From fe8a778365536cde36828302e416764744409c6b Mon Sep 17 00:00:00 2001 From: Galactic Ketchup Date: Tue, 24 Nov 2015 13:39:56 -0500 Subject: [PATCH] Complexity is Key I got it to work perfectly! The output is a beautiful Peirce Quincuncial projection. My main problem before was that this projection requires a complex function called cn(u,k), and every single definition on the internet was exceedingly vague. Luckily, I found a package online that could calculate cn for me, which meant that I didn't need to do any crazy integration or calculus whatsoever. --- .classpath | 3 +- bin/MapProjections.class | Bin 6660 -> 5901 bytes bin/Number.class | Bin 0 -> 2433 bytes input/color.png | Bin 428403 -> 428323 bytes output/myMap.jpg | Bin 13351 -> 103054 bytes src/MapProjections.java | 63 +++++++--------------- src/Number.java | 112 +++++++++++++++++++++++++++++++++++++++ 7 files changed, 134 insertions(+), 44 deletions(-) create mode 100644 bin/Number.class create mode 100644 src/Number.java diff --git a/.classpath b/.classpath index b8abb35..27f50e4 100644 --- a/.classpath +++ b/.classpath @@ -2,6 +2,7 @@ - + + diff --git a/bin/MapProjections.class b/bin/MapProjections.class index 72853413f8a148a9a7518647dcc32f150bba2e64..ad2325b30d7202bde80cd64da4f651b213f846f7 100644 GIT binary patch delta 3128 zcmaJ@e{_@O6@G4$d`*+DX=xis1hhbal+soKTUw;8P-u&V!!p;(^lS?yw4rSh+LXy3 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aa707ef..4d6bf30 100644 --- a/src/MapProjections.java +++ b/src/MapProjections.java @@ -5,7 +5,8 @@ import java.util.Scanner; import javax.imageio.ImageIO; -import org.apache.commons.math3.complex.Complex; +import ellipticFunctions.Jacobi; +import mfc.field.Complex; /** * @@ -16,10 +17,10 @@ import org.apache.commons.math3.complex.Complex; * */ public class MapProjections { - private static final int QUINCUNCIAL = 3; + private static final int QUINCUNCIAL = 4; private static final int EQUIRECTANGULAR = 1; private static final int MERCATOR = 2; - private static final int POLAR = 4; + private static final int POLAR = 3; @@ -78,37 +79,13 @@ public class MapProjections { /* PROJECTION METHODS: Return RGB at a given pixel based on a reference map and a unique projection method */ public static int quincuncial(final double lat0, final double lon0, final double orientation, final int width, final int height, int x, int y, BufferedImage ref) { // a tessalatable square map - final double dx = .01; - - double phi, lambda; // the correct phi and lambda combination is the one where func goes to 0. - double phiMin = -Math.PI/2; - double phiMax = Math.PI/2; - double lamMin = -Math.PI; - double lamMax = Math.PI; - - double[] error = new double[3]; - int i = 0; - do { - phi = (phiMax+phiMin)/2.0; - lambda = (lamMax+lamMin)/2.0; - - error[0] = func(phi, lambda, 2.0*x/width-1, 2.0*y/height-1); - error[1] = func(phi+dx, lambda, 2.0*x/width-1, 2.0*y/height-1); - error[2] = func(phi, lambda+dx, 2.0*x/width-1, 2.0*y/height-1); - - if (error[0] > error[1]) // phi is too small - phiMin = phi; - else // phi is too big - phiMax = phi; - if (error[0] > error[2]) // lambda is too small - lamMin = lambda; - else // lambda is too big - lamMax = lambda; - - i ++; - } while (phiMax-phiMin > Math.PI/ref.getHeight() && lamMax-lamMin > 2*Math.PI/ref.getWidth() && i < 256); - - return getColor(phi,lambda,ref); + Complex u = new Complex(3.7116*x/width, 3.7116*y/height-1.8558); // don't ask me where 3.7116 come from because I have no idea + Complex k = new Complex(Math.sqrt(0.5)); // the rest comes from some fancy complex calculus stuff + Complex ans = Jacobi.cn(u, k); + double p = 2*Math.atan(ans.abs()); + double theta = Math.atan2(ans.getRe(), ans.getIm()); + double