/**
* Test relation between this Pnt and circumcircle of a simplex.
* @param simplex the simplex (as an array of Pnts)
* @return -1, 0, or +1 for inside, on, or outside of circumcircle
*/
public int vsCircumcircle(Pnt[] simplex)
{
Pnt[] matrix = new Pnt[simplex.Length + 1];
for (int i = 0; i < simplex.Length; i++)
{
matrix[i] = simplex[i].extend(new double[] { 1, simplex[i].dot(simplex[i]) });
}
matrix[simplex.Length] = this.extend(new double[] { 1, this.dot(this) });
double d = determinant(matrix);
int result = -1;
if (d > 0)
{
result = 1;
}
else if (d == 0)
{
result = 0;
}
if (content(simplex) < 0)
{
result = -result;
}
return(result);
}
/**
* Locate the triangle with point (a Pnt) inside (or on) it.
* @param point the Pnt to locate
* @return triangle (Simplex<Pnt>) that holds the point; null if no such triangle
*/
public Simplex locate(Pnt point) {
Simplex triangle = mostRecent;
if (!this.contains(triangle)) triangle = null;
// Try a directed walk (this works fine in 2D, but can fail in 3D)
Set visited = new HashSet();
while (triangle != null) {
if (visited.contains(triangle)) { // This should never happen
Console.WriteLine("Warning: Caught in a locate loop");
break;
}
visited.add(triangle);
// Corner opposite point
Pnt corner = point.isOutside((Pnt[]) triangle.toArray(new Pnt[0]));
if (corner == null) return triangle;
triangle = this.neighborOpposite(corner, triangle);
}
// No luck; try brute force
Console.WriteLine("Warning: Checking all triangles for " + point);
for (Iterator it = this.iterator(); it.hasNext();) {
Simplex tri = (Simplex) it.next();
if (point.isOutside((Pnt[]) tri.toArray(new Pnt[0])) == null) return tri;
}
// No such triangle
Console.WriteLine("Warning: No triangle holds " + point);
return null;
}
/**
* Main program (used for testing).
*/
public static void main(String[] args)
{
Pnt p = new Pnt(1, 2, 3);
Console.WriteLine("Pnt created: " + p);
Pnt[] matrix1 = { new Pnt(1, 2), new Pnt(3, 4) };
Pnt[] matrix2 = { new Pnt(7, 0, 5), new Pnt(2, 4, 6), new Pnt(3, 8, 1) };
Console.WriteLine("Results should be -2 and -288: ");
Console.WriteLine(determinant(matrix1) + " " + determinant(matrix2));
Pnt p1 = new Pnt(1, 1); Pnt p2 = new Pnt(-1, 1);
Console.WriteLine("Angle between " + p1 + " and " + p2 + ": " + p1.angle(p2));
Console.WriteLine(p1 + " subtract " + p2 + ": " + p1.subtract(p2));
Pnt v0 = new Pnt(0, 0), v1 = new Pnt(1, 1), v2 = new Pnt(2, 2);
Pnt[] vs = { v0, new Pnt(0, 1), new Pnt(1, 0) };
Pnt vp = new Pnt(.1, .1);
Console.WriteLine(vp + " isInside " + toString(vs) + ": " + vp.isInside(vs));
Console.WriteLine(v1 + " isInside " + toString(vs) + ": " + v1.isInside(vs));
Console.WriteLine(vp + " vsCircumcircle " + toString(vs) + ": " +
vp.vsCircumcircle(vs));
Console.WriteLine(v1 + " vsCircumcircle " + toString(vs) + ": " +
v1.vsCircumcircle(vs));
Console.WriteLine(v2 + " vsCircumcircle " + toString(vs) + ": " +
v2.vsCircumcircle(vs));
Console.WriteLine("Circumcenter of " + toString(vs) + " is " + circumcenter(vs));
}
/* Basic Drawing Methods */
/**
* Draw a point.
