Mega Code Archive
Collection of geometry utility methods
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/*
* (C) 2004 - Geotechnical Software Services
*
* This code is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
//package no.geosoft.cc.geometry;
/**
* Collection of geometry utility methods. All methods are static.
*
* @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
*/
public final class Geometry
{
/**
* Return true if c is between a and b.
*/
private static boolean isBetween (int a, int b, int c)
{
return b > a ? c >= a && c <= b : c >= b && c <= a;
}
/**
* Return true if c is between a and b.
*/
private static boolean isBetween (double a, double b, double c)
{
return b > a ? c >= a && c <= b : c >= b && c <= a;
}
/**
* Check if two double precision numbers are "equal", i.e. close enough
* to a given limit.
*
* @param a First number to check
* @param b Second number to check
* @param limit The definition of "equal".
* @return True if the twho numbers are "equal", false otherwise
*/
private static boolean equals (double a, double b, double limit)
{
return Math.abs (a - b) < limit;
}
/**
* Check if two double precision numbers are "equal", i.e. close enough
* to a prespecified limit.
*
* @param a First number to check
* @param b Second number to check
* @return True if the twho numbers are "equal", false otherwise
*/
private static boolean equals (double a, double b)
{
return equals (a, b, 1.0e-5);
}
/**
* Return smallest of four numbers.
*
* @param a First number to find smallest among.
* @param b Second number to find smallest among.
* @param c Third number to find smallest among.
* @param d Fourth number to find smallest among.
* @return Smallest of a, b, c and d.
*/
private static double min (double a, double b, double c, double d)
{
return Math.min (Math.min (a, b), Math.min (c, d));
}
/**
* Return largest of four numbers.
*
* @param a First number to find largest among.
* @param b Second number to find largest among.
* @param c Third number to find largest among.
* @param d Fourth number to find largest among.
* @return Largest of a, b, c and d.
*/
private static double max (double a, double b, double c, double d)
{
return Math.max (Math.max (a, b), Math.max (c, d));
}
/**
* Check if a specified point is inside a specified rectangle.
*
* @param x0, y0, x1, y1 Upper left and lower right corner of rectangle
* (inclusive)
* @param x,y Point to check.
* @return True if the point is inside the rectangle,
* false otherwise.
*/
public static boolean isPointInsideRectangle (int x0, int y0, int x1, int y1,
int x, int y)
{
return x >= x0 && x < x1 && y >= y0 && y < y1;
}
/**
* Check if a given point is inside a given (complex) polygon.
*
* @param x, y Polygon.
* @param pointX, pointY Point to check.
* @return True if the given point is inside the polygon, false otherwise.
*/
public static boolean isPointInsidePolygon (double[] x, double[] y,
double pointX, double pointY)
{
boolean isInside = false;
int nPoints = x.length;
int j = 0;
for (int i = 0; i < nPoints; i++) {
j++;
if (j == nPoints) j = 0;
if (y[i] < pointY && y[j] >= pointY || y[j] < pointY && y[i] >= pointY) {
if (x[i] + (pointY - y[i]) / (y[j] - y[i]) * (x[j] - x[i]) < pointX) {
isInside = !isInside;
}
}
}
return isInside;
}
/**
* Check if a given point is inside a given polygon. Integer domain.
*
* @param x, y Polygon.
* @param pointX, pointY Point to check.
* @return True if the given point is inside the polygon, false otherwise.
*/
public static boolean isPointInsidePolygon (int[] x, int[] y,
int pointX, int pointY)
{
boolean isInside = false;
int nPoints = x.length;
int j = 0;
for (int i = 0; i < nPoints; i++) {
j++;
if (j == nPoints) j = 0;
if (y[i] < pointY && y[j] >= pointY || y[j] < pointY && y[i] >= pointY) {
if (x[i] + (double) (pointY - y[i]) / (double) (y[j] - y[i]) *
(x[j] - x[i]) < pointX) {
isInside = !isInside;
}
}
}
return isInside;
}
/**
* Find the point on the line p0,p1 [x,y,z] a given fraction from p0.
* Fraction of 0.0 whould give back p0, 1.0 give back p1, 0.5 returns
* midpoint of line p0,p1 and so on. F
* raction can be >1 and it can be negative to return any point on the
* line specified by p0,p1.
*
* @param p0 First coordinale of line [x,y,z].
* @param p0 Second coordinale of line [x,y,z].
* @param fractionFromP0 Point we are looking for coordinates of
* @param p Coordinate of point we are looking for
*/
public static double[] computePointOnLine (double[] p0, double[] p1,
double fractionFromP0)
{
double[] p = new double[3];
p[0] = p0[0] + fractionFromP0 * (p1[0] - p0[0]);
p[1] = p0[1] + fractionFromP0 * (p1[1] - p0[1]);
p[2] = p0[2] + fractionFromP0 * (p1[2] - p0[2]);
return p;
}
/**
* Find the point on the line defined by x0,y0,x1,y1 a given fraction
* from x0,y0. 2D version of method above..
*
* @param x0, y0 First point defining the line
* @param x1, y1 Second point defining the line
* @param fractionFrom0 Distance from (x0,y0)
* @return x, y Coordinate of point we are looking for
*/
public static double[] computePointOnLine (double x0, double y0,
double x1, double y1,
double fractionFrom0)
{
double[] p0 = {x0, y0, 0.0};
double[] p1 = {x1, y1, 0.0};
double[] p = Geometry.computePointOnLine (p0, p1, fractionFrom0);
double[] r = {p[0], p[1]};
return r;
}
/**
* Extend a given line segment to a specified length.
*
* @param p0, p1 Line segment to extend [x,y,z].
* @param toLength Length of new line segment.
* @param anchor Specifies the fixed point during extension.
* If anchor is 0.0, p0 is fixed and p1 is adjusted.
* If anchor is 1.0, p1 is fixed and p0 is adjusted.
* If anchor is 0.5, the line is adjusted equally in each
* direction and so on.
