Develop Reference

How to write a cosine theorem using Java?

How to write this theorem correctly as is written in the formula?
package com.company;
public class Exercise8 {
public static void main(String[] args) {
double AB = 6;
double AC = 16;
double Angle = 60;
double CosOfAngle = 0.5;
// Почему-то значение косинуса 60 градусов вместо 0.5, пишет
// -0.9524129804151563 ? ? ? (Do not pay attention)
// Formula is BC^2 = AB^2 + AC^2 - 2AB*AC * cos A
double bc = (2 * (Math.pow(AB, 2) + Math.pow(AC, 2) - ((AB * AC))) * CosOfAngle);
double BC = Math.sqrt(bc);
double P = AB + BC + AC;
double p = 0.5 * P; // Где p - полупериметр
double S0 = (p * ((p - AB) * (p - BC) * (p - AC)));
double S1 = Math.sqrt(S0);
double S = Math.round(S1);
System.out.println("Perimeter of triangle is : " + P + " cm ");
System.out.println("Area of triangle is : " + S + " cm^2 ");
}
}

The mistake is in this line:
double bc = (2 * (Math.pow(AB, 2) + Math.pow(AC, 2) - ((AB * AC))) * CosOfAngle);
which should be:
double bc = Math.pow(AB, 2) + Math.pow(AC, 2) - 2 * AB * AC * CosOfAngle;
You were multiplying the whole formula by 2, whereas only the cosine part needs to be multiplied by two. There were too many confusing parenthesis. Removing them made it a lot clearer.

This seems simple to me:
// https://www.mathsisfun.com/algebra/trig-cosine-law.html
public double lawOfCosines(double a, double b, double angleInRadians) {
return Math.sqrt(a*a + b*b - 2.0*a*b*Math.cos(angleInRadians));
}

Monte Carlo calculation of pi using randomly generated data in Java

I'm working on a program that calculates pi based on randomly generated float numbers that represent x,y co-ordinates on a graph. Each x, y co-ordinate is raised by the power of 2 and stored in two separate arrays. The co-ordinates are distributed uniformly on a graph of interval of 0,1.
The program adds the x, y co-ordinates and if they are less than 1 then the points are located within a circle of diameter 1, illustrated in the diagram below.
I then used the formula,
π ≈ 4 w / n
to work out pi. Where, w is the count of the points within the circle and n is the number of x or y co-ordinates within the arrays.
When I set n up to 10,000,000 (the size of the array) it generates the most accurate calculation of pi of 15-16 decimal places. However after dedicating 4GB of RAM to the run config and setting n to 100,000,000 pi ends up being 0.6710...
I was wondering why this may be happening? Sorry if this is a stupid question.. code is below.
import java.text.DecimalFormat;
import java.util.Random;
public class random_pi {
public random_pi() {
float x2_store[] = new float[10000000];
float y2_store[] = new float[10000000];
float w = 0;
Random rand = new Random();
DecimalFormat df2 = new DecimalFormat("#,###,###");
for (int i = 0; i < x2_store.length; i++) {
float x2 = (float) Math.pow(rand.nextFloat(), 2);
x2_store[i] = x2;
float y2 = (float) Math.pow(rand.nextFloat(), 2);
y2_store[i] = y2;
}
for (int i = 0; i < x2_store.length; i++) {
if (x2_store[i] + y2_store[i] < 1) {
w++;
}
}
System.out.println("w: "+w);
float numerator = (4*w);
System.out.printf("4*w: " + (numerator));
System.out.println("\nn: " + df2.format(x2_store.length));
float pi = numerator / x2_store.length;
String fmt = String.format("%.20f", pi);
System.out.println(fmt);
String pi_string = Double.toString(Math.abs(pi));
int intP = pi_string.indexOf('.');
int decP = pi_string.length() - intP - 1;
System.out.println("decimal places: " + decP);
}
public static void main(String[] args) {
new random_pi();
}
}