* @param point the Pnt to draw
*/
public void draw(Pnt point)
{
int r = pointRadius;
int x = (int)point.coord(0);
int y = (int)point.coord(1);
g.fillOval(x - r, y - r, r + r, r + r);
}
/**
* Perpendicular bisector of two Pnts.
* Works in any dimension. The coefficients are returned as a Pnt of one
* higher dimension (e.g., (A,B,C,D) for an equation of the form
* Ax + By + Cz + D = 0).
* @param point the other point
* @return the coefficients of the perpendicular bisector
*/
public Pnt bisector(Pnt point)
{
int dim = dimCheck(point);
Pnt diff = this.subtract(point);
Pnt sum = this.add(point);
double dot = diff.dot(sum);
return(diff.extend(new double[] { -dot / 2 }));
}
/**
* Check that dimensions match.
* @param p the Pnt to check (against this Pnt)
* @return the dimension of the Pnts
* @throws IllegalArgumentException if dimension fail to match
*/
public int dimCheck(Pnt p)
{
int len = this.coordinates.Length;
if (len != p.coordinates.Length)
{
throw new InvalidOperationException("Dimension mismatch");
}
return(len);
}
/**
* Add.
* @param p the other Pnt
* @return a new Pnt = this + p
*/
public Pnt add(Pnt p)
{
int len = dimCheck(p);
double[] coords = new double[len];
for (int i = 0; i < len; i++)
{
coords[i] = this.coordinates[i] + p.coordinates[i];
}
return(new Pnt(coords));
}
/**
* Dot product.
* @param p the other Pnt
* @return dot product of this Pnt and p
*/
public double dot(Pnt p)
{
int len = dimCheck(p);
double sum = 0;
for (int i = 0; i < len; i++)
{
sum += this.coordinates[i] * p.coordinates[i];
}
return(sum);
}
/**
* Draw all the Voronoi edges.
*/
public void drawAllVoronoi()
{
// Loop through all the edges of the DT (each is done twice)
for (Iterator it = dt.iterator(); it.hasNext();)
{
Simplex triangle = (Simplex)it.next();
for (Iterator otherIt = dt.neighbors(triangle).iterator(); otherIt.hasNext();)
{
Simplex other = (Simplex)otherIt.next();
Pnt p = Pnt.circumcenter((Pnt[])triangle.toArray(new Pnt[0]));
Pnt q = Pnt.circumcenter((Pnt[])other.toArray(new Pnt[0]));
draw(p, q);
}
}
}
/**
* Draw a circle.
* @param center the center of the circle
* @param radius the circle's radius
* @param fillColor; null implies no fill
*/
public void draw(Pnt center, double radius, Color fillColor)
{
int x = (int)center.coord(0);
int y = (int)center.coord(1);
int r = (int)radius;
if (fillColor != null)
{
Color temp = g.getColor();
g.setColor(fillColor);
g.fillOval(x - r, y - r, r + r, r + r);
g.setColor(temp);
}
g.drawOval(x - r, y - r, r + r, r + r);
}
/* Pnts as simplices */
/**
* Determine the signed content (i.e., area or volume, etc.) of a simplex.
* @param simplex the simplex (as an array of Pnts)
* @return the signed content of the simplex
*/
public static double content(Pnt[] simplex)
{
Pnt[] matrix = new Pnt[simplex.Length];
for (int i = 0; i < matrix.Length; i++)
{
matrix[i] = simplex[i].extend(new double[] { 1 });
}
int fact = 1;
for (int i = 1; i < matrix.Length; i++)
{
fact = fact * i;
}
return(determinant(matrix) / fact);
}
/**
* Mouse press.
* @param e the MouseEvent
*/
public void mousePressed(MouseEvent e)
{
if (e.getComponent() != this)
{
return;
}
Pnt point = new Pnt(e.getX(), e.getY());
if (debug)
{
Console.WriteLine("Click " + point);
}
dt.delaunayPlace(point);
repaint();
}
/**
* Test if this Pnt is on a simplex.