*/
public static void extendLine (double[] p0, double[] p1, double toLength,
double anchor)
{
double[] p = Geometry.computePointOnLine (p0, p1, anchor);
double length0 = toLength * anchor;
double length1 = toLength * (1.0 - anchor);
Geometry.extendLine (p, p0, length0);
Geometry.extendLine (p, p1, length1);
}
/**
* Extend a given line segment to a given length and holding the first
* point of the line as fixed.
*
* @param p0, p1 Line segment to extend. p0 is fixed during extension
* @param length Length of new line segment.
*/
public static void extendLine (double[] p0, double[] p1, double toLength)
{
double oldLength = Geometry.length (p0, p1);
double lengthFraction = oldLength != 0.0 ? toLength / oldLength : 0.0;
p1[0] = p0[0] + (p1[0] - p0[0]) * lengthFraction;
p1[1] = p0[1] + (p1[1] - p0[1]) * lengthFraction;
p1[2] = p0[2] + (p1[2] - p0[2]) * lengthFraction;
}
/**
* Return the length of a vector.
*
* @param v Vector to compute length of [x,y,z].
* @return Length of vector.
*/
public static double length (double[] v)
{
return Math.sqrt (v[0]*v[0] + v[1]*v[1] + v[2]*v[2]);
}
/**
* Compute distance between two points.
*
* @param p0, p1 Points to compute distance between [x,y,z].
* @return Distance between points.
*/
public static double length (double[] p0, double[] p1)
{
double[] v = Geometry.createVector (p0, p1);
return length (v);
}
/**
* Compute the length of the line from (x0,y0) to (x1,y1)
*
* @param x0, y0 First line end point.
* @param x1, y1 Second line end point.
* @return Length of line from (x0,y0) to (x1,y1).
*/
public static double length (int x0, int y0, int x1, int y1)
{
return Geometry.length ((double) x0, (double) y0,
(double) x1, (double) y1);
}
/**
* Compute the length of the line from (x0,y0) to (x1,y1)
*
* @param x0, y0 First line end point.
* @param x1, y1 Second line end point.
* @return Length of line from (x0,y0) to (x1,y1).
*/
public static double length (double x0, double y0, double x1, double y1)
{
double dx = x1 - x0;
double dy = y1 - y0;
return Math.sqrt (dx*dx + dy*dy);
}
/**
* Compute the length of a polyline.
*
* @param x, y Arrays of x,y coordinates
* @param nPoints Number of elements in the above.
* @param isClosed True if this is a closed polygon, false otherwise
* @return Length of polyline defined by x, y and nPoints.
*/
public static double length (int[] x, int[] y, boolean isClosed)
{
double length = 0.0;
int nPoints = x.length;
for (int i = 0; i < nPoints-1; i++)
length += Geometry.length (x[i], y[i], x[i+1], y[i+1]);
// Add last leg if this is a polygon
if (isClosed && nPoints > 1)
length += Geometry.length (x[nPoints-1], y[nPoints-1], x[0], y[0]);
return length;
}
/**
* Return distance bwetween the line defined by (x0,y0) and (x1,y1)
* and the point (x,y).
* Ref: http://astronomy.swin.edu.au/pbourke/geometry/pointline/
* The 3D case should be similar.
*
* @param x0, y0 First point of line.
* @param x1, y1 Second point of line.
* @param x, y, Point to consider.
* @return Distance from x,y down to the (extended) line defined
* by x0, y0, x1, y1.
*/
public static double distance (int x0, int y0, int x1, int y1,
int x, int y)
{
// If x0,y0,x1,y1 is same point, we return distance to that point
double length = Geometry.length (x0, y0, x1, y1);
if (length == 0.0)
return Geometry.length (x0, y0, x, y);
// If u is [0,1] then (xp,yp) is on the line segment (x0,y0),(x1,y1).
double u = ((x - x0) * (x1 - x0) + (y - y0) * (y1 - y0)) /
(length * length);
// This is the intersection point of the normal.
// TODO: Might consider returning this as well.
double xp = x0 + u * (x1 - x0);
double yp = y0 + u * (y1 - y0);
length = Geometry.length (xp, yp, x, y);
return length;
}
/**
* Find the angle between twree points. P0 is center point
*
* @param p0, p1, p2 Three points finding angle between [x,y,z].
* @return Angle (in radians) between given points.
*/
public static double computeAngle (double[] p0, double[] p1, double[] p2)
{
double[] v0 = Geometry.createVector (p0, p1);
double[] v1 = Geometry.createVector (p0, p2);
double dotProduct = Geometry.computeDotProduct (v0, v1);
double length1 = Geometry.length (v0);
double length2 = Geometry.length (v1);
double denominator = length1 * length2;
double product = denominator != 0.0 ? dotProduct / denominator : 0.0;
double angle = Math.acos (product);
return angle;
}
/**
* Compute the dot product (a scalar) between two vectors.
*
* @param v0, v1 Vectors to compute dot product between [x,y,z].
* @return Dot product of given vectors.
*/
public static double computeDotProduct (double[] v0, double[] v1)
{
return v0[0] * v1[0] + v0[1] * v1[1] + v0[2] * v1[2];
}
/**
* Compute the cross product (a vector) of two vectors.
*
* @param v0, v1 Vectors to compute cross product between [x,y,z].
* @param crossProduct Cross product of specified vectors [x,y,z].
*/
public static double[] computeCrossProduct (double[] v0, double[] v1)
{
double crossProduct[] = new double[3];
crossProduct[0] = v0[1] * v1[2] - v0[2] * v1[1];
crossProduct[1] = v0[2] * v1[0] - v0[0] * v1[2];
crossProduct[2] = v0[0] * v1[1] - v0[1] * v1[0];
return crossProduct;
}
/**
* Construct the vector specified by two points.
*
* @param p0, p1 Points the construct vector between [x,y,z].
* @return v Vector from p0 to p1 [x,y,z].
*/
public static double[] createVector (double[] p0, double[] p1)
{
double v[] = {p1[0] - p0[0], p1[1] - p0[1], p1[2] - p0[2]};
return v;
}
/**
* Check if two points are on the same side of a given line.
