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Added triangle intersection test. Seems to work on a few tests - need… 
…s some graphics fixes.
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Andrew Lawson authored and Andrew Lawson committed Dec 9, 2014
1 parent 11ce7a3 commit af83cfb
Showing 1 changed file with 120 additions and 21 deletions.
141 changes: 120 additions & 21 deletions geometric_separators.pde
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Expand Up @@ -4,7 +4,7 @@ import java.lang.Boolean;
import java.util.Random; import java.util.Random;
import org.jblas.*; import org.jblas.*;
import org.apache.commons.math3.linear.*; import org.apache.commons.math3.linear.*;
import org.apache.commons.math3.linear.SingularValueDecomposition; import org.apache.commons.math3.linear.LUDecomposition;


int reset_x = 140; int reset_x = 140;
int reset_y = 460; int reset_y = 460;
Expand Down Expand Up @@ -70,37 +70,39 @@ void mousePressed() {
// Get Radon point // Get Radon point
PVector getRadonPoint(ArrayList<PVector> points) { PVector getRadonPoint(ArrayList<PVector> points) {
PVector radonPoint = null; PVector radonPoint = null;
radonPoint = radonTetrx(points); radonPoint = inTetrahedron(points);
if (radonPoint == null) { if (radonPoint == null) {
radonPoint = radonIntersect(); System.out.println("Intersect");
radonPoint = intersectTri(points);
} }
return radonPoint; return radonPoint;
} }


// Tests if a point is within a tetrahedron // Tests if a point is within a tetrahedron
PVector radonTetra(ArrayList<PVector> points) { PVector inTetrahedron(ArrayList<PVector> points) {
PVector radonPoint = null; PVector radonPoint = null;
for (int i = 0; i < points.size(); i++) { for (int i = 0; i < points.size(); i++) {
ArrayList<PVector> pointsCopy = new ArrayList<PVector>(points); ArrayList<PVector> pointsCopy = new ArrayList<PVector>(points);
PVector testPoint = pointsCopy.get(i); PVector testPoint = pointsCopy.get(i);
pointsCopy.remove(i); pointsCopy.remove(i);
// Test if every determinant has the same sign // Test if every determinant has the same sign
RealMatrix d0Matrix = getDetMatrix(pointsCopy.get(0), pointsCopy.get(1), pointsCopy.get(2), pointsCopy.get(3); System.out.println(pointsCopy.size());
RealMatrix d1Matrix = getDetMatrix(testPoint, pointsCopy.get(1), pointsCopy.get(2), pointsCopy.get(3); RealMatrix d0Matrix = getDetMatrix(pointsCopy.get(0), pointsCopy.get(1), pointsCopy.get(2), pointsCopy.get(3));
RealMatrix d2Matrix = getDetMatrix(pointsCopy.get(0), testPoint, pointsCopy.get(2), pointsCopy.get(3); RealMatrix d1Matrix = getDetMatrix(testPoint, pointsCopy.get(1), pointsCopy.get(2), pointsCopy.get(3));
RealMatrix d3Matrix = getDetMatrix(pointsCopy.get(0), pointsCopy.get(1), testPoint, pointsCopy.get(3); RealMatrix d2Matrix = getDetMatrix(pointsCopy.get(0), testPoint, pointsCopy.get(2), pointsCopy.get(3));
RealMatrix d4Matrix = getDetMatrix(pointsCopy.get(0), pointsCopy.get(1), pointsCopy.get(2), testPoint; RealMatrix d3Matrix = getDetMatrix(pointsCopy.get(0), pointsCopy.get(1), testPoint, pointsCopy.get(3));
RealMatrix d4Matrix = getDetMatrix(pointsCopy.get(0), pointsCopy.get(1), pointsCopy.get(2), testPoint);
// Compute determinants // Compute determinants
ArrayList<double> detList = new ArrayList<double>(); ArrayList<Double> detList = new ArrayList<Double>();
double d0 = new SingularValueDecomposition(d0Matrix).getDeterminant(); double d0 = new LUDecomposition(d0Matrix).getDeterminant();
detList.add(d0); detList.add(d0);
double d1 = new SingularValueDecomposition(d1Matrix).getDeterminant(); double d1 = new LUDecomposition(d1Matrix).getDeterminant();
detList.add(d1); detList.add(d1);
double d2 = new SingularValueDecomposition(d2Matrix).getDeterminant(); double d2 = new LUDecomposition(d2Matrix).getDeterminant();
detList.add(d2); detList.add(d2);
double d3 = new SingularValueDecomposition(d3Matrix).getDeterminant(); double d3 = new LUDecomposition(d3Matrix).getDeterminant();
detList.add(d3); detList.add(d3);
double d4 = new SingularValueDecomposition(d4Matrix).getDeterminant(); double d4 = new LUDecomposition(d4Matrix).getDeterminant();
detList.add(d4); detList.add(d4);
// If the sign test passes // If the sign test passes
if (areSameSign(detList)) { if (areSameSign(detList)) {
Expand All @@ -112,8 +114,103 @@ PVector radonTetra(ArrayList<PVector> points) {
} }