* @param simplex the simplex (an array of Pnts)
* @return the simplex Pnt that "witnesses" on-ness (or null if not on)
*/
public Pnt isOn(Pnt[] simplex)
{
int[] result = this.relation(simplex);
Pnt witness = null;
for (int i = 0; i < result.Length; i++)
{
if (result[i] == 0)
{
witness = simplex[i];
}
else if (result[i] > 0)
{
return(null);
}
}
return(witness);
}
/**
* Place a new point site into the DT.
* @param site the new Pnt
* @return set of all new triangles created
*/
public Set delaunayPlace(Pnt site) {
Set newTriangles = new HashSet();
Set oldTriangles = new HashSet();
Set doneSet = new HashSet();
LinkedList waitingQ = new LinkedList();
// Locate containing triangle
if (debug) Console.WriteLine("Locate");
Simplex triangle = locate(site);
// Give up if no containing triangle or if site is already in DT
var triangle_null = triangle == null;
if (triangle_null || triangle.contains(site)) return newTriangles;
// Find Delaunay cavity (those triangles with site in their circumcircles)
if (debug) Console.WriteLine("Cavity");
waitingQ.add(triangle);
while (!waitingQ.isEmpty()) {
triangle = (Simplex) waitingQ.removeFirst();
if (site.vsCircumcircle((Pnt[]) triangle.toArray(new Pnt[0])) == 1) continue;
oldTriangles.add(triangle);
Iterator it = this.neighbors(triangle).iterator();
for (; it.hasNext();) {
Simplex tri = (Simplex) it.next();
if (doneSet.contains(tri)) continue;
doneSet.add(tri);
waitingQ.add(tri);
}
}
// Create the new triangles
if (debug) Console.WriteLine("Create");
for (Iterator it = Simplex.boundary(oldTriangles).iterator(); it.hasNext();) {
Set facet = (Set) it.next();
facet.add(site);
newTriangles.add(new Simplex(facet));
}
// Replace old triangles with new triangles
if (debug) Console.WriteLine("Update");
this.update(oldTriangles, newTriangles);
// Update mostRecent triangle
if (!newTriangles.isEmpty()) mostRecent = (Simplex) newTriangles.iterator().next();
return newTriangles;
}
/**
* Locate the triangle with point (a Pnt) inside (or on) it.
* @param point the Pnt to locate
* @return triangle (Simplex<Pnt>) that holds the point; null if no such triangle
*/
public Simplex locate(Pnt point)
{
Simplex triangle = mostRecent;
if (!this.contains(triangle))
{
triangle = null;
}
// Try a directed walk (this works fine in 2D, but can fail in 3D)
Set visited = new HashSet();
while (triangle != null)
{
if (visited.contains(triangle)) // This should never happen
{
Console.WriteLine("Warning: Caught in a locate loop");
break;
}
visited.add(triangle);
// Corner opposite point
Pnt corner = point.isOutside((Pnt[])triangle.toArray(new Pnt[0]));
if (corner == null)
{
return(triangle);
}
triangle = this.neighborOpposite(corner, triangle);
}
// No luck; try brute force
Console.WriteLine("Warning: Checking all triangles for " + point);
for (Iterator it = this.iterator(); it.hasNext();)
{
Simplex tri = (Simplex)it.next();
if (point.isOutside((Pnt[])tri.toArray(new Pnt[0])) == null)
{
return(tri);
}
}
// No such triangle
Console.WriteLine("Warning: No triangle holds " + point);
return(null);
}
/**
* Draw all the empty circles (one for each triangle) of the DT.
*/
public void drawAllCircles()
{
// Loop through all triangles of the DT
for (Iterator it = dt.iterator(); it.hasNext();)
{
Simplex triangle = (Simplex)it.next();
for (Iterator otherIt = initialTriangle.iterator(); otherIt.hasNext();)
{
Pnt p = (Pnt)otherIt.next();
if (triangle.contains(p))
{
triangle = null;
break;
}
}
if (triangle != null)
{
Pnt c = Pnt.circumcenter((Pnt[])triangle.toArray(new Pnt[0]));
double radius = c.subtract((Pnt)triangle.iterator().next()).magnitude();
draw(c, radius, null);
}
}
}
/**
* Circumcenter of a simplex.