The problem is here:
float w = 0;
float numerator = (4*w);
float precision is not enough, change it to int or double:
Like this working sample code:
import java.text.DecimalFormat;
import java.util.Random;
public class random_pi {
public random_pi() {
float x2_store[] = new float[100000000];
float y2_store[] = new float[100000000];
int w = 0;
Random rand = new Random();
DecimalFormat df2 = new DecimalFormat("#,###,###");
for (int i = 0; i < x2_store.length; i++) {
float x2 = (float) Math.pow(rand.nextFloat(), 2);
x2_store[i] = x2;
float y2 = (float) Math.pow(rand.nextFloat(), 2);
y2_store[i] = y2;
}
for (int i = 0; i < x2_store.length; i++) {
if (x2_store[i] + y2_store[i] < 1) {
w++;
}
}
System.out.println("w: "+w);
int numerator = (4*w);
System.out.printf("4*w: " + (numerator));
System.out.println("\nn: " + df2.format(x2_store.length));
float pi = ((float)numerator) / x2_store.length;
String fmt = String.format("%.20f", pi);
System.out.println(fmt);
String pi_string = Double.toString(Math.abs(pi));
int intP = pi_string.indexOf('.');
int decP = pi_string.length() - intP - 1;
System.out.println("decimal places: " + decP);
}
public static void main(String[] args) {
new random_pi();
}
}
output:
w: 78544041
4*w: 314176164
n: 100,000,000
3.14176154136657700000
decimal places: 15
And you don't need to store the results, like this working sample code:
import java.text.DecimalFormat;
import java.util.Random;
public class pi {
public pi() {
double n=100000000;
double w = 0;
Random rand = new Random();
DecimalFormat df2 = new DecimalFormat("#,###,###");
for (int i = 0; i < n; i++) {
double x = rand.nextFloat();
double y = rand.nextFloat();
if ((x*x + y*y) < 1.0) w++;
}
System.out.println("w: "+w);//w: 7852372.0
double numerator = (4*w);
System.out.printf("4*w: " + (numerator));//4*w: 3.1409488E7
System.out.println("\nn: " + df2.format(n));//n: 10,000,000
double pi = numerator / n;
final String fmt = String.format("%.20f", pi);
System.out.println(fmt);//3.14094877243042000000
String pi_string = Double.toString(Math.abs(pi));
int intP = pi_string.indexOf('.');
int decP = pi_string.length() - intP - 1;
System.out.println("decimal places: " + decP);//decimal places: 14
}
public static void main(String[] args) {
new random_pi();
}
}
output:
w: 78539606
4*w: 314158424
n: 100,000,000
3.14158439636230470000
decimal places: 16

Trying to calculate sunrise...ain't getting the right answer

This is my current code:
public class Sunpos {
final private double Pi = Math.PI;
final private double eul = 2.71828182845904523552 ;
final private double sonauf = 90;
final private double RAD = 0.017453292519943295769236907684886;
public double sunrisefinal (double Breitengrad, double Laengengrad, int tagzahl, int sommerzeit, int nacht) {
double lngHour = Laengengrad/15;
double t = tagzahl + ((6 - lngHour)/24);
// double ab = tagzahl + ((18 - lngHour)/24);
double M = (0.9856 * t) - 3.289;
double L = M + (1.916 * Math.sin(M)) + (0.020 * Math.sin(2 * M)) + 282.634;
if (L >= 359) { L -= 360; }
else if (L < 0) { L += 360; }
double RA = (Math.atan(0.91764 * Math.tan(Pi/180)*L));
if (RA >= 359) { RA -= 360; }
else if (RA < 0) { RA += 360; }
double Lquadrant = (Math.floor(L/90)*90);
double RAquadrant = (Math.floor(RA/90))*90;
RA = RA + (Lquadrant - RAquadrant);
RA = RA/15;
double sinDec = 0.39782 * Math.sin((Pi/180)*L);
double cosDec = (180/Pi)*(Math.cos(Math.asin(sinDec)));
double cosH = (Math.cos((Pi/180)*sonauf)-(sinDec*Math.sin((Pi/180)*Breitengrad)))/(cosDec * Math.cos((Pi/180)*Breitengrad));
double H = 360 - Math.acos(cosH);
H /= 15;
double T = H + RA -(0.06571 * t) - 6.622;
double UTC = T - lngHour;
if (UTC >= 23) { UTC -= 24; }
else if (UTC < 0) { UTC += 24; }
double locTime = UTC; // Fuer die schweiz!
System.out.println(locTime);
return(0);
}
The inputs are the following: ( 50, 10, 294, 1, 0). The last 2 can be ignored.
Now I am basing this on the following page:
http://williams.best.vwh.net/sunrise_sunset_algorithm.htm
The code should be complete according to the site, but I don't get anywhere near the supposed results. I should get around 7.5 for today but I'm getting a 9.358.
Now, that might be because something with radiants/degrees? I can't quite get my Mind into that, as I've been trying to insert those converters (Pi/180) into the code, without any usable result.
Can anyone tell me where to put them or point me in the right direction? I've spent waaaay too much time on this already, and now I'm so close.

