¿Existe un algoritmo estándar / recomendado para simplificar un polígono sin reducir ninguno de sus límites originales?
En este momento estoy usando TopologyPreservingSimplifer dentro de JTS y me encuentro con problemas más adelante en mi aplicación cuando me encuentro con polígonos "con pérdida". Idealmente, me gustaría producir polígonos simplificados que sean más pequeños que el casco convexo pero que sigan siendo un superconjunto de mi polígono original.
Actualizar:
Eventualmente se me ocurrió un algoritmo ciertamente imperfecto que coloca un "envoltorio" alrededor del polígono de entrada, lo encoge hasta que las áreas excedentes no excedan un porcentaje del área total de la entrada, luego ejecuta un simplificador de línea con un umbral mucho más fino para eliminar cualquier punto redundante a lo largo de líneas rectas. 100% dependiente de los datos, pero veo un 80% de compresión de vértices con un mínimo de áreas en exceso. Todos los comentarios / comentarios apreciados:
public class LosslessPolygonSimplifier {
protected final static Logger logger = Logger.getLogger(LosslessPolygonSimplifier.class.getName());
public static Polygon simplify(Polygon input) {
final double AREA_THRESHOLD = 0.005; // allow excesses up to half a percent of total original area
final double LINE_THRESHOLD = 0.0001; // fine threshold to strip straight lines
try {
if (!input.isSimple()) {
logger.warning("Attempting to simplify complex polygon!");
}
Polygon simple = simplifyInternal(input, AREA_THRESHOLD, LINE_THRESHOLD);
return simple;
}
catch (Exception e) {
logger.log(Level.WARNING, "Failed to simplify. Resorting to convex hull.\n " + input.toText(), e);
try {
// worst case scenario - fall back to convex hull
// probably a result of a bow-tie LINESTRING that doubles back on itself due to precision loss?
return (Polygon) input.convexHull();
}
catch (Exception e2) {
// Is this even possible? Polygons that cross the anti-meridian?
logger.log(Level.SEVERE, "Failed to simplify to convex hull: " + input.toText(), e2);
return input; // Garbage In, Garbage Out
}
}
}
// TODO avoid creating triangles on long straight edges
public static Polygon simplifyInternal(Polygon original, double areaThreshold, double lineThreshold) {
GeometryFactory gf = new GeometryFactory();
Geometry excesses, excess, keepTotal, keepA, keepB, chA, chB, keep = null, elim = null;
Polygon simplified = null, wrapper = (Polygon) original.convexHull();
try {
boolean done = false;
while (!done) {
done = true;
excesses = wrapper.difference(original);
for (int i = 0; i < excesses.getNumGeometries(); i++) {
excess = excesses.getGeometryN(i);
if (excess.getArea() / original.getArea() > areaThreshold) {
done = false; // excess too big - try to split then shrink
keepTotal = excess.intersection(original);
keepA = gf.createGeometryCollection(null);
keepB = gf.createGeometryCollection(null);
for (int j = 0; j < keepTotal.getNumGeometries(); j++) {
if (j < keepTotal.getNumGeometries() / 2) {
keepA = keepA.union(keepTotal.getGeometryN(j));
}
else {
keepB = keepB.union(keepTotal.getGeometryN(j));
}
}
chA = keepA.convexHull();
chB = keepB.convexHull();
keep = gf.createMultiPolygon(null);
if (chA instanceof Polygon) {
keep = keep.union(chA);
}
if (chB instanceof Polygon) {
keep = keep.union(chB);
}
elim = excess.difference(keep);
wrapper = (Polygon) wrapper.difference(elim);
}
}
}
new Assert(wrapper.getArea() >= original.getArea());
new Assert(wrapper.getArea() <= original.convexHull().getArea());
simplified = (Polygon) com.vividsolutions.jts.simplify.TopologyPreservingSimplifier.simplify(wrapper, lineThreshold);
new Assert(simplified.getNumPoints() <= original.getNumPoints());
new Assert(simplified.getNumInteriorRing() == 0);
new Assert(simplified.isSimple());
return simplified;
}
catch (Exception e) {
if (original.isSimple()) {
StringBuilder sb = new StringBuilder();
sb.append("Failed to simplify non-complex polygon!");
sb.append("\noriginal: " + original.toText());
sb.append("\nwrapper: " + (null == wrapper ? "" : wrapper.toText()));
sb.append("\nsimplified: " + (null == simplified ? "" : simplified.toText()));
sb.append("\nkeep: " + (null == keep ? "" : keep.toText()));
sb.append("\nelim: " + (null == elim ? "" : elim.toText()));
logger.log(Level.SEVERE, sb.toString());
}
throw e;
}
}}