* @param simplex the simplex (as an array of Pnts)
* @return the circumcenter (a Pnt) of simplex
*/
public static Pnt circumcenter(Pnt[] simplex)
{
int dim = simplex[0].dimension();
if (simplex.Length - 1 != dim)
{
throw new InvalidOperationException("Dimension mismatch");
}
Pnt[] matrix = new Pnt[dim];
for (int i = 0; i < dim; i++)
{
matrix[i] = simplex[i].bisector(simplex[i + 1]);
}
Pnt hCenter = cross(matrix); // Center in homogeneous coordinates
double last = hCenter.coordinates[dim];
double[] result = new double[dim];
for (int i = 0; i < dim; i++)
{
result[i] = hCenter.coordinates[i] / last;
}
return(new Pnt(result));
}
/**
* Equality.
* @param other the other Object to compare to
* @return true iff the Pnts have the same coordinates
*/
public bool equals(object other)
{
// ficme: jsc should insert parenthesis
var other_is_Pnt = (other is Pnt);
if (!other_is_Pnt)
{
return(false);
}
Pnt p = (Pnt)other;
if (this.coordinates.Length != p.coordinates.Length)
{
return(false);
}
for (int i = 0; i < this.coordinates.Length; i++)
{
if (this.coordinates[i] != p.coordinates[i])
{
return(false);
}
}
return(true);
}
/**
* Angle (in radians) between two Pnts (treated as vectors).
* @param p the other Pnt
* @return the angle (in radians) between the two Pnts
*/
public double angle(Pnt p)
{
return(Math.Acos(this.dot(p) / (this.magnitude() * p.magnitude())));
}
/**
* Draw a line segment.
* @param endA one endpoint
* @param endB the other endpoint
*/
public void draw(Pnt endA, Pnt endB)
{
g.drawLine((int)endA.coord(0), (int)endA.coord(1),
(int)endB.coord(0), (int)endB.coord(1));
}
/**
* Draw a line segment.
* @param endA one endpoint
* @param endB the other endpoint
*/
public void draw(Pnt endA, Pnt endB)
{
g.drawLine((int)endA.coord(0), (int)endA.coord(1),
(int)endB.coord(0), (int)endB.coord(1));
}
/**
* Mouse press.
* @param e the MouseEvent
*/
public void mousePressed(MouseEvent e)
{
if (e.getComponent() != this) return;
Pnt point = new Pnt(e.getX(), e.getY());
if (debug) Console.WriteLine("Click " + point);
dt.delaunayPlace(point);
repaint();
}
/**
* Circumcenter of a simplex.
* @param simplex the simplex (as an array of Pnts)
* @return the circumcenter (a Pnt) of simplex
*/
public static Pnt circumcenter(Pnt[] simplex)
{
int dim = simplex[0].dimension();
if (simplex.Length - 1 != dim)
throw new InvalidOperationException("Dimension mismatch");
Pnt[] matrix = new Pnt[dim];
for (int i = 0; i < dim; i++)
matrix[i] = simplex[i].bisector(simplex[i + 1]);
Pnt hCenter = cross(matrix); // Center in homogeneous coordinates
double last = hCenter.coordinates[dim];
double[] result = new double[dim];
for (int i = 0; i < dim; i++) result[i] = hCenter.coordinates[i] / last;
return new Pnt(result);
}
/**
* Test if this Pnt is inside a simplex.
* @param simplex the simplex (an arary of Pnts)
* @return true iff this Pnt is inside simplex.
*/
public bool isInside(Pnt[] simplex)
{
int[] result = this.relation(simplex);
for (int i = 0; i < result.Length; i++) if (result[i] >= 0) return false;
return true;
}
/**
* Test if this Pnt is outside of simplex.
* @param simplex the simplex (an array of Pnts)
* @return the simplex Pnt that "witnesses" outsideness (or null if not outside)
*/
public Pnt isOutside(Pnt[] simplex)
{
int[] result = this.relation(simplex);
for (int i = 0; i < result.Length; i++)
{
if (result[i] > 0) return simplex[i];
}
return null;
}
/**
* Check that dimensions match.