I'll just post my implementation here in case people need it (ported from the same source as yours)
https://gist.github.com/zhong-j-yu/2232343b14a5b5ef5b9d
public class SunRiseSetAlgo
{
static double calcSunrise(int dayOfYear, double localOffset, double latitude, double longitude)
{
return calc(dayOfYear, localOffset, latitude, longitude, true);
}
static double calcSunset(int dayOfYear, double localOffset, double latitude, double longitude)
{
return calc(dayOfYear, localOffset, latitude, longitude, false);
}
// http://williams.best.vwh.net/sunrise_sunset_algorithm.htm
static double calc(int dayOfYear, double localOffset, double latitude, double longitude, boolean rise)
{
//1. first calculate the day of the year
// int N1 = floor(275 * month / 9.0);
// int N2 = floor((month + 9) / 12.0);
// int N3 = (1 + floor((year - 4 * floor(year / 4.0) + 2) / 3.0));
// int N = N1 - (N2 * N3) + day - 30;
int N = dayOfYear;
//2. convert the longitude to hour value and calculate an approximate time
double lngHour = longitude / 15;
double t = rise?
N + (( 6 - lngHour) / 24) :
N + ((18 - lngHour) / 24);
//3. calculate the Sun's mean anomaly
double M = (0.9856 * t) - 3.289;
//4. calculate the Sun's true longitude
double L = M + (1.916 * sin(M)) + (0.020 * sin(2 * M)) + 282.634;
L = mod(L, 360);
//5a. calculate the Sun's right ascension
double RA = atan(0.91764 * tan(L));
RA = mod(RA, 360);
//5b. right ascension value needs to be in the same quadrant as L
double Lquadrant = (floor( L/90)) * 90;
double RAquadrant = (floor(RA/90)) * 90;
RA = RA + (Lquadrant - RAquadrant);
//5c. right ascension value needs to be converted into hours
RA = RA / 15;
//6. calculate the Sun's declination
double sinDec = 0.39782 * sin(L);
double cosDec = cos(asin(sinDec));
//7a. calculate the Sun's local hour angle
double zenith = 90 + 50.0/60;
double cosH = (cos(zenith) - (sinDec * sin(latitude))) / (cosDec * cos(latitude));
if (cosH > 1)
throw new Error("the sun never rises on this location (on the specified date");
if (cosH < -1)
throw new Error("the sun never sets on this location (on the specified date");
//7b. finish calculating H and convert into hours
double H = rise?
360 - acos(cosH) :
acos(cosH);
H = H / 15;
//8. calculate local mean time of rising/setting
double T = H + RA - (0.06571 * t) - 6.622;
//9. adjust back to UTC
double UT = T - lngHour;
//10. convert UT value to local time zone of latitude/longitude
double localT = UT + localOffset;
localT = mod(localT, 24);
return localT;
}
static int floor(double d){ return (int)Math.floor(d); }
static double sin(double degree)
{
return Math.sin(degree*Math.PI/180);
}
static double cos(double degree)
{
return Math.cos(degree*Math.PI/180);
}
static double tan(double degree)
{
return Math.tan(degree*Math.PI/180);
}
static double atan(double x)
{
return Math.atan(x) *180/Math.PI;
}
static double asin(double x)
{
return Math.asin(x) *180/Math.PI;
}
static double acos(double x)
{
return Math.acos(x) *180/Math.PI;
}
static double mod(double x, double lim)
{
return x - lim * floor(x/lim);
}
}

