/// <summary>
/// This routine simply tests for robustness of the ToString function.
/// </summary>
private static void WriteRepeatedSqrt(DD xdd)
{
int count = 0;
while (xdd.ToDoubleValue() > 1e-300)
{
count++;
// if (count == 100)
// count = count;
double x = xdd.ToDoubleValue();
var xSqrt = xdd.Sqrt();
string s = xSqrt.ToString();
// System.Console.WriteLine((count + ": " + s);
var xSqrt2 = DD.Parse(s);
var xx = xSqrt2.Multiply(xSqrt2);
double err = Math.Abs(xx.ToDoubleValue() - x);
// assertTrue(err < 1e-10);
xdd = xSqrt;
// square roots converge on 1 - stop when very close
var distFrom1DD = xSqrt.Subtract(DD.ValueOf(1.0));
double distFrom1 = distFrom1DD.ToDoubleValue();
if (Math.Abs(distFrom1) < 1.0e-40)
{
break;
}
}
}
/// <summary>
/// Tests if a point is inside the circle defined by
/// the triangle with vertices a, b, c (oriented counter-clockwise).
/// </summary>
/// <remarks>
/// The computation uses <see cref="DD"/> arithmetic for robustness.
/// </remarks>
/// <param name="a">A vertex of the triangle</param>
/// <param name="b">A vertex of the triangle</param>
/// <param name="c">A vertex of the triangle</param>
/// <param name="p">The point to test</param>
/// <returns>true if this point is inside the circle defined by the points a, b, c</returns>
public static bool IsInCircleDDSlow(
Coordinate a, Coordinate b, Coordinate c,
Coordinate p)
{
DD px = DD.ValueOf(p.X);
DD py = DD.ValueOf(p.Y);
DD ax = DD.ValueOf(a.X);
DD ay = DD.ValueOf(a.Y);
DD bx = DD.ValueOf(b.X);
DD by = DD.ValueOf(b.Y);
DD cx = DD.ValueOf(c.X);
DD cy = DD.ValueOf(c.Y);
DD aTerm = (ax.Multiply(ax).Add(ay.Multiply(ay)))
.Multiply(TriAreaDDSlow(bx, by, cx, cy, px, py));
DD bTerm = (bx.Multiply(bx).Add(by.Multiply(by)))
.Multiply(TriAreaDDSlow(ax, ay, cx, cy, px, py));
DD cTerm = (cx.Multiply(cx).Add(cy.Multiply(cy)))
.Multiply(TriAreaDDSlow(ax, ay, bx, by, px, py));
DD pTerm = (px.Multiply(px).Add(py.Multiply(py)))
.Multiply(TriAreaDDSlow(ax, ay, bx, by, cx, cy));
DD sum = aTerm.Subtract(bTerm).Add(cTerm).Subtract(pTerm);
bool isInCircle = sum.ToDoubleValue() > 0;
return(isInCircle);
}
private static void CheckErrorBound(String tag, DD x, DD y, double errBound)
{
DD err = x.Subtract(y).Abs();
Console.WriteLine(tag + " err=" + err);
var isWithinEps = err.ToDoubleValue() <= errBound;
Assert.True(isWithinEps);
}
private static void CheckParse(String str, DD expectedVal,
double relErrBound)
{
DD xdd = DD.Parse(str);
double err = xdd.Subtract(expectedVal).ToDoubleValue();
double relErr = err / xdd.ToDoubleValue();
Console.WriteLine("Parsed= " + xdd + " rel err= " + relErr);
Assert.IsTrue(err <= relErrBound);
}
/// <summary>
/// This routine simply tests for robustness of the toString function.
/// </summary>
static void WriteRepeatedSqr(DD xdd)
{
if (xdd.GreaterOrEqualThan(DD.ValueOf(1)))
{
throw new ArgumentException("Argument must be < 1");
}
int count = 0;
while (xdd.ToDoubleValue() > 1e-300)
{
count++;
double x = xdd.ToDoubleValue();
var xSqr = xdd.Sqr();
string s = xSqr.ToString();
// System.Console.WriteLine(count + ": " + s);
var xSqr2 = DD.Parse(s);
xdd = xSqr;
}
}
/// <summary>
/// Tests if a point is inside the circle defined by
/// the triangle with vertices a, b, c (oriented counter-clockwise).