lambda = p-Math.PI/2; + return getColor(lambda,theta,ref); } @@ -182,17 +159,17 @@ public class MapProjections { /* PRECONDITION: -1 <= x,y <= 1 */ private static double func(double p, double l, double x, double y) { // a super complicated function that calculates stuff for peirce quincuncial final double rt2 = Math.sqrt(2); - Complex X = new Complex(rt2*Math.tan(p/2)*Math.cos(l), rt2*Math.tan(p/2)*Math.sin(l)); - Complex Z = new Complex(x,y); // the point on the map + Number X = new Number(rt2*Math.tan(p/2), l); + Number Z = new Number(x,y,true); // the point on the map // X*sqrt(-X^2/2 + 1)/2 - Complex radical1 = X.multiply(X.multiply(X).divide(-2).add(1).pow(.5)).divide(2); + Number radical1 = X.times(X.sqrd().over(-2).plus(1)).over(2); // asin(X/sqrt(2))/sqrt(2) - Complex arcSin = X.divide(rt2).asin().divide(rt2); + Number arcSin = Number.asin(X.over(rt2)).over(rt2); // X*sqrt(-X^2/4 + 1) - Complex radical2 = X.multiply(X.multiply(X).divide(-4).add(1).pow(.5)); -// 2*Z + pi*sqrt(2)/8 - Complex finalBit = Z.multiply(2).subtract(Math.PI*rt2/8); - System.out.println("F("+X+","+Z+") = "+(radical1.subtract(arcSin).subtract(radical2).subtract(finalBit)).abs()); - return (radical1.subtract(arcSin).subtract(radical2).subtract(finalBit)).abs(); + Number radical2 = X.times(Number.sqrt(X.sqrd().over(-4).plus(1))); +// 2*Z - pi*sqrt(2)/8 + Number finalBit = Z.times(2).minus(Math.PI*rt2/8); + //System.out.println("F("+X+","+Z+") = "+(radical1.subtract(arcSin).subtract(radical2).subtract(finalBit)).abs()); + return Number.abs(radical1.minus(radical2).minus(arcSin).minus(finalBit)); } } \ No newline at end of file diff --git a/src/Number.java b/src/Number.java new file mode 100644 index 0000000..c0a839c --- /dev/null +++ b/src/Number.java @@ -0,0 +1,112 @@ +public class Number { + private double r; + private double theta; + + public static final Number ONE = new Number(1,0); + + + + + public Number(double mag, double ang) { + r = mag; + theta = ang; + } + + + public Number(double x, double y, boolean cartesian) { + r = Math.hypot(x, y); + theta = Math.atan2(y, x); + } + + + + + public Number plus(Number that) { + return new Number (this.x()+that.x(), this.y()+that.y(), true); + } + + + public Number plus(double x) { + return new Number (this.x()+x, this.y(), true); + } + + + public Number minus(Number that) { + return new Number (this.x()-that.x(), this.y()-that.y(), true); + } + + + public Number minus(double x) { + return new Number (this.x()-x, this.y(), true); + } + + + public Number times(Number that) { + return new Number (this.r()*that.r(), this.theta()+that.theta()); + } + + + public Number times(double x) { + return new Number (r*x, theta); + } + + + public Number over(double x) { + return new Number (r/x, theta); + } + + + public Number sqrd() { // squares it + return new Number (r*r, theta*2); + } + + + public Number timesI() { // multiplies it by i + return new Number (-y(), x()); + } + + + public Number overI() { // multiplies by negative I + return new Number (y(), -x()); + } + + + public static Number sqrt(Number z) { // sqrts it + return new Number (Math.sqrt(z.r()), z.theta()/2); + } + + + public static Number ln(Number z) { + return new Number (Math.log(z.r()), z.theta(), true); + } + + + public static Number asin(Number z) { + return Number.ln(z.timesI().plus(Number.sqrt(Number.ONE.minus(z.sqrd())))).overI(); + } + + + public static double abs(Number z) { + return z.r(); + } + + + public double r() { + return r; + } + + + public double theta() { + return theta; + } + + + public double x() { + return r*Math.cos(theta); + } + + + public double y() { + return r*Math.sin(theta); + } +} \ No newline at end of file