Everone seems to link to this http://williams.best.vwh.net/sunrise_sunset_algorithm.htm
which doesn't exist anymore. Why not try something that gets updated once in a while like https://en.wikipedia.org/wiki/Sunrise_equation
Then if you like you could help edit it to make it better.

basic math equation math to java code

so i have a math equation that i need to use in java but for some reason my code is giving me small errors :(
the math equation is describe on this web page in the section extra credit
my current code outpouts 4000 and the answere is 4005 what am i duing wrong ?
my test class lookes like this
public class MainActivity {
public static void main(String[] args) throws Exception{
double baseMaterial =556;
int me =5;
int ml = 10;
int extraMaterial = 3444;
System.out.println(""+calculateMiniralTotal(baseMaterial,me,ml,extraMaterial));
}
public static double calculateMiniralTotal(double perfekt,int me,int ml,int extraMaterial) {
double s = (perfekt + (perfekt * (10 / (ml + 1)) / 100));
s = Math.round(s);
double r = s + (perfekt * (0.25 - (0.05 * me)));
r = Math.round(r);
double q = extraMaterial + (extraMaterial * (0.25 - (0.05 * me)));
q = Math.round(q);
//double r=q;
r = r + q;
return Math.round(r);
}
}

You are performing integer division with (10 / (ml + 1)) / 100, which in Java must result in another int. Your ml is 10, and in Java, 10 / 11 is 0, not 0.909..., and nothing is added to s.
Use a double literal or cast to double to force floating-point computations.
double s = (perfekt + (perfekt * (10.0 / (ml + 1)) / 100));
or
double s = (perfekt + (perfekt * ( (double) 10 / (ml + 1)) / 100));
Making either change makes the output:
4005.0

When you multiply a double by an int you get an int back.
public class Main
{
public static void main(String[] args)
throws Exception
{
double baseMaterial = 556;
int me = 5;
int ml = 10;
int extraMaterial = 3444;
System.out.println("" + calculateMiniralTotal(baseMaterial, me, ml, extraMaterial));
}
public static double calculateMiniralTotal(double perfekt, int me, int ml, int extraMaterial)
{
double s = (perfekt + (perfekt * (10.0 / (ml + 1)) / 100.0)); // <-- changed from 10 to 10.0 and 100 to 100.0. This way they are doubles too
s = Math.round(s);
double r = s + (perfekt * (0.25 - (0.05 * me)));
r = Math.round(r);
double q = extraMaterial + (extraMaterial * (0.25 - (0.05 * me)));
q = Math.round(q);
// double r=q;
r = r + q;
return Math.round(r);
}
}

