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import java.util.*;
import java.util.Map.*;
import java.lang.Boolean;
int reset_x = 140;
int reset_y = 460;
int reset_w = 100;
int reset_h = 25;
int calc_x = 250;
int calc_y = 460;
int calc_w = 100;
int calc_h = 25;
PShape reset;
PShape calculate;
PShape sphere;
PVector centerPoint;
ArrayList<PVector> rawInput = new ArrayList<PVector>();
Comparator<PVector> compareX, compareXRev, compareY, compareYRev;
// Triple used for returning three items
private class ReturnTriple {
public float sum;
public float dist;
public HashMap<PVector, Float> memoize;
public ReturnTriple(float sum, float dist, HashMap<PVector, Float> memoize) {
this.sum = sum;
this.dist = dist;
this.memoize = memoize;
}
}
// Double used for returning centerpoint and sphere
private class CenterAndSphere {
public PVector center;
public PShape sphere;
public CenterAndSphere(PVector center, PShape sphere) {
this.center = center;
this.sphere = sphere;
}
}
// Setup
void setup() {
background(255);
size(500,500,P2D);
// Create buttons
reset = createShape(RECT, reset_x, reset_y, reset_w, reset_h);
calculate = createShape(RECT, calc_x, calc_y, calc_w, calc_h);
sphere = null;
noLoop();
compareX = new Comparator<PVector>() {
public int compare(PVector p1, PVector p2) {
if (p1.x < p2.x) {
return -1;
}
else if (p2.x < p1.x) {
return 1;
}
else {
return 0;
}
}
};
compareXRev = new Comparator<PVector>() {
public int compare(PVector p1, PVector p2) {
if (p1.x > p2.x) {
return -1;
}
else if (p2.x > p1.x) {
return 1;
}
else {
return 0;
}
}
};
compareY = new Comparator<PVector>() {
public int compare(PVector p1, PVector p2) {
if (p1.y < p2.y) {
return -1;
}
else if (p2.y < p1.y) {
return 1;
}
else {
return 0;
}
}
};
compareYRev = new Comparator<PVector>() {
public int compare(PVector p1, PVector p2) {
if (p1.y > p2.y) {
return -1;
}
else if (p2.y > p1.y) {
return 1;
}
else {
return 0;
}
}
};
}
// On mouse press
void mousePressed() {
// If mouse presses reset button
if ((mouseX >= reset_x && mouseX <= (reset_x + reset_w)) &&
(mouseY >= reset_y && mouseY <= (reset_y + reset_h))) {
// Reset input and background
rawInput.clear();
centerPoint = null;
sphere = null;
}
// If mouse presses calculate button
else if ((mouseX >= calc_x && mouseX <= (calc_x + calc_w)) &&
(mouseY >= calc_y && mouseY <= (calc_y + calc_h))) {
// Run algorithm
CenterAndSphere returnVals = getSeparator(rawInput);
sphere = returnVals.sphere;
centerPoint = returnVals.center;
}
else {
// Create new 2D point from mouse coordinates
PVector prelim_point = new PVector(mouseX, mouseY);
// Lift to 3D with the squared magnitude of the original point
PVector final_point = new PVector(prelim_point.x, prelim_point.y,
(float)Math.pow(prelim_point.mag(), 2));
rawInput.add(final_point);
}
redraw();
}
// Get geometric separator
CenterAndSphere getSeparator(ArrayList<PVector> input) {
// Algorithm
// 1. Get centerpoint
PVector centerPoint = approxCenterpoint(input);
// 2. Get random unit vector in 3D
PVector unitVector = PVector.random3D();
// 3. Get radius
float radius = getRadius(centerPoint, unitVector);
// 4. Output sphere separator
float[] sphereAttributes = getSphereAttr(centerPoint, unitVector, radius);
PShape separator = createShape(ELLIPSE, sphereAttributes);
CenterAndSphere returnVals = new CenterAndSphere(centerPoint, separator);
return returnVals;
}
// Get radius for our separator
float getRadius(PVector centerPoint, PVector unitVector) {
System.out.println(centerPoint.mag());
System.out.println(centerPoint.z);
System.out.println(centerPoint.z - centerPoint.mag());
PVector centerPoint2D = new PVector(centerPoint.x, centerPoint.y);
float num = (float)Math.sqrt(centerPoint.z - Math.pow(centerPoint2D.mag(), 2));
return num / Math.abs(unitVector.z);
}
// Get the attributes for the sphere separators
float[] getSphereAttr(PVector centerPoint, PVector unitVector, float radius) {
PVector unitVectorCopy = new PVector(unitVector.x, unitVector.y, unitVector.z);
PVector centerPointCopy = new PVector(centerPoint.x, centerPoint.y);
unitVectorCopy.mult(radius);
centerPointCopy.sub(unitVectorCopy);
float x = centerPointCopy.x - radius;
float y = centerPointCopy.y - radius;
float z = centerPointCopy.z - radius;
float[] attributes = {x, y, 2 * radius, 2 * radius};
return attributes;
}
// Get geometric median
PVector getGeometricMedian(ArrayList<PVector> input) {
if (input.size() == 0) {
System.out.println("You don't have any input points!");
return null;
}
else if (input.size() == 1) {
return input.get(0);
}
else {
// Get the point
HashMap<PVector, Float> total = new HashMap<PVector, Float>();
HashMap<PVector, Float> x = getAxisMin(input, false);
HashMap<PVector, Float> y = getAxisMin(input, true);
Set<PVector> keys = x.keySet();
for (PVector key : keys) {
total.put(key, x.get(key) + y.get(key));
}
ArrayList<Entry<PVector, Float>> sortedList = new ArrayList<Entry<PVector, Float>>(total.entrySet());
Collections.sort(sortedList, new Comparator<Entry<PVector, Float>>() {