* Algorithm from Sedgewick page 350.
*
* @param x0, y0, x1, y1 The line.
* @param px0, py0 First point.
* @param px1, py1 Second point.
* @return <0 if points on opposite sides.
* =0 if one of the points is exactly on the line
* >0 if points on same side.
*/
private static int sameSide (double x0, double y0, double x1, double y1,
double px0, double py0, double px1, double py1)
{
int sameSide = 0;
double dx = x1 - x0;
double dy = y1 - y0;
double dx1 = px0 - x0;
double dy1 = py0 - y0;
double dx2 = px1 - x1;
double dy2 = py1 - y1;
// Cross product of the vector from the endpoint of the line to the point
double c1 = dx * dy1 - dy * dx1;
double c2 = dx * dy2 - dy * dx2;
if (c1 != 0 && c2 != 0)
sameSide = c1 < 0 != c2 < 0 ? -1 : 1;
else if (dx == 0 && dx1 == 0 && dx2 == 0)
sameSide = !isBetween (y0, y1, py0) && !isBetween (y0, y1, py1) ? 1 : 0;
else if (dy == 0 && dy1 == 0 && dy2 == 0)
sameSide = !isBetween (x0, x1, px0) && !isBetween (x0, x1, px1) ? 1 : 0;
return sameSide;
}
/**
* Check if two points are on the same side of a given line. Integer domain.
*
* @param x0, y0, x1, y1 The line.
* @param px0, py0 First point.
* @param px1, py1 Second point.
* @return <0 if points on opposite sides.
* =0 if one of the points is exactly on the line
* >0 if points on same side.
*/
private static int sameSide (int x0, int y0, int x1, int y1,
int px0, int py0, int px1, int py1)
{
return sameSide ((double) x0, (double) y0, (double) x1, (double) y1,
(double) px0, (double) py0, (double) px1, (double) py1);
}
/**
* Check if two line segments intersects. Integer domain.
*
* @param x0, y0, x1, y1 End points of first line to check.
* @param x2, yy, x3, y3 End points of second line to check.
* @return True if the two lines intersects.
*/
public static boolean isLineIntersectingLine (int x0, int y0, int x1, int y1,
int x2, int y2, int x3, int y3)
{
int s1 = Geometry.sameSide (x0, y0, x1, y1, x2, y2, x3, y3);
int s2 = Geometry.sameSide (x2, y2, x3, y3, x0, y0, x1, y1);
return s1 <= 0 && s2 <= 0;
}
/**
* Check if a specified line intersects a specified rectangle.
* Integer domain.
*
* @param lx0, ly0 1st end point of line
* @param ly1, ly1 2nd end point of line
* @param x0, y0, x1, y1 Upper left and lower right corner of rectangle
* (inclusive).
* @return True if the line intersects the rectangle,
* false otherwise.
*/
public static boolean isLineIntersectingRectangle (int lx0, int ly0,
int lx1, int ly1,
int x0, int y0,
int x1, int y1)
{
// Is one of the line endpoints inside the rectangle
if (Geometry.isPointInsideRectangle (x0, y0, x1, y1, lx0, ly0) ||
Geometry.isPointInsideRectangle (x0, y0, x1, y1, lx1, ly1))
return true;
// If it intersects it goes through. Need to check three sides only.
// Check against top rectangle line
if (Geometry.isLineIntersectingLine (lx0, ly0, lx1, ly1,
x0, y0, x1, y0))
return true;
// Check against left rectangle line
if (Geometry.isLineIntersectingLine (lx0, ly0, lx1, ly1,
x0, y0, x0, y1))
return true;
// Check against bottom rectangle line
if (Geometry.isLineIntersectingLine (lx0, ly0, lx1, ly1,
x0, y1, x1, y1))
return true;
return false;
}
/**
* Check if a specified polyline intersects a specified rectangle.
* Integer domain.
*
* @param x, y Polyline to check.
* @param x0, y0, x1, y1 Upper left and lower left corner of rectangle
* (inclusive).
* @return True if the polyline intersects the rectangle,
* false otherwise.
*/
public static boolean isPolylineIntersectingRectangle (int[] x, int[] y,
int x0, int y0,
int x1, int y1)
{
if (x.length == 0) return false;
if (Geometry.isPointInsideRectangle (x[0], y[0], x0, y0, x1, y1))
return true;
else if (x.length == 1)
return false;
for (int i = 1; i < x.length; i++) {
if (x[i-1] != x[i] || y[i-1] != y[i])
if (Geometry.isLineIntersectingRectangle (x[i-1], y[i-1],
x[i], y[i],
x0, y0, x1, y1))
return true;
}
return false;
}
/**
* Check if a specified polygon intersects a specified rectangle.
* Integer domain.
*
* @param x X coordinates of polyline.
* @param y Y coordinates of polyline.
* @param x0 X of upper left corner of rectangle.
* @param y0 Y of upper left corner of rectangle.
* @param x1 X of lower right corner of rectangle.
* @param y1 Y of lower right corner of rectangle.
* @return True if the polyline intersects the rectangle, false otherwise.
*/
public static boolean isPolygonIntersectingRectangle (int[] x, int[] y,
int x0, int y0,
int x1, int y1)
{
int n = x.length;
if (n == 0)
return false;
if (n == 1)
return Geometry.isPointInsideRectangle (x0, y0, x1, y1, x[0], y[0]);
//
// If the polyline constituting the polygon intersects the rectangle
// the polygon does too.
//
if (Geometry.isPolylineIntersectingRectangle (x, y, x0, y0, x1, y1))
return true;
// Check last leg as well
if (Geometry.isLineIntersectingRectangle (x[n-2], y[n-2], x[n-1], y[n-1],
x0, y0, x1, y1))
return true;
//
// The rectangle and polygon are now completely including each other
// or separate.
//
if (Geometry.isPointInsidePolygon (x, y, x0, y0) ||
Geometry.isPointInsideRectangle (x0, y0, x1, y1, x[0], y[0]))
return true;
// Separate
return false;
}
/**
* Compute the area of the specfied polygon.