// Tests if a ray intersects a triangle // Tests if a ray intersects a triangle
void radonIntersect(ArrayList<PVector> points) { PVector intersectTri(ArrayList<PVector> points) {
PVector point;
// Triangle of Points 1, 2, 3
point = testIntersect(points.get(0), points.get(1), points.get(2), points.get(3), points.get(4));
if (point != null) {
return point;
}
// Triangle of Points 1, 2, 4
point = testIntersect(points.get(0), points.get(1), points.get(3), points.get(2), points.get(4));
if (point != null) {
return point;
}
// Triangle of Points 1, 2, 5
point = testIntersect(points.get(0), points.get(1), points.get(4), points.get(2), points.get(3));
if (point != null) {
return point;
}
// Triangle of Points 1, 3, 4
point = testIntersect(points.get(0), points.get(2), points.get(3), points.get(1), points.get(4));
if (point != null) {
return point;
}
// Triangle of Points 1, 3, 5
point = testIntersect(points.get(0), points.get(2), points.get(4), points.get(2), points.get(3));
if (point != null) {
return point;
}
// Triangle of Points 1, 4, 5
point = testIntersect(points.get(0), points.get(3), points.get(4), points.get(1), points.get(2));
if (point != null) {
return point;
}
// Triangle of Points 2, 3, 4
point = testIntersect(points.get(1), points.get(2), points.get(3), points.get(0), points.get(4));
if (point != null) {
return point;
}
// Triangle of Points 2, 3, 5
point = testIntersect(points.get(1), points.get(2), points.get(4), points.get(0), points.get(3));
if (point != null) {
return point;
}
// Triangle of Points 2, 4, 5
point = testIntersect(points.get(1), points.get(3), points.get(4), points.get(0), points.get(2));
if (point != null) {
return point;
}
return null;
}


// Test ray triangle intersection
PVector testIntersect(PVector t1, PVector t2, PVector t3, PVector r1, PVector r2) {
PVector a = new PVector(t2.x, t2.y, t2.z);
a.sub(t1);
PVector b = new PVector(t3.x, t3.y, t3.z);
b.sub(t1);
PVector crossProd = a.cross(b);
// Get ray direction
PVector rayDir = new PVector(r2.x, r2.y, r2.z);
rayDir.sub(r1);
PVector w0 = new PVector(r1.x, r1.y, r1.z);
w0.sub(t1);
float x = -1 * crossProd.dot(w0);
float y = crossProd.dot(rayDir);
// Get intersection point of the plane
float r = x / y;
// No intersection
if (r < 0) {
System.out.println("No intersect.");
return null;
}
rayDir.mult(r);
PVector point = new PVector(r1.x, r1.y, r1.z);
point.add(rayDir);
// Is the point inside of the triangle?
float aDot = a.dot(a);
float abDot = a.dot(b);
float bDot = b.dot(b);
PVector w = new PVector(point.x, point.y, point.z);
w.sub(t1);
float waDot = w.dot(a);
float wbDot = w.dot(b);
float d = (abDot * abDot) - (aDot * bDot);
float s = ((abDot * wbDot) - (bDot * waDot)) / d;
float t = ((abDot * waDot) - (aDot * wbDot)) / d;
// Check if the point is outside
if (s < 0 || s > 1) {
System.out.println("Outside.");
return null;
}
else if (t < 0 || (s + t) > 1) {
System.out.println("Outside.");
return null;
}
// Otherwise it's inside we can return it
System.out.println("Inside");
return point;
} }


// Get the determinant matrix for a set of points // Get the determinant matrix for a set of points
Expand All @@ -125,13 +222,14 @@ RealMatrix getDetMatrix(PVector p1, PVector p2, PVector p3, PVector p4) {
} }


// Checks if a list of doubles all have the same sign // Checks if a list of doubles all have the same sign
boolean areSameSign(ArrayList<double> detList) { boolean areSameSign(ArrayList<Double> detList) {
int negDet = 0; int negDet = 0;
for (double det : detList) { for (double det : detList) {
if (det < 0) { if (det < 0) {
negDet++; negDet++;
} }
} }
System.out.println("negDet" + Integer.toString(negDet));
if (negDet == 0 || negDet == detList.size()) { if (negDet == 0 || negDet == detList.size()) {
return true; return true;
} }
Expand All @@ -141,12 +239,12 @@ boolean areSameSign(ArrayList<double> detList) {
} }


// Convert float array to double array // Convert float array to double array
float[][] toDoubleArray(float[][] array) { double[][] toDoubleArray(float[][] array) {
int numRows = array.length; int numRows = array.length;
int numCols = array[0].length; int numCols = array[0].length;
double[][] doubleArray = new double[numRows][numCols]; double[][] doubleArray = new double[numRows][numCols];
for (int i = 0; i < array.length { for (int i = 0; i < array.length; i++) {
for (int j = 0; j < array[i].length { for (int j = 0; j < array[i].length; j++) {
doubleArray[i][j] = (double)array[i][j]; doubleArray[i][j] = (double)array[i][j];
} }
} }
Expand Down Expand Up @@ -195,7 +293,7 @@ ArrayList<ArrayList<PVector>> samplePoints(ArrayList<PVector> input) {
pointList.add(inputCopy.get(index)); pointList.add(inputCopy.get(index));
inputCopy.remove(index); inputCopy.remove(index);
// Create new set on max size // Create new set on max size
if (pointList.size() == 4) { if (pointList.size() == 5) {
setList.add(pointList); setList.add(pointList);
pointList = new ArrayList<PVector>(); pointList = new ArrayList<PVector>();
} }
Expand All @@ -218,6 +316,7 @@ PVector approxCenterpoint(ArrayList<PVector> input) {
ArrayList<ArrayList<PVector>> setList = samplePoints(input); ArrayList<ArrayList<PVector>> setList = samplePoints(input);
ArrayList<PVector> radonList = new ArrayList<PVector>(); ArrayList<PVector> radonList = new ArrayList<PVector>();
for (ArrayList<PVector> list : setList) { for (ArrayList<PVector> list : setList) {
System.out.println(list.size());
PVector radonPoint = getRadonPoint(list); PVector radonPoint = getRadonPoint(list);
radonList.add(radonPoint); radonList.add(radonPoint);
} }
Expand Down

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