinate of the starting point of line 2 |
| 33 |
* @param tx x coordinate of the ending point of line 2 |
| 34 |
* @param ty y coordinate of the ending point of line 2 |
| 35 |
* @return <code>true</code> if the two line segments formed by the given coordinates |
| 36 |
* cross |
| 37 |
* @since 3.1 |
| 38 |
*/ |
| 39 |
public static boolean linesIntersect(int ux, int uy, int vx, int vy, |
| 40 |
int sx, int sy, int tx, int ty) { |
| 41 |
/* |
| 42 |
* Given the segments: u-------v. s-------t. If s->t is inside the triangle u-v-s, |
| 43 |
* then check whether the line u->u splits the line s->t. |
| 44 |
*/ |
| 45 |
/* Values are casted to long to avoid integer overflows */ |
| 46 |
long usX = (long) ux - sx; |
| 47 |
long usY = (long) uy - sy; |
| 48 |
long vsX = (long) vx - sx; |
| 49 |
long vsY = (long) vy - sy; |
| 50 |
long stX = (long) sx - tx; |
| 51 |
long stY = (long) sy - ty; |
| 52 |
if (productSign(cross(vsX, vsY, stX, stY), cross(stX, stY, usX, usY)) >= 0) { |
| 53 |
long vuX = (long) vx - ux; |
| 54 |
long vuY = (long) vy - uy; |
| 55 |
long utX = (long) ux - tx; |
| 56 |
long utY = (long) uy - ty; |
| 57 |
return productSign(cross(-usX, -usY, vuX, vuY), cross(vuX, vuY, utX, utY)) <= 0; |
| 58 |
} |
| 59 |
return false; |
| 60 |
} |
| 61 |
|
| 62 |
private static int productSign(long x, long y) { |
| 63 |
if (x == 0 || y == 0) { |
| 64 |
return 0; |
| 65 |
} else if (x < 0 ^ y < 0) { |
| 66 |
return -1; |
| 67 |
} |
| 68 |
return 1; |
| 69 |
} |
| 70 |
|
| 71 |
private static long cross(long x1, long y1, long x2, long y2) { |
| 72 |
return x1 * y2 - x2 * y1; |
| 73 |
} |
| 74 |
|
83 |
|
|
|
84 |
if (ua >= 0 && ua <= 1 && ub >= 0 && ub <= 1) { |
| 85 |
// intersecting |
| 86 |
return true; |
| 87 |
} |
| 88 |
// non intersecting |
| 89 |
return false; |
| 90 |
} |
| 91 |
|
| 75 |
/** |
92 |
/** |
| 76 |
* @see PointList#polylineContainsPoint(int, int, int) |
93 |
* @see PointList#polylineContainsPoint(int, int, int) |
| 77 |
* @since 3.5 |
94 |
* @since 3.5 |