*
* @param x X coordinates of polygon.
* @param y Y coordinates of polygon.
* @return Area of specified polygon.
*/
public static double computePolygonArea (double[] x, double[] y)
{
int n = x.length;
double area = 0.0;
for (int i = 0; i < n - 1; i++)
area += (x[i] * y[i+1]) - (x[i+1] * y[i]);
area += (x[n-1] * y[0]) - (x[0] * y[n-1]);
area *= 0.5;
return area;
}
/**
* Compute the area of the specfied polygon.
*
* @param xy Geometry of polygon [x,y,...]
* @return Area of specified polygon.
*/
public static double computePolygonArea (double[] xy)
{
int n = xy.length;
double area = 0.0;
for (int i = 0; i < n - 2; i += 2)
area += (xy[i] * xy[i+3]) - (xy[i+2] * xy[i+1]);
area += (xy[xy.length-2] * xy[1]) - (xy[0] * xy[xy.length-1]);
area *= 0.5;
return area;
}
/**
* Compute centorid (center of gravity) of specified polygon.
*
* @param x X coordinates of polygon.
* @param y Y coordinates of polygon.
* @return Centroid [x,y] of specified polygon.
*/
public static double[] computePolygonCentroid (double[] x, double[] y)
{
double cx = 0.0;
double cy = 0.0;
int n = x.length;
for (int i = 0; i < n - 1; i++) {
double a = x[i] * y[i+1] - x[i+1] * y[i];
cx += (x[i] + x[i+1]) * a;
cy += (y[i] + y[i+1]) * a;
}
double a = x[n-1] * y[0] - x[0] * y[n-1];
cx += (x[n-1] + x[0]) * a;
cy += (y[n-1] + y[0]) * a;
double area = Geometry.computePolygonArea (x, y);
cx /= 6 * area;
cy /= 6 * area;
return new double[] {cx, cy};
}
/**
* Find the 3D extent of a polyline.
*
* @param x X coordinates of polyline.
* @param y Y coordinates of polyline.
* @param z Z coordinates of polyline.
* May be null if this is a 2D case.
* @param xExtent Will upon return contain [xMin,xMax].
* @param yExtent Will upon return contain [xMin,xMax].
* @param zExtent Will upon return contain [xMin,xMax]. Unused (may be
* set to null) if z is null.
*/
public static void findPolygonExtent (double[] x, double[] y, double[] z,
double[] xExtent,
double[] yExtent,
double[] zExtent)
{
double xMin = +Double.MAX_VALUE;
double xMax = -Double.MAX_VALUE;
double yMin = +Double.MAX_VALUE;
double yMax = -Double.MAX_VALUE;
double zMin = +Double.MAX_VALUE;
double zMax = -Double.MAX_VALUE;
for (int i = 0; i < x.length; i++) {
if (x[i] < xMin) xMin = x[i];
if (x[i] > xMax) xMax = x[i];
if (y[i] < yMin) yMin = y[i];
if (y[i] > yMax) yMax = y[i];
if (z != null) {
if (z[i] < zMin) zMin = z[i];
if (z[i] > zMax) zMax = z[i];
}
}
xExtent[0] = xMin;
xExtent[1] = xMax;
yExtent[0] = yMin;
yExtent[1] = yMax;
if (z != null) {
zExtent[0] = zMin;
zExtent[1] = zMax;
}
}
/**
* Find the extent of a polygon.
*
* @param x X coordinates of polygon.
* @param y Y coordinates of polygon.
* @param xExtent Will upon return contain [xMin, xMax]
* @param yExtent Will upon return contain [yMin, yMax]
*/
public static void findPolygonExtent (int[] x, int[] y,
int[] xExtent, // xMin, xMax
int[] yExtent) // yMin, yMax
{
int xMin = + Integer.MAX_VALUE;
int xMax = - Integer.MAX_VALUE;
int yMin = + Integer.MAX_VALUE;
int yMax = - Integer.MAX_VALUE;
for (int i = 0; i < x.length; i++) {
if (x[i] < xMin) xMin = x[i];
if (x[i] > xMax) xMax = x[i];
if (y[i] < yMin) yMin = y[i];
if (y[i] > yMax) yMax = y[i];
}
xExtent[0] = xMin;
xExtent[1] = xMax;
yExtent[0] = yMin;
yExtent[1] = yMax;
}
/**
* Compute the intersection between two line segments, or two lines
* of infinite length.
*
* @param x0 X coordinate first end point first line segment.
* @param y0 Y coordinate first end point first line segment.
* @param x1 X coordinate second end point first line segment.
* @param y1 Y coordinate second end point first line segment.
* @param x2 X coordinate first end point second line segment.
* @param y2 Y coordinate first end point second line segment.
* @param x3 X coordinate second end point second line segment.
* @param y3 Y coordinate second end point second line segment.
* @param intersection[2] Preallocated by caller to double[2]
* @return -1 if lines are parallel (x,y unset),
* -2 if lines are parallel and overlapping (x, y center)
* 0 if intesrection outside segments (x,y set)
* +1 if segments intersect (x,y set)
*/
public static int findLineSegmentIntersection (double x0, double y0,
double x1, double y1,
double x2, double y2,
double x3, double y3,
double[] intersection)
{
// TODO: Make limit depend on input domain
final double LIMIT = 1e-5;
final double INFINITY = 1e10;
double x, y;
//
// Convert the lines to the form y = ax + b
//
// Slope of the two lines
double a0 = Geometry.equals (x0, x1, LIMIT) ?
INFINITY : (y0 - y1) / (x0 - x1);
double a1 = Geometry.equals (x2, x3, LIMIT) ?