/// </summary>
/// <remarks>
/// The computation uses <see cref="DD"/> arithmetic for robustness, but a faster approach.
/// </remarks>
/// <param name="a">A vertex of the triangle</param>
/// <param name="b">A vertex of the triangle</param>
/// <param name="c">A vertex of the triangle</param>
/// <param name="p">The point to test</param>
/// <returns>true if this point is inside the circle defined by the points a, b, c</returns>
public static bool IsInCircleDDFast(
Coordinate a, Coordinate b, Coordinate c,
Coordinate p)
{
DD aTerm = (DD.Sqr(a.X) + DD.Sqr(a.Y)) * TriAreaDDFast(b, c, p);
DD bTerm = (DD.Sqr(b.X) + DD.Sqr(b.Y)) * TriAreaDDFast(a, c, p);
DD cTerm = (DD.Sqr(c.X) + DD.Sqr(c.Y)) * TriAreaDDFast(a, b, p);
DD pTerm = (DD.Sqr(p.X) + DD.Sqr(p.Y)) * TriAreaDDFast(a, b, c);
DD sum = aTerm - bTerm + cTerm - pTerm;
bool isInCircle = sum.ToDoubleValue() > 0;
return(isInCircle);
}
/// <summary>
/// Tests that printing values with many decimal places works.
/// This tests the correctness and robustness of both output and input.
/// </summary>
static void WriteAndReadSqrt(double x)
{
DD xdd = DD.ValueOf(x);
DD xSqrt = xdd.Sqrt();
String s = xSqrt.ToString();
// System.out.println(s);
DD xSqrt2 = DD.Parse(s);
DD xx = xSqrt2 * xSqrt2;
String xxStr = xx.ToString();
// System.out.println("==> " + xxStr);
DD xx2 = DD.Parse(xxStr);
double err = Math.Abs(xx2.ToDoubleValue() - x);
Assert.IsTrue(err < 1e-10);
}
/// <summary>
/// Computes the arctangent based on the Taylor series expansion
/// <para/>
/// arctan(x) = x - x^3 / 3 + x^5 / 5 - x^7 / 7 + ...
/// </summary>
/// <param name="x">The argument</param>
/// <returns>An approximation to the arctangent of the input</returns>
private static DD ArcTan(DD x)
{
var t = x;
var t2 = t.Sqr();
var at = new DD(0.0);
var two = new DD(2.0);
var k = 0;
var d = new DD(1.0);
var sign = 1;
while (t.ToDoubleValue() > DD.Epsilon)
{
k++;
at = sign < 0 ? at.Subtract(t.Divide(d)) : at.Add(t.Divide(d));
d = d.Add(two);
t = t.Multiply(t2);
sign = -sign;
}
Console.WriteLine("Computed DD.atan(): " + at
+ " Math.atan = " + Math.Atan(x.ToDoubleValue()));
return(at);
}
/// <summary>
///
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="c"></param>
/// <param name="p"></param>
/// <returns></returns>
public static bool IsInCircleDDNormalized(
Coordinate a, Coordinate b, Coordinate c,
Coordinate p)
{
DD adx = DD.ValueOf(a.X) - p.X;
DD ady = DD.ValueOf(a.Y) - p.Y;
DD bdx = DD.ValueOf(b.X) - p.X;
DD bdy = DD.ValueOf(b.Y) - p.Y;
DD cdx = DD.ValueOf(c.X) - p.X;
DD cdy = DD.ValueOf(c.Y) - p.Y;
DD abdet = adx * bdy - bdx * ady;
DD bcdet = bdx * cdy - cdx * bdy;
DD cadet = cdx * ady - adx * cdy;
DD alift = adx * adx + ady * ady;
DD blift = bdx * bdx + bdy * bdy;
DD clift = cdx * cdx + cdy * cdy;
DD sum = alift * bcdet + blift * cadet + clift * abdet;
bool isInCircle = sum.ToDoubleValue() > 0;
return(isInCircle);
}
/// <summary>
/// Tests if a point is inside the circle defined by the points a, b, c.