* @param p the Pnt to check (against this Pnt)
* @return the dimension of the Pnts
* @throws IllegalArgumentException if dimension fail to match
*/
public int dimCheck(Pnt p)
{
int len = this.coordinates.Length;
if (len != p.coordinates.Length)
throw new InvalidOperationException("Dimension mismatch");
return len;
}
/**
* Place a new point site into the DT.
* @param site the new Pnt
* @return set of all new triangles created
*/
public Set delaunayPlace(Pnt site)
{
Set newTriangles = new HashSet();
Set oldTriangles = new HashSet();
Set doneSet = new HashSet();
LinkedList waitingQ = new LinkedList();
// Locate containing triangle
if (debug)
{
Console.WriteLine("Locate");
}
Simplex triangle = locate(site);
// Give up if no containing triangle or if site is already in DT
var triangle_null = triangle == null;
if (triangle_null || triangle.contains(site))
{
return(newTriangles);
}
// Find Delaunay cavity (those triangles with site in their circumcircles)
if (debug)
{
Console.WriteLine("Cavity");
}
waitingQ.add(triangle);
while (!waitingQ.isEmpty())
{
triangle = (Simplex)waitingQ.removeFirst();
if (site.vsCircumcircle((Pnt[])triangle.toArray(new Pnt[0])) == 1)
{
continue;
}
oldTriangles.add(triangle);
Iterator it = this.neighbors(triangle).iterator();
for (; it.hasNext();)
{
Simplex tri = (Simplex)it.next();
if (doneSet.contains(tri))
{
continue;
}
doneSet.add(tri);
waitingQ.add(tri);
}
}
// Create the new triangles
if (debug)
{
Console.WriteLine("Create");
}
for (Iterator it = Simplex.boundary(oldTriangles).iterator(); it.hasNext();)
{
Set facet = (Set)it.next();
facet.add(site);
newTriangles.add(new Simplex(facet));
}
// Replace old triangles with new triangles
if (debug)
{
Console.WriteLine("Update");
}
this.update(oldTriangles, newTriangles);
// Update mostRecent triangle
if (!newTriangles.isEmpty())
{
mostRecent = (Simplex)newTriangles.iterator().next();
}
return(newTriangles);
}
/* Pnts as simplices */
/**
* Determine the signed content (i.e., area or volume, etc.) of a simplex.
* @param simplex the simplex (as an array of Pnts)
* @return the signed content of the simplex
*/
public static double content(Pnt[] simplex)
{
Pnt[] matrix = new Pnt[simplex.Length];
for (int i = 0; i < matrix.Length; i++)
matrix[i] = simplex[i].extend(new double[] { 1 });
int fact = 1;
for (int i = 1; i < matrix.Length; i++) fact = fact * i;
return determinant(matrix) / fact;
}
/**
* Add.
* @param p the other Pnt
* @return a new Pnt = this + p
*/
public Pnt add(Pnt p)
{
int len = dimCheck(p);
double[] coords = new double[len];
for (int i = 0; i < len; i++)
coords[i] = this.coordinates[i] + p.coordinates[i];
return new Pnt(coords);
}
/**
* Relation between this Pnt and a simplex (represented as an array of Pnts).
* Result is an array of signs, one for each vertex of the simplex, indicating
* the relation between the vertex, the vertex's opposite facet, and this
* Pnt. <pre>
* -1 means Pnt is on same side of facet
* 0 means Pnt is on the facet
* +1 means Pnt is on opposite side of facet</pre>
* @param simplex an array of Pnts representing a simplex
* @return an array of signs showing relation between this Pnt and the simplex
* @throws IllegalArgumentExcpetion if the simplex is degenerate
*/
public int[] relation(Pnt[] simplex)
{
/* In 2D, we compute the cross of this matrix:
* 1 1 1 1
* p0 a0 b0 c0
* p1 a1 b1 c1
* where (a, b, c) is the simplex and p is this Pnt. The result
* is a vector in which the first coordinate is the signed area
* (all signed areas are off by the same constant factor) of
* the simplex and the remaining coordinates are the *negated*
* signed areas for the simplices in which p is substituted for
* each of the vertices. Analogous results occur in higher dimensions.
