// Generates a new polygon by dragging a polygon through an angle, and taking all the points it
// touched (and a few extras for overestimation)
// Only valid for convex polygons, and small rotations (20 degrees or less)
// stroke from theta1 to theta2
public static Polygon strokeRot(double theta1, double theta2, Polygon poly) {
Polygon poly1 = mul(Mat.rotation(theta1), poly);
Polygon poly2 = mul(Mat.rotation(theta2), poly);
Polygon stroked = combine(poly1, poly2);
ArrayList<Mat> cornerVerts;
Polygon corner;
int thisVertex, prevVertex, nextVertex;
Mat origin = Mat.encodePoint(0, 0);
Mat cornerVert1a, cornerVert1b;
Mat cornerVert2a, cornerVert2b;
double actualDist, desiredDist;
Mat cornerTransform;
for (thisVertex = 0; thisVertex < poly.vertices.size(); thisVertex++) {
if (thisVertex == 0) {
prevVertex = poly.vertices.size() - 1;
} else {
prevVertex = thisVertex - 1;
}
if (thisVertex == poly.vertices.size() - 1) {
nextVertex = 0;
} else {
nextVertex = thisVertex + 1;
}
cornerVerts = new ArrayList<Mat>();
cornerVerts.add(poly2.vertices.get(nextVertex));
cornerVerts.add(origin);
cornerVerts.add(poly1.vertices.get(prevVertex));
cornerVert1a = poly1.vertices.get(thisVertex);
cornerVert2a = poly2.vertices.get(thisVertex);
actualDist = ptSegDistance(cornerVert1a, cornerVert2a, origin);
desiredDist = Mat.dist(cornerVert1a, Mat.encodePoint(0, 0));
cornerTransform = Mat.mul(desiredDist / actualDist, Mat.eye(4));
cornerVert1b = Mat.mul(cornerTransform, cornerVert1a);
cornerVert2b = Mat.mul(cornerTransform, cornerVert2a);
cornerVert1b =
lineSegIntersection(
cornerVert1b, cornerVert2b, poly1.vertices.get(prevVertex), cornerVert1a);
cornerVert2b =
lineSegIntersection(
cornerVert1b, cornerVert2b, poly2.vertices.get(nextVertex), cornerVert2a);
cornerVerts.add(cornerVert1b);
cornerVerts.add(cornerVert2b);
corner = new Polygon(cornerVerts);
stroked = combine(stroked, corner);
}
return stroked;
}
public static Mat lineSegIntersection(Mat e00, Mat e01, Mat e10, Mat e11) {
double x0 = e00.data[0][0];
double y0 = e00.data[1][0];
double x1 = e10.data[0][0];
double y1 = e10.data[1][0];
double x, y;
double m0, m1;
if (x0 == e01.data[0][0]) {
m1 = (y1 - e11.data[1][0]) / (x1 - e11.data[0][0]);
x = x0;
y = m1 * (x - x1) + y1;
} else if (x1 == e11.data[0][0]) {
m0 = (y0 - e01.data[1][0]) / (x0 - e01.data[0][0]);
x = x1;
y = m0 * (x - x0) + y0;
} else {
m0 = (y0 - e01.data[1][0]) / (x0 - e01.data[0][0]);
m1 = (y1 - e11.data[1][0]) / (x1 - e11.data[0][0]);
// System.err.println("m0 = " + m0);
// System.err.println("m1 = " + m1);
x = (m0 * x0 - m1 * x1 - y0 + y1) / (m0 - m1);
y = m1 * (x - x1) + y1;
// System.err.println("x = " + x);
// System.err.println("y = " + y);
}
return Mat.encodePoint(x, y);
}
public void addObstacle(PolygonObstacle obstacle) {
ArrayList<Mat> vertices = new ArrayList<Mat>();
for (Point2D.Double vert : obstacle.getVertices()) {
vertices.add(Mat.encodePoint(vert.x, vert.y));
}
addObstacle(new Polygon(vertices));
}