INFINITY : (y2 - y3) / (x2 - x3);
double b0 = y0 - a0 * x0;
double b1 = y2 - a1 * x2;
// Check if lines are parallel
if (Geometry.equals (a0, a1)) {
if (!Geometry.equals (b0, b1))
return -1; // Parallell non-overlapping
else {
if (Geometry.equals (x0, x1)) {
if (Math.min (y0, y1) < Math.max (y2, y3) ||
Math.max (y0, y1) > Math.min (y2, y3)) {
double twoMiddle = y0 + y1 + y2 + y3 -
Geometry.min (y0, y1, y2, y3) -
Geometry.max (y0, y1, y2, y3);
y = (twoMiddle) / 2.0;
x = (y - b0) / a0;
}
else return -1; // Parallell non-overlapping
}
else {
if (Math.min (x0, x1) < Math.max (x2, x3) ||
Math.max (x0, x1) > Math.min (x2, x3)) {
double twoMiddle = x0 + x1 + x2 + x3 -
Geometry.min (x0, x1, x2, x3) -
Geometry.max (x0, x1, x2, x3);
x = (twoMiddle) / 2.0;
y = a0 * x + b0;
}
else return -1;
}
intersection[0] = x;
intersection[1] = y;
return -2;
}
}
// Find correct intersection point
if (Geometry.equals (a0, INFINITY)) {
x = x0;
y = a1 * x + b1;
}
else if (Geometry.equals (a1, INFINITY)) {
x = x2;
y = a0 * x + b0;
}
else {
x = - (b0 - b1) / (a0 - a1);
y = a0 * x + b0;
}
intersection[0] = x;
intersection[1] = y;
// Then check if intersection is within line segments
double distanceFrom1;
if (Geometry.equals (x0, x1)) {
if (y0 < y1)
distanceFrom1 = y < y0 ? Geometry.length (x, y, x0, y0) :
y > y1 ? Geometry.length (x, y, x1, y1) : 0.0;
else
distanceFrom1 = y < y1 ? Geometry.length (x, y, x1, y1) :
y > y0 ? Geometry.length (x, y, x0, y0) : 0.0;
}
else {
if (x0 < x1)
distanceFrom1 = x < x0 ? Geometry.length (x, y, x0, y0) :
x > x1 ? Geometry.length (x, y, x1, y1) : 0.0;
else
distanceFrom1 = x < x1 ? Geometry.length (x, y, x1, y1) :
x > x0 ? Geometry.length (x, y, x0, y0) : 0.0;
}
double distanceFrom2;
if (Geometry.equals (x2, x3)) {
if (y2 < y3)
distanceFrom2 = y < y2 ? Geometry.length (x, y, x2, y2) :
y > y3 ? Geometry.length (x, y, x3, y3) : 0.0;
else
distanceFrom2 = y < y3 ? Geometry.length (x, y, x3, y3) :
y > y2 ? Geometry.length (x, y, x2, y2) : 0.0;
}
else {
if (x2 < x3)
distanceFrom2 = x < x2 ? Geometry.length (x, y, x2, y2) :
x > x3 ? Geometry.length (x, y, x3, y3) : 0.0;
else
distanceFrom2 = x < x3 ? Geometry.length (x, y, x3, y3) :
x > x2 ? Geometry.length (x, y, x2, y2) : 0.0;
}
return Geometry.equals (distanceFrom1, 0.0) &&
Geometry.equals (distanceFrom2, 0.0) ? 1 : 0;
}
/**
* Find the intersections between a polygon and a straight line.
*
* NOTE: This method is only guaranteed to work if the polygon
* is first preprocessed so that "unneccesary" vertices are removed
* (i.e vertices on the straight line between its neighbours).
*
* @param x X coordinates of polygon.
* @param y Y coordinates of polygon.
* @param x0 X first end point of line.
* @param x0 Y first end point of line.
* @param x0 X second end point of line.
* @param x0 Y second end point of line.
* @return Intersections [x,y,x,y...].
*/
public static double[] findLinePolygonIntersections (double[] x, double[] y,
double x0, double y0,
double x1, double y1)
{
double x2, y2, x3, y3;
double xi, yi;
int nPoints = x.length;
int nIntersections = 0;
double[] intersections = new double[24]; // Result vector x,y,x,y,...
double[] intersection = new double[2]; // Any given intersection x,y
for (int i = 0; i < nPoints; i++) {
int next = i == nPoints - 1 ? 0 : i + 1;
// The line segment of the polyline to check
x2 = x[i];
y2 = y[i];
x3 = x[next];
y3 = y[next];
boolean isIntersecting = false;
// Ignore segments of zero length
if (Geometry.equals (x2, x3) && Geometry.equals (y2, y3))
continue;
int type = Geometry.findLineSegmentIntersection (x0, y0, x1, y1,
x2, y2, x3, y3,
intersection);
if (type == -2) { // Overlapping
int p1 = i == 0 ? nPoints - 1 : i - 1;
int p2 = next == nPoints - 1 ? 0 : next + 1;
int side = Geometry.sameSide (x0, y0, x1, y1,
x[p1], y[p1], x[p2], y[p2]);
if (side < 0)
isIntersecting = true;
}
else if (type == 1)
isIntersecting = true;
// Add the intersection point
if (isIntersecting) {
// Reallocate if necessary
if (nIntersections << 1 == intersections.length) {
double[] newArray = new double[nIntersections << 2];
System.arraycopy (intersections, 0, newArray, 0,
intersections.length);
intersections = newArray;
}
// Then add
intersections[nIntersections << 1 + 0] = intersection[0];
intersections[nIntersections << 1 + 1] = intersection[1];
nIntersections++;
}
}
if (nIntersections == 0) return null;
// Reallocate result so array match number of intersections
double[] finalArray = new double[nIntersections << 2];
System.arraycopy (intersections, 0, finalArray, 0, finalArray.length);
return finalArray;
}
/**
* Return the geometry of an ellipse based on its four top points.
* Integer domain. The method use the generic createEllipse()
* method for the main task, and then transforms this according
* to any rotation or skew defined by the given top points.
*
* @param x X array of four top points of ellipse.
* @param y Y array of four top points of ellipse.
* @return Geometry of ellipse [x,y,x,y...].