*/
int dim = simplex.Length - 1;
if (this.dimension() != dim)
throw new InvalidOperationException("Dimension mismatch");
/* Create and load the matrix */
Pnt[] matrix = new Pnt[dim + 1];
/* First row */
double[] coords = new double[dim + 2];
for (int j = 0; j < coords.Length; j++) coords[j] = 1;
matrix[0] = new Pnt(coords);
/* Other rows */
for (int i = 0; i < dim; i++)
{
coords[0] = this.coordinates[i];
for (int j = 0; j < simplex.Length; j++)
coords[j + 1] = simplex[j].coordinates[i];
matrix[i + 1] = new Pnt(coords);
}
/* Compute and analyze the vector of areas/volumes/contents */
Pnt vector = cross(matrix);
double content = vector.coordinates[0];
int[] result = new int[dim + 1];
for (int i = 0; i < result.Length; i++)
{
double value = vector.coordinates[i + 1];
if (Math.Abs(value) <= 1.0e-6 * Math.Abs(content)) result[i] = 0;
else if (value < 0) result[i] = -1;
else result[i] = 1;
}
if (content < 0)
{
for (int i = 0; i < result.Length; i++) result[i] = -result[i];
}
if (content == 0)
{
for (int i = 0; i < result.Length; i++) result[i] = Math.Abs(result[i]);
}
return result;
}
/**
* Angle (in radians) between two Pnts (treated as vectors).
* @param p the other Pnt
* @return the angle (in radians) between the two Pnts
*/
public double angle(Pnt p)
{
return Math.Acos(this.dot(p) / (this.magnitude() * p.magnitude()));
}
/**
* Test if this Pnt is on a simplex.
* @param simplex the simplex (an array of Pnts)
* @return the simplex Pnt that "witnesses" on-ness (or null if not on)
*/
public Pnt isOn(Pnt[] simplex)
{
int[] result = this.relation(simplex);
Pnt witness = null;
for (int i = 0; i < result.Length; i++)
{
if (result[i] == 0) witness = simplex[i];
else if (result[i] > 0) return null;
}
return witness;
}
/**
* Perpendicular bisector of two Pnts.
* Works in any dimension. The coefficients are returned as a Pnt of one
* higher dimension (e.g., (A,B,C,D) for an equation of the form
* Ax + By + Cz + D = 0).
* @param point the other point
* @return the coefficients of the perpendicular bisector
*/
public Pnt bisector(Pnt point)
{
int dim = dimCheck(point);
Pnt diff = this.subtract(point);
Pnt sum = this.add(point);
double dot = diff.dot(sum);
return diff.extend(new double[] { -dot / 2 });
}
/**
* Test relation between this Pnt and circumcircle of a simplex.
* @param simplex the simplex (as an array of Pnts)
* @return -1, 0, or +1 for inside, on, or outside of circumcircle
*/
public int vsCircumcircle(Pnt[] simplex)
{
Pnt[] matrix = new Pnt[simplex.Length + 1];
for (int i = 0; i < simplex.Length; i++)
matrix[i] = simplex[i].extend(new double[] { 1, simplex[i].dot(simplex[i]) });
matrix[simplex.Length] = this.extend(new double[] { 1, this.dot(this) });
double d = determinant(matrix);
int result = -1;
if (d > 0)
result = 1;
else if (d == 0)
result = 0;
if (content(simplex) < 0) result = -result;
return result;
}
/* Pnts as matrices */
/**
* Create a String for a matrix.
* @param matrix the matrix (an array of Pnts)
* @return a String represenation of the matrix
*/
public static string toString(Pnt[] matrix)
{
var buf = new StringBuilder("{");
for (int i = 0; i < matrix.Length; i++) buf.Append(" " + matrix[i]);
buf.Append(" }");
return buf.ToString();
}
/**
* Main program (used for testing).