public int compare(Entry<PVector, Float> entry1, Entry<PVector, Float> entry2) {
return (int)(entry1.getValue() - entry2.getValue());
}
});
return sortedList.get(0).getKey();
}
}
// Sample input points into sets of 4
ArrayList<ArrayList<PVector>> samplePoints(ArrayList<PVector> input) {
ArrayList<PVector> inputCopy = new ArrayList<PVector>(input);
ArrayList<ArrayList<PVector>> setList = new ArrayList<ArrayList<PVector>>();
ArrayList<PVector> pointList = new ArrayList<PVector>();
// While there are still points, split into sets
while (inputCopy.size() > 0) {
double rnd = new Random().nextDouble();
int index = (int)(rnd * 10) % inputCopy.size();
// Add to set
pointList.add(inputCopy.get(index));
inputCopy.remove(index);
// Create new set on max size
if (pointList.size() == 4) {
setList.add(pointList);
pointList = new ArrayList<PVector>();
}
}
// Add most recent unempty set to list
if (pointList.size() > 0) {
setList.add(pointList);
}
return setList;
}
// Approximate the centerpoint
PVector approxCenterpoint(ArrayList<PVector> input) {
if (input.size() == 0) {
System.out.println("You don't have any input points!");
return null;
}
else {
// Algorithm
// Repeat 1 - 3 until one point remains and return that point
while (input.size() > 1) {
// 1. Sample points into groups of 4
ArrayList<ArrayList<PVector>> setList = samplePoints(input);
// 2. Compute radon point of each group (geometric median)
ArrayList<PVector> radonList = new ArrayList<PVector>();
for (ArrayList<PVector> list : setList) {
PVector radonPoint = getGeometricMedian(list);
radonList.add(radonPoint);
}
// 3. Set input to be new radon points
input = radonList;
}
return input.get(0);
}
}
// Calculate the distance with the input, memoization
float calcDist(int i, PVector currentPoint, ArrayList<PVector> input, boolean isY) {
// For each point before i, calculate distance to i
PVector prevPoint;
float sum = 0;
for (int j = 0; j < i; j++) {
prevPoint = input.get(j);
if (isY) {
sum += currentPoint.y - prevPoint.y;
}
else {
sum += currentPoint.x - prevPoint.x;
}
}
return sum;
}
// Calculate prev sum (i - 1) and the point distance from i
ReturnTriple calcLastSum(int i, PVector currentPoint, PVector nextPoint, ArrayList<PVector> input, HashMap<PVector, Float> memoize, boolean isY) {
// Calculate for squares
float sum, dist;
// If possible, reuse solution
if (memoize.containsKey(currentPoint)) {
sum = memoize.get(currentPoint);
}
// Otherwise, calculate
else {
sum = calcDist(i, currentPoint, input, isY);
memoize.put(currentPoint, sum);
}
if (isY) {
dist = nextPoint.y - currentPoint.y;
}
else {
dist = nextPoint.x - currentPoint.x;
}
return new ReturnTriple(sum, dist, memoize);
}
// Get sums and sums of squares of distances for an input
HashMap<PVector, Float> getSums(ArrayList<PVector> input, boolean isY) {
// Memoization hash tables
HashMap<PVector, Float> sumSquaresMemoize = new HashMap<PVector, Float>();
ReturnTriple returnTriple = new ReturnTriple(0, 0, null);
PVector currentPoint, nextPoint;
float sum, dist;
for (int i = 0; i < input.size() - 1; i++) {
currentPoint = input.get(i);
nextPoint = input.get(i + 1);
// Calculate sum of squares
returnTriple = calcLastSum(i, currentPoint, nextPoint, input, sumSquaresMemoize, isY);
sumSquaresMemoize = returnTriple.memoize;
sumSquaresMemoize.put(nextPoint, returnTriple.sum + (float)(i * Math.pow(returnTriple.dist, 2)) + (2 * i * returnTriple.dist));
}
return sumSquaresMemoize;
}
// Get minimum point for given axis input
HashMap<PVector, Float> getAxisMin(ArrayList<PVector> input, boolean isY) {
HashMap<PVector, Float> sumSquaresLeft, sumSquaresRight;
HashMap<PVector, Float> totalSumSquares = new HashMap<PVector, Float>();
// Get left distances
if (isY) {
Collections.sort(input, compareY);
}
else {
Collections.sort(input, compareX);
}
sumSquaresLeft = getSums(input, isY);
// Get right distances
if (isY) {
Collections.sort(input, compareYRev);
}
else {
Collections.sort(input, compareXRev);
}
sumSquaresRight = getSums(input, isY);
// Calculate total sum and store it
for (int i = 0; i < sumSquaresLeft.size(); i++) {
PVector point = input.get(i);
totalSumSquares.put(point, sumSquaresLeft.get(point) + sumSquaresRight.get(point));
}
return totalSumSquares;
}
// Draw
void draw() {
background(255);
shape(reset);
shape(calculate);
fill(50);
textSize(20);
text("Geometric Separators", 140, 20);
textSize(12);
text("Reset.", reset_x + 30, reset_y + 15);
text("Calculate.", calc_x + 25, calc_y + 15);
// Draw input
for (PVector point : rawInput) {
strokeWeight(4);
point(point.x, point.y);
}
// Draw center point
if (centerPoint != null) {
strokeWeight(6);
point(centerPoint.x, centerPoint.y);
System.out.println("x-coordinate: " + Float.toString(centerPoint.x));
System.out.println("y-coordinate: " + Float.toString(centerPoint.y));
}
// Draw separator sphere projected to 2D
if (sphere != null) {
strokeWeight(6);
shape(sphere);
}
}
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