/// The computation uses <see cref="NetTopologySuite.Mathematics.DD"/> arithmetic for robustness.
/// </summary>
/// <param name="a">A vertex of the triangle</param>
/// <param name="b">A vertex of the triangle</param>
/// <param name="c">A vertex of the triangle</param>
/// <param name="p">The point to test</param>
/// <returns><value>true</value> if this point is inside the circle defined by the points a, b, c</returns>
public static bool IsInCircleDD3(
Coordinate a, Coordinate b, Coordinate c,
Coordinate p)
{
DD adx = DD.ValueOf(a.X) - (p.X);
DD ady = DD.ValueOf(a.Y) - (p.Y);
DD bdx = DD.ValueOf(b.X) - (p.X);
DD bdy = DD.ValueOf(b.Y) - (p.Y);
DD cdx = DD.ValueOf(c.X) - (p.X);
DD cdy = DD.ValueOf(c.Y) - (p.Y);
DD abdet = adx * bdy - (bdx * ady);
DD bcdet = bdx * cdy - (cdx * bdy);
DD cadet = cdx * ady - (adx * cdy);
DD alift = adx * adx - (ady * ady);
DD blift = bdx * bdx - (bdy * bdy);
DD clift = cdx * cdx - (cdy * cdy);
DD sum = alift * bcdet + blift * cadet + clift * abdet;
var isInCircle = sum.ToDoubleValue() > 0;
return(isInCircle);
}
/// <summary>
/// Computes the arctangent based on the Taylor series expansion
/// <para/>
/// arctan(x) = x - x^3 / 3 + x^5 / 5 - x^7 / 7 + ...
/// </summary>
/// <param name="x">The argument</param>
/// <returns>An approximation to the arctangent of the input</returns>
private static DD ArcTan(DD x)
{
var t = x;
var t2 = t.Sqr();
var at = new DD(0.0);
var two = new DD(2.0);
var k = 0;
var d = new DD(1.0);
var sign = 1;
while (t.ToDoubleValue() > DD.Epsilon)
{
k++;
at = sign < 0 ? at.Subtract(t.Divide(d)) : at.Add(t.Divide(d));
d = d.Add(two);
t = t.Multiply(t2);
sign = -sign;
}
Console.WriteLine("Computed DD.atan(): " + at
+ " Math.atan = " + Math.Atan(x.ToDoubleValue()));
return at;
}
/**
* This routine simply tests for robustness of the toString function.
*
* @param xdd
*/
static void WriteRepeatedSqr(DD xdd)
{
if (xdd.GreaterOrEqualThan(DD.ValueOf(1)))
throw new ArgumentException("Argument must be < 1");
int count = 0;
while (xdd.ToDoubleValue() > 1e-300) {
count++;
double x = xdd.ToDoubleValue();
DD xSqr = xdd.Sqr();
String s = xSqr.ToString();
Console.WriteLine(count + ": " + s);
DD xSqr2 = DD.Parse(s);
xdd = xSqr;
}
}
/**
* This routine simply tests for robustness of the toString function.
*
* @param xdd
*/
private static void WriteRepeatedSqrt(DD xdd)
{
int count = 0;
while (xdd.ToDoubleValue() > 1e-300) {
count++;
//if (count == 100)
// count = count;
double x = xdd.ToDoubleValue();
DD xSqrt = xdd.Sqrt();
String s = xSqrt.ToString();
// System.out.println(count + ": " + s);
DD xSqrt2 = DD.Parse(s);
DD xx = xSqrt2.Multiply(xSqrt2);
double err = Math.Abs(xx.ToDoubleValue() - x);
//assertTrue(err < 1e-10);
xdd = xSqrt;
// square roots converge on 1 - stop when very close
DD distFrom1DD = xSqrt.Subtract(DD.ValueOf(1.0));
double distFrom1 = distFrom1DD.ToDoubleValue();
if (Math.Abs(distFrom1) < 1.0e-40)
break;
}
}