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geometric_separators/geometric_separators.pde
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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); | |
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) { | |
float num = (float)Math.sqrt(centerPoint.z - centerPoint.mag()); | |
return num / Math.abs(unitVector.z); | |
} | |
// Get the attributes for the sphere separators | |
float[] getSphereAttr(PVector centerPoint, PVector unitVector, float radius) { | |
PVector center = centerPoint.sub(unitVector.mult(radius)); | |
float x = center.x - radius; | |
float y = center.y - radius; | |
float z = center.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); | |
} | |
} |