*/
public static int[] createEllipse (int[] x, int[] y)
{
// Center of ellipse
int x0 = (x[0] + x[2]) / 2;
int y0 = (y[0] + y[2]) / 2;
// Angle between axis define skew
double[] p0 = {(double) x0, (double) y0, 0.0};
double[] p1 = {(double) x[0], (double) y[0], 0.0};
double[] p2 = {(double) x[1], (double) y[1], 0.0};
double axisAngle = Geometry.computeAngle (p0, p1, p2);
// dx / dy
double dx = Geometry.length (x0, y0, x[1], y[1]);
double dy = Geometry.length (x0, y0, x[0], y[0]) * Math.sin (axisAngle);
// Create geometry for unrotated / unsheared ellipse
int[] ellipse = createEllipse (x0, y0, (int) Math.round (dx),
(int) Math.round (dy));
int nPoints = ellipse.length / 2;
// Shear if neccessary. If angle is close to 90 there is no shear.
// If angle is close to 0 or 180 shear is infinite, and we set
// it to zero as well.
if (!Geometry.equals (axisAngle, Math.PI/2.0, 0.1) &&
!Geometry.equals (axisAngle, Math.PI, 0.1) &&
!Geometry.equals (axisAngle, 0.0, 0.1)) {
double xShear = 1.0 / Math.tan (axisAngle);
for (int i = 0; i < nPoints; i++)
ellipse[i*2 + 0] += Math.round ((ellipse[i*2 + 1] - y0) * xShear);
}
// Rotate
int ddx = x[1] - x0;
int ddy = y0 - y[1];
double angle;
if (ddx == 0 && ddy == 0) angle = 0.0;
else if (ddx == 0) angle = Math.PI / 2.0;
else angle = Math. atan ((double) ddy /
(double) ddx);
double cosAngle = Math.cos (angle);
double sinAngle = Math.sin (angle);
for (int i = 0; i < nPoints; i++) {
int xr = (int) Math.round (x0 +
(ellipse[i*2+0] - x0) * cosAngle -
(ellipse[i*2+1] - y0) * sinAngle);
int yr = (int) Math.round (y0 -
(ellipse[i*2+1] - y0) * cosAngle -
(ellipse[i*2+0] - x0) * sinAngle);
ellipse[i*2+0] = xr;
ellipse[i*2+1] = yr;
}
return ellipse;
}
/**
* Create the geometry for an unrotated, unskewed ellipse.
* Integer domain.
*
* @param x0 X center of ellipse.
* @param y0 Y center of ellipse.
* @param dx X ellipse radius.
* @param dy Y ellipse radius.
* @return Ellipse geometry [x,y,x,y,...].
*/
public static int[] createEllipse (int x0, int y0, int dx, int dy)
{
// Make sure deltas are positive
dx = Math.abs (dx);
dy = Math.abs (dy);
// This is an approximate number of points we need to make a smooth
// surface on a quater of the ellipse
int nPoints = dx > dy ? dx : dy;
nPoints /= 2;
if (nPoints < 1) nPoints = 1;
// Allocate arrays for holding the complete set of vertices around
// the ellipse. Note that this is a complete ellipse: First and last
// point coincide.
int[] ellipse = new int[nPoints*8 + 2];
// Compute some intermediate results to save time in the inner loop
int dxdy = dx * dy;
int dx2 = dx * dx;
int dy2 = dy * dy;
// Handcode the entries in the four "corner" points of the ellipse,
// i.e. at point 0, 90, 180, 270 and 360 degrees
ellipse[nPoints*0 + 0] = x0 + dx;
ellipse[nPoints*0 + 1] = y0;
ellipse[nPoints*8 + 0] = x0 + dx;
ellipse[nPoints*8 + 1] = y0;
ellipse[nPoints*2 + 0] = x0;
ellipse[nPoints*2 + 1] = y0 - dy;
ellipse[nPoints*4 + 0] = x0 - dx;
ellipse[nPoints*4 + 1] = y0;
ellipse[nPoints*6 + 0] = x0;
ellipse[nPoints*6 + 1] = y0 + dy;
// Find the angle step
double angleStep = nPoints > 0 ? Math.PI / 2.0 / nPoints : 0.0;
// Loop over angles from 0 to 90. The rest of the ellipse can be derrived
// from this first quadrant. For each angle set the four corresponding
// ellipse points.
double a = 0.0;
for (int i = 1; i < nPoints; i++) {
a += angleStep;
double t = Math.tan (a);
double x = (double) dxdy / Math.sqrt (t * t * dx2 + dy2);
double y = x * t;
int xi = (int) (x + 0.5);
int yi = (int) (y + 0.5);
ellipse[(nPoints*0 + i) * 2 + 0] = x0 + xi;
ellipse[(nPoints*2 - i) * 2 + 0] = x0 - xi;
ellipse[(nPoints*2 + i) * 2 + 0] = x0 - xi;
ellipse[(nPoints*4 - i) * 2 + 0] = x0 + xi;
ellipse[(nPoints*0 + i) * 2 + 1] = y0 - yi;
ellipse[(nPoints*2 - i) * 2 + 1] = y0 - yi;
ellipse[(nPoints*2 + i) * 2 + 1] = y0 + yi;
ellipse[(nPoints*4 - i) * 2 + 1] = y0 + yi;
}
return ellipse;
}
/**
* Create the geometry for an unrotated, unskewed ellipse.
* Floating point domain.
*
* @param x0 X center of ellipse.
* @param y0 Y center of ellipse.
* @param dx X ellipse radius.
* @param dy Y ellipse radius.
* @return Ellipse geometry [x,y,x,y,...].