// occupancy grid is indexed from (xMin, yMin)
public boolean[][] getOccupancyGrid(int nCellsLinear) {
System.err.println("GOT HERE YO!");
int i, j;
double xLow, xHigh, yLow, yHigh;
double maxDimension = Math.max(xMax - xMin, yMax - yMin);
double resolutionLinear = maxDimension / nCellsLinear;
Polygon resolutionCellSpace;
resolutionCellSpace =
new Polygon(
Arrays.asList(
Mat.encodePoint(-1 * resolutionLinear / 2, -1 * resolutionLinear / 2),
Mat.encodePoint(-1 * resolutionLinear / 2, resolutionLinear / 2),
Mat.encodePoint(resolutionLinear / 2, resolutionLinear / 2),
Mat.encodePoint(resolutionLinear / 2, -1 * resolutionLinear / 2)));
reflectedRobot = Polygon.minkowskiSumSimple(reflectedRobot, resolutionCellSpace);
ArrayList<Polygon> csObstacles = getCSObstacles();
System.err.println("GOT HERE as well.");
boolean[][] occupancyGrid = new boolean[nCellsLinear][nCellsLinear];
for (i = 0; i < nCellsLinear; i++) {
xLow = xMin + resolutionLinear * i;
xHigh = xLow + resolutionLinear;
for (j = 0; j < nCellsLinear; j++) {
yLow = yMin + resolutionLinear * j;
yHigh = yLow + resolutionLinear;
if (i == 9 && j == 6) {
System.err.print("(" + i + ", " + j + ") ");
System.err.println("(" + ((xLow + xHigh) / 2) + ", " + ((yLow + yHigh) / 2) + ")");
}
occupancyGrid[i][j] = true;
for (Polygon obstacle : csObstacles) {
if (Polygon.pointInPolygon(
obstacle, Mat.encodePoint((xLow + xHigh) / 2, (yLow + yHigh) / 2))) {
occupancyGrid[i][j] = false;
break;
}
}
}
}
System.err.println("GOT HERE TOO!");
return occupancyGrid;
}
// occupancy grid is indexed from (xMin, yMin, 0)
public boolean[][][] getOccupancyGrid(int nCellsLinear, int nCellsAngular) {
int i, j, k;
double xLow, xHigh, yLow, yHigh, thetaLow, thetaHigh;
double maxDimension = Math.max(xMax - xMin, yMax - yMin);
double resolutionLinear = maxDimension / nCellsLinear;
double resolutionAngular = 2 * Math.PI / nCellsAngular;
Polygon strokedRobot;
ArrayList<Polygon> thetaObstacles;
Polygon resolutionCellSpace;
boolean[][][] occupancyGrid = new boolean[nCellsLinear][nCellsLinear][nCellsAngular];
for (i = 0; i < nCellsLinear; i++) {
xLow = xMin + resolutionLinear * i;
xHigh = xLow + resolutionLinear;
for (j = 0; j < nCellsLinear; j++) {
yLow = yMin + resolutionLinear * j;
yHigh = yLow + resolutionLinear;
for (k = 0; k < nCellsAngular; k++) {
thetaLow = resolutionAngular * k;
thetaHigh = thetaLow + resolutionAngular;
resolutionCellSpace =
new Polygon(
Arrays.asList(
Mat.encodePoint(xLow, yLow),
Mat.encodePoint(xLow, yHigh),
Mat.encodePoint(xHigh, yHigh),
Mat.encodePoint(xHigh, yLow)));
strokedRobot = Polygon.strokeRot(thetaLow, thetaHigh, reflectedRobot);
occupancyGrid[i][j][k] = true;
for (Polygon obstacle : obstacles) {
if (Polygon.polygonsIntersect(
resolutionCellSpace, Polygon.minkowskiSum(obstacle, strokedRobot))) {
occupancyGrid[i][j][k] = false;
break;
}
}
}
}
}
return occupancyGrid;
}
public static void tests() {
System.err.println("HEY!");
Mat p0 = Mat.encodePoint(0, 0);
Mat p1 = Mat.encodePoint(1, .1);