*/
public static void main(String[] args)
{
Pnt p = new Pnt(1, 2, 3);
Console.WriteLine("Pnt created: " + p);
Pnt[] matrix1 = { new Pnt(1, 2), new Pnt(3, 4) };
Pnt[] matrix2 = { new Pnt(7, 0, 5), new Pnt(2, 4, 6), new Pnt(3, 8, 1) };
Console.WriteLine("Results should be -2 and -288: ");
Console.WriteLine(determinant(matrix1) + " " + determinant(matrix2));
Pnt p1 = new Pnt(1, 1); Pnt p2 = new Pnt(-1, 1);
Console.WriteLine("Angle between " + p1 + " and " + p2 + ": " + p1.angle(p2));
Console.WriteLine(p1 + " subtract " + p2 + ": " + p1.subtract(p2));
Pnt v0 = new Pnt(0, 0), v1 = new Pnt(1, 1), v2 = new Pnt(2, 2);
Pnt[] vs = { v0, new Pnt(0, 1), new Pnt(1, 0) };
Pnt vp = new Pnt(.1, .1);
Console.WriteLine(vp + " isInside " + toString(vs) + ": " + vp.isInside(vs));
Console.WriteLine(v1 + " isInside " + toString(vs) + ": " + v1.isInside(vs));
Console.WriteLine(vp + " vsCircumcircle " + toString(vs) + ": " +
vp.vsCircumcircle(vs));
Console.WriteLine(v1 + " vsCircumcircle " + toString(vs) + ": " +
v1.vsCircumcircle(vs));
Console.WriteLine(v2 + " vsCircumcircle " + toString(vs) + ": " +
v2.vsCircumcircle(vs));
Console.WriteLine("Circumcenter of " + toString(vs) + " is " + circumcenter(vs));
}
/**
* Compute the determinant of a matrix (array of Pnts).
* This is not an efficient implementation, but should be adequate
* for low dimension.
* @param matrix the matrix as an array of Pnts
* @return the determinnant of the input matrix
* @throws IllegalArgumentException if dimensions are wrong
*/
public static double determinant(Pnt[] matrix)
{
if (matrix.Length != matrix[0].dimension())
throw new InvalidOperationException("Matrix is not square");
var columns = new bool[matrix.Length];
for (int i = 0; i < matrix.Length; i++) columns[i] = true;
return determinant(matrix, 0, columns);
}
/* Basic Drawing Methods */
/**
* Draw a point.
* @param point the Pnt to draw
*/
public void draw(Pnt point)
{
int r = pointRadius;
int x = (int)point.coord(0);
int y = (int)point.coord(1);
g.fillOval(x - r, y - r, r + r, r + r);
}
/**
* Compute the determinant of a submatrix specified by starting row
* and by "active" columns.
* @param matrix the matrix as an array of Pnts
* @param row the starting row
* @param columns a boolean array indicating the "active" columns
* @return the determinant of the specified submatrix
* @throws ArrayIndexOutOfBoundsException if dimensions are wrong
*/
private static double determinant(Pnt[] matrix, int row, bool[] columns)
{
if (row == matrix.Length) return 1;
double sum = 0;
int sign = 1;
for (int col = 0; col < columns.Length; col++)
{
// fixme: ldelem bool should be supported
var columns_col = columns[col];
if (columns_col)
{
columns[col] = false;
sum += sign * matrix[row].coordinates[col] *
determinant(matrix, row + 1, columns);
columns[col] = true;
sign = -sign;
}
}
return sum;
}
/**
* Draw a circle.
* @param center the center of the circle
* @param radius the circle's radius
* @param fillColor; null implies no fill
*/
public void draw(Pnt center, double radius, Color fillColor)
{
int x = (int)center.coord(0);
int y = (int)center.coord(1);
int r = (int)radius;
if (fillColor != null)
{
Color temp = g.getColor();
g.setColor(fillColor);
g.fillOval(x - r, y - r, r + r, r + r);
g.setColor(temp);
}
g.drawOval(x - r, y - r, r + r, r + r);
}
/**
* Compute generalized cross-product of the rows of a matrix.