*/
public static double[] createEllipse (double x0, double y0,
double dx, double dy)
{
// Make sure deltas are positive
dx = Math.abs (dx);
dy = Math.abs (dy);
// As we don't know the resolution of the appliance of the ellipse
// we create one vertex per 2nd degree. The nPoints variable holds
// number of points in a quater of the ellipse.
int nPoints = 45;
// Allocate arrays for holding the complete set of vertices around
// the ellipse. Note that this is a complete ellipse: First and last
// point coincide.
double[] ellipse = new double[nPoints*8 + 2];
// Compute some intermediate results to save time in the inner loop
double dxdy = dx * dy;
double dx2 = dx * dx;
double dy2 = dy * dy;
// Handcode the entries in the four "corner" points of the ellipse,
// i.e. at point 0, 90, 180, 270 and 360 degrees
ellipse[nPoints*0 + 0] = x0 + dx;
ellipse[nPoints*0 + 1] = y0;
ellipse[nPoints*8 + 0] = x0 + dx;
ellipse[nPoints*8 + 1] = y0;
ellipse[nPoints*2 + 0] = x0;
ellipse[nPoints*2 + 1] = y0 - dy;
ellipse[nPoints*4 + 0] = x0 - dx;
ellipse[nPoints*4 + 1] = y0;
ellipse[nPoints*6 + 0] = x0;
ellipse[nPoints*6 + 1] = y0 + dy;
// Find the angle step
double angleStep = nPoints > 0 ? Math.PI / 2.0 / nPoints : 0.0;
// Loop over angles from 0 to 90. The rest of the ellipse can be derrived
// from this first quadrant. For each angle set the four corresponding
// ellipse points.
double a = 0.0;
for (int i = 1; i < nPoints; i++) {
a += angleStep;
double t = Math.tan (a);
double x = (double) dxdy / Math.sqrt (t * t * dx2 + dy2);
double y = x * t + 0.5;
ellipse[(nPoints*0 + i) * 2 + 0] = x0 + x;
ellipse[(nPoints*2 - i) * 2 + 0] = x0 - x;
ellipse[(nPoints*2 + i) * 2 + 0] = x0 - x;
ellipse[(nPoints*4 - i) * 2 + 0] = x0 + x;
ellipse[(nPoints*0 + i) * 2 + 1] = y0 - y;
ellipse[(nPoints*2 - i) * 2 + 1] = y0 - y;
ellipse[(nPoints*2 + i) * 2 + 1] = y0 + y;
ellipse[(nPoints*4 - i) * 2 + 1] = y0 + y;
}
return ellipse;
}
/**
* Create geometry for a circle. Integer domain.
*
* @param x0 X center of circle.
* @param y0 Y center of circle.
* @param radius Radius of circle.
* @return Geometry of circle [x,y,...]
*/
public static int[] createCircle (int x0, int y0, int radius)
{
return createEllipse (x0, y0, radius, radius);
}
/**
* Create geometry for a circle. Floating point domain.
*
* @param x0 X center of circle.
* @param y0 Y center of circle.
* @param radius Radius of circle.
* @return Geometry of circle [x,y,...]
*/
public static double[] createCircle (double x0, double y0, double radius)
{
return createEllipse (x0, y0, radius, radius);
}
/**
* Create the geometry of a sector of an ellipse.
*
* @param x0 X coordinate of center of ellipse.
* @param y0 Y coordinate of center of ellipse.
* @param dx X radius of ellipse.
* @param dy Y radius of ellipse.
* @param angle0 First angle of sector (in radians).
* @param angle1 Second angle of sector (in radians).
* @return Geometry of secor [x,y,...]
*/
public static int[] createSector (int x0, int y0, int dx, int dy,
double angle0, double angle1)
{
// Determine a sensible number of points for arc
double angleSpan = Math.abs (angle1 - angle0);
double arcDistance = Math.max (dx, dy) * angleSpan;
int nPoints = (int) Math.round (arcDistance / 15);
double angleStep = angleSpan / (nPoints - 1);
int[] xy = new int[nPoints*2 + 4];
int index = 0;
for (int i = 0; i < nPoints; i++) {
double angle = angle0 + angleStep * i;
double x = dx * Math.cos (angle);
double y = dy * Math.sin (angle);
xy[index+0] = x0 + (int) Math.round (x);
xy[index+1] = y0 - (int) Math.round (y);
index += 2;
}
// Start and end geometry at center of ellipse to make it a closed polygon
xy[nPoints*2 + 0] = x0;
xy[nPoints*2 + 1] = y0;
xy[nPoints*2 + 2] = xy[0];
xy[nPoints*2 + 3] = xy[1];
return xy;
}
/**
* Create the geometry of a sector of a circle.
*
* @param x0 X coordinate of center of ellipse.
* @param y0 Y coordinate of center of ellipse.
* @param dx X radius of ellipse.
* @param dy Y radius of ellipse.
* @param angle0 First angle of sector (in radians).
* @param angle1 Second angle of sector (in radians).
* @return Geometry of secor [x,y,...]
*/
public static int[] createSector (int x0, int y0, int radius,
double angle0, double angle1)
{
return createSector (x0, y0, radius, radius, angle0, angle1);
}
/**
* Create the geometry of an arrow. The arrow is positioned at the
* end (last point) of the specified polyline, as follows:
*
* 0,4--,
* \ --,
* \ --,
* \ --,
* \ --,
* -------------------------3-----------1
* / --'
* / --'
* / --'
* / --'
* 2--'
*
* @param x X coordinates of polyline of where arrow is positioned
* in the end. Must contain at least two points.
* @param y Y coordinates of polyline of where arrow is positioned
* in the end.
* @param length Length along the main axis from point 1 to the
* projection of point 0.
* @param angle Angle between the main axis and the line 1,0
* (and 1,2) in radians.
* @param inset Specification of point 3 [0.0-1.0], 1.0 will put
* point 3 at distance length from 1, 0.0 will put it
* at point 1.
* @return Array of the five coordinates [x,y,...].