Mat p2 = Mat.encodePoint(.1, 1);
Mat p3 = Mat.encodePoint(-1, -.1);
Mat p4 = Mat.encodePoint(-.1, -1);
Mat p5 = Mat.encodePoint(0.0001, 0);
Mat p6 = Mat.encodePoint(-0.0001, 0);
if (!lineSegIntersect(p1, p3, p2, p4)) {
try {
throw new Exception();
} catch (Exception e) {
e.printStackTrace();
System.err.println("hey there");
System.exit(1);
}
}
if (lineSegIntersect(p1, p4, p2, p3)) {
try {
throw new Exception();
} catch (Exception e) {
e.printStackTrace();
System.err.println("hey there");
System.exit(1);
}
}
if (lineSegIntersect(p1, p5, p2, p4)) {
try {
throw new Exception();
} catch (Exception e) {
e.printStackTrace();
System.err.println("hey there");
System.exit(1);
}
}
if (!lineSegIntersect(p1, p6, p2, p4)) {
try {
throw new Exception();
} catch (Exception e) {
e.printStackTrace();
System.err.println("hey there");
System.exit(1);
}
}
Mat inter = lineSegIntersection(p1, p3, p2, p4);
if (inter.data[0][0] != 0 || inter.data[1][0] != 0) {
try {
throw new Exception();
} catch (Exception e) {
e.printStackTrace();
System.err.println("hey there");
System.exit(1);
}
}
}
// assumes that there will be no enclosed empty spaces in the result, and that the result will
// be contiguous, and that everything is convex
public static Polygon minkowskiSumSimple(Polygon poly1, Polygon poly2) {
ArrayList<Mat> verts = new ArrayList<Mat>();
for (Mat v1 : poly1.vertices) {
for (Mat v2 : poly2.vertices) {
verts.add(Mat.add(v1, v2));
}
}
ArrayList<Point2D.Double> points = new ArrayList<Point2D.Double>();
for (Mat v : verts) {
points.add(new Point2D.Double(v.data[0][0], v.data[1][0]));
}
PolygonObstacle po = GeomUtils.convexHull(points);
verts = new ArrayList<Mat>();
for (Point2D.Double vert : po.getVertices()) {
verts.add(Mat.encodePoint(vert.x, vert.y));
}
return new Polygon(verts);
}
private void constructor(
Polygon robot,
double boundaryXMin,
double boundaryYMin,
double boundaryXMax,
double boundaryYMax) {
Polygon.tests();
cSpaceObstacles.setWrap(-1 * Math.PI, Math.PI);
xMin = boundaryXMin;
yMin = boundaryYMin;
xMax = boundaryXMax;
yMax = boundaryYMax;
reflectedRobot = Polygon.mul(Mat.mul(-1, Mat.eye(4)), robot);
ArrayList<List<Mat>> boundaries = new ArrayList<List<Mat>>();
boundaries.add(
Arrays.asList(
Mat.encodePoint(xMin - 0, yMin - 1),
Mat.encodePoint(xMin - 0, yMax + 1),
Mat.encodePoint(xMin - 1, yMax + 1),
Mat.encodePoint(xMin - 1, yMin - 1)));
boundaries.add(
Arrays.asList(
Mat.encodePoint(xMax + 0, yMin - 1),
Mat.encodePoint(xMax + 0, yMax + 1),
Mat.encodePoint(xMax + 1, yMax + 1),
Mat.encodePoint(xMax + 1, yMin - 1)));
boundaries.add(
Arrays.asList(
Mat.encodePoint(xMin - 1, yMin - 0),
Mat.encodePoint(xMax + 1, yMin - 0),
Mat.encodePoint(xMax + 1, yMin - 1),
Mat.encodePoint(xMin - 1, yMin - 1)));
boundaries.add(
Arrays.asList(
Mat.encodePoint(xMin - 1, yMax + 0),
Mat.encodePoint(xMax + 1, yMax + 0),
Mat.encodePoint(xMax + 1, yMax + 1),
Mat.encodePoint(xMin - 1, yMax + 1)));
for (List<Mat> boundary : boundaries) {
addObstacle(new Polygon(boundary));
}
}