* The result is a Pnt perpendicular (as a vector) to each row of
* the matrix. This is not an efficient implementation, but should
* be adequate for low dimension.
* @param matrix the matrix of Pnts (one less row than the Pnt dimension)
* @return a Pnt perpendicular to each row Pnt
* @throws IllegalArgumentException if matrix is wrong shape
*/
public static Pnt cross(Pnt[] matrix)
{
int len = matrix.Length + 1;
if (len != matrix[0].dimension())
throw new InvalidOperationException("Dimension mismatch");
var columns = new bool[len];
for (int i = 0; i < len; i++) columns[i] = true;
double[] result = new double[len];
int sign = 1;
try
{
for (int i = 0; i < len; i++)
{
columns[i] = false;
result[i] = sign * determinant(matrix, 0, columns);
columns[i] = true;
sign = -sign;
}
}
catch //(ArrayIndexOutOfBoundsException e)
{
throw new InvalidOperationException("Matrix is wrong shape");
}
return new Pnt(result);
}
/**
* Dot product.
* @param p the other Pnt
* @return dot product of this Pnt and p
*/
public double dot(Pnt p)
{
int len = dimCheck(p);
double sum = 0;
for (int i = 0; i < len; i++)
sum += this.coordinates[i] * p.coordinates[i];
return sum;
}
/**
* Relation between this Pnt and a simplex (represented as an array of Pnts).
* Result is an array of signs, one for each vertex of the simplex, indicating
* the relation between the vertex, the vertex's opposite facet, and this
* Pnt. <pre>
* -1 means Pnt is on same side of facet
* 0 means Pnt is on the facet
* +1 means Pnt is on opposite side of facet</pre>
* @param simplex an array of Pnts representing a simplex
* @return an array of signs showing relation between this Pnt and the simplex
* @throws IllegalArgumentExcpetion if the simplex is degenerate
*/
public int[] relation(Pnt[] simplex)
{
/* In 2D, we compute the cross of this matrix:
* 1 1 1 1
* p0 a0 b0 c0
* p1 a1 b1 c1
* where (a, b, c) is the simplex and p is this Pnt. The result
* is a vector in which the first coordinate is the signed area
* (all signed areas are off by the same constant factor) of
* the simplex and the remaining coordinates are the *negated*
* signed areas for the simplices in which p is substituted for
* each of the vertices. Analogous results occur in higher dimensions.
*/
int dim = simplex.Length - 1;
if (this.dimension() != dim)
{
throw new InvalidOperationException("Dimension mismatch");
}
/* Create and load the matrix */
Pnt[] matrix = new Pnt[dim + 1];
/* First row */
double[] coords = new double[dim + 2];
for (int j = 0; j < coords.Length; j++)
{
coords[j] = 1;
}
matrix[0] = new Pnt(coords);
/* Other rows */
for (int i = 0; i < dim; i++)
{
coords[0] = this.coordinates[i];
for (int j = 0; j < simplex.Length; j++)
{
coords[j + 1] = simplex[j].coordinates[i];
}
matrix[i + 1] = new Pnt(coords);
}
/* Compute and analyze the vector of areas/volumes/contents */
Pnt vector = cross(matrix);
double content = vector.coordinates[0];
int[] result = new int[dim + 1];
for (int i = 0; i < result.Length; i++)
{
double value = vector.coordinates[i + 1];
if (Math.Abs(value) <= 1.0e-6 * Math.Abs(content))
{
result[i] = 0;
}
else if (value < 0)
{
result[i] = -1;
}
else
{
result[i] = 1;
}
}
if (content < 0)
{
for (int i = 0; i < result.Length; i++)
{
result[i] = -result[i];
}
}
if (content == 0)
{
for (int i = 0; i < result.Length; i++)
{
result[i] = Math.Abs(result[i]);
}
}
return(result);
}