*/
public static int[] createArrow (int[] x, int[] y,
double length, double angle, double inset)
{
int[] arrow = new int[10];
int x0 = x[x.length - 1];
int y0 = y[y.length - 1];
arrow[2] = x0;
arrow[3] = y0;
// Find position of interior of the arrow along the polyline
int[] pos1 = new int[2];
Geometry.findPolygonPosition (x, y, length, pos1);
// Angles
double dx = x0 - pos1[0];
double dy = y0 - pos1[1];
// Polyline angle
double v = dx == 0.0 ? Math.PI / 2.0 : Math.atan (Math.abs (dy / dx));
v = dx > 0.0 && dy <= 0.0 ? Math.PI + v :
dx > 0.0 && dy >= 0.0 ? Math.PI - v :
dx <= 0.0 && dy < 0.0 ? -v :
dx <= 0.0 && dy > 0.0 ? +v : 0.0;
double v0 = v + angle;
double v1 = v - angle;
double edgeLength = length / Math.cos (angle);
arrow[0] = x0 + (int) Math.round (edgeLength * Math.cos (v0));
arrow[1] = y0 - (int) Math.round (edgeLength * Math.sin (v0));
arrow[4] = x0 + (int) Math.round (edgeLength * Math.cos (v1));
arrow[5] = y0 - (int) Math.round (edgeLength * Math.sin (v1));
double c1 = inset * length;
arrow[6] = x0 + (int) Math.round (c1 * Math.cos (v));
arrow[7] = y0 - (int) Math.round (c1 * Math.sin (v));
// Close polygon
arrow[8] = arrow[0];
arrow[9] = arrow[1];
return arrow;
}
/**
* Create geometry for an arrow along the specified line and with
* tip at x1,y1. See general method above.
*
* @param x0 X first end point of line.
* @param y0 Y first end point of line.
* @param x1 X second end point of line.
* @param y1 Y second end point of line.
* @param length Length along the main axis from point 1 to the
* projection of point 0.
* @param angle Angle between the main axis and the line 1,0
* (and 1.2)
* @param inset Specification of point 3 [0.0-1.0], 1.0 will put
* point 3 at distance length from 1, 0.0 will put it
* at point 1.
* @return Array of the four coordinates [x,y,...].
*/
public static int[] createArrow (int x0, int y0, int x1, int y1,
double length, double angle, double inset)
{
int[] x = {x0, x1};
int[] y = {y0, y1};
return createArrow (x, y, length, angle, inset);
}
/**
* Create geometry for a rectangle. Returns a closed polygon; first
* and last points matches. Integer domain.
*
* @param x0 X corner of rectangle.
* @param y0 Y corner of rectangle.
* @param width Width (may be negative to indicate leftwards direction)
* @param height Height (may be negative to indicaten upwards direction)
*/
public static int[] createRectangle (int x0, int y0, int width, int height)
{
return new int[] {x0, y0,
x0 + (width - 1), y0,
x0 + (width - 1), y0 + (height - 1),
x0, y0 + (height - 1),
x0, y0};
}
/**
* Create geometry for a rectangle. Returns a closed polygon; first
* and last points matches. Floating point domain.
*
* @param x0 X corner of rectangle.
* @param y0 Y corner of rectangle.
* @param width Width (may be negative to indicate leftwards direction)
* @param height Height (may be negative to indicaten upwards direction)
*/
public static double[] createRectangle (double x0, double y0,
double width, double height)
{
return new double[] {x0, y0,
x0 + width, y0,
x0 + width, y0 + height,
x0, y0 + height,
x0, y0};
}
/**
* Create geometry of a star. Integer domain.
*
* @param x0 X center of star.
* @param y0 Y center of star.
* @param innerRadius Inner radis of arms.
* @param outerRadius Outer radius of arms.
* @param nArms Number of arms.
* @return Geometry of star [x,y,x,y,...].
*/
public static int[] createStar (int x0, int y0,
int innerRadius, int outerRadius,
int nArms)
{
int nPoints = nArms * 2 + 1;
int[] xy = new int[nPoints * 2];
double angleStep = 2.0 * Math.PI / nArms / 2.0;
for (int i = 0; i < nArms * 2; i++) {
double angle = i * angleStep;
double radius = (i % 2) == 0 ? innerRadius : outerRadius;
double x = x0 + radius * Math.cos (angle);
double y = y0 + radius * Math.sin (angle);
xy[i*2 + 0] = (int) Math.round (x);
xy[i*2 + 1] = (int) Math.round (y);
}
// Close polygon
xy[nPoints*2 - 2] = xy[0];
xy[nPoints*2 - 1] = xy[1];
return xy;
}
/**
* Create geometry of a star. Floating point domain.
*
* @param x0 X center of star.
* @param y0 Y center of star.
* @param innerRadius Inner radis of arms.
* @param outerRadius Outer radius of arms.
* @param nArms Number of arms.
* @return Geometry of star [x,y,x,y,...].
*/
public static double[] createStar (double x0, double y0,
double innerRadius, double outerRadius,
int nArms)
{
int nPoints = nArms * 2 + 1;
double[] xy = new double[nPoints * 2];
double angleStep = 2.0 * Math.PI / nArms / 2.0;
for (int i = 0; i < nArms * 2; i++) {
double angle = i * angleStep;
double radius = (i % 2) == 0 ? innerRadius : outerRadius;
xy[i*2 + 0] = x0 + radius * Math.cos (angle);
xy[i*2 + 1] = y0 + radius * Math.sin (angle);
}
// Close polygon
xy[nPoints*2 - 2] = xy[0];
xy[nPoints*2 - 1] = xy[1];
return xy;
}
/**
* Return the x,y position at distance "length" into the given polyline.
*
* @param x X coordinates of polyline
* @param y Y coordinates of polyline
* @param length Requested position
* @param position Preallocated to int[2]
* @return True if point is within polyline, false otherwise
*/
public static boolean findPolygonPosition (int[] x, int[] y,
double length,
int[] position)
{
if (length < 0) return false;
double accumulatedLength = 0.0;
for (int i = 1; i < x.length; i++) {
double legLength = Geometry.length (x[i-1], y[i-1], x[i], y[i]);
if (legLength + accumulatedLength >= length) {
double part = length - accumulatedLength;
double fraction = part / legLength;
position[0] = (int) Math.round (x[i-1] + fraction * (x[i] - x[i-1]));
position[1] = (int) Math.round (y[i-1] + fraction * (y[i] - y[i-1]));
return true;
}
accumulatedLength += legLength;
}
// Length is longer than polyline
return false;
}
}
]]>