Perlin noise value range

I used perlin noise to generate a 2D height map. At first i tried some parameters manually and found a good combination of amplitude, persistence,... for my job.
Now that i'm developing the program, i added the feature for user to change the map parameters and make a new map for himself but now i see that for certain parameters (Mostly octaves and frequency) the values are not in the range i used to see. I thought that if a set Amplitude = 20, the values(heights) i get from it will be in e.g [0,20] or [-10,10] or [-20,20] ranges but now i see that Amplitude is not the only parameter that controls output range.
My question is: Is there an exact mathematical formula (a function of Amplitude, Octaves, Frequency and persistence) to compute the range or i should take a lot of samples (like 100,000) and check minimum and maximum values of them to guess the aproximate range?
Note: The following code is an implementation of perlin noise that one of stackoverflow guys worte it in C and i ported it to java.
PerlinNoiseParameters.java
public class PerlinNoiseParameters {
public double persistence;
public double frequency;
public double amplitude;
public int octaves;
public int randomseed;
public PerlinNoiseParameters(double persistence, double frequency, double amplitude, int octaves, int randomseed) {
this.ChangeParameters(persistence, frequency, amplitude, octaves, randomseed);
}
public void ChangeParameters(double persistence, double frequency, double amplitude, int octaves, int randomseed) {
this.persistence = persistence;
this.frequency = frequency;
this.amplitude = amplitude;
this.octaves = octaves;
this.randomseed = 2 + randomseed * randomseed;
}
}
PerlinNoiseGenerator.java
public class PerlinNoiseGenerator {
PerlinNoiseParameters parameters;
public PerlinNoiseGenerator() {
}
public PerlinNoiseGenerator(PerlinNoiseParameters parameters) {
this.parameters = parameters;
}
public void ChangeParameters(double persistence, double frequency, double amplitude, int octaves, int randomseed) {
parameters.ChangeParameters(persistence, frequency, amplitude, octaves, randomseed);
}
public void ChangeParameters(PerlinNoiseParameters newParams) {
parameters = newParams;
}
public double get(double x, double y) {
return parameters.amplitude * Total(x, y);
}
private double Total(double i, double j) {
double t = 0.0f;
double _amplitude = 1;
double freq = parameters.frequency;
for (int k = 0; k < parameters.octaves; k++) {
t += GetValue(j * freq + parameters.randomseed, i * freq + parameters.randomseed)
* _amplitude;
_amplitude *= parameters.persistence;
freq *= 2;
}
return t;
}
private double GetValue(double x, double y) {
int Xint = (int) x;
int Yint = (int) y;
double Xfrac = x - Xint;
double Yfrac = y - Yint;
double n01 = Noise(Xint - 1, Yint - 1);
double n02 = Noise(Xint + 1, Yint - 1);
double n03 = Noise(Xint - 1, Yint + 1);
double n04 = Noise(Xint + 1, Yint + 1);
double n05 = Noise(Xint - 1, Yint);
double n06 = Noise(Xint + 1, Yint);
double n07 = Noise(Xint, Yint - 1);
double n08 = Noise(Xint, Yint + 1);
double n09 = Noise(Xint, Yint);
double n12 = Noise(Xint + 2, Yint - 1);
double n14 = Noise(Xint + 2, Yint + 1);
double n16 = Noise(Xint + 2, Yint);
double n23 = Noise(Xint - 1, Yint + 2);
double n24 = Noise(Xint + 1, Yint + 2);
double n28 = Noise(Xint, Yint + 2);
double n34 = Noise(Xint + 2, Yint + 2);
double x0y0 = 0.0625 * (n01 + n02 + n03 + n04) + 0.1250
* (n05 + n06 + n07 + n08) + 0.2500 * n09;
double x1y0 = 0.0625 * (n07 + n12 + n08 + n14) + 0.1250
* (n09 + n16 + n02 + n04) + 0.2500 * n06;
double x0y1 = 0.0625 * (n05 + n06 + n23 + n24) + 0.1250
* (n03 + n04 + n09 + n28) + 0.2500 * n08;
double x1y1 = 0.0625 * (n09 + n16 + n28 + n34) + 0.1250
* (n08 + n14 + n06 + n24) + 0.2500 * n04;
double v1 = Interpolate(x0y0, x1y0, Xfrac);
double v2 = Interpolate(x0y1, x1y1, Xfrac);
double fin = Interpolate(v1, v2, Yfrac);
return fin;
}
private double Interpolate(double x, double y, double a) {
double negA = 1.0 - a;
double negASqr = negA * negA;
double fac1 = 3.0 * (negASqr) - 2.0 * (negASqr * negA);
double aSqr = a * a;
double fac2 = 3.0 * aSqr - 2.0 * (aSqr * a);
return x * fac1 + y * fac2;
}
private double Noise(int x, int y) {
int n = x + y * 57;
n = (n << 13) ^ n;
int t = (n * (n * n * 15731 + 789221) + 1376312589) & 0x7fffffff;
return 1.0 - (double) t * 0.931322574615478515625e-9;
}
}

The range of a single perlin noise step is:
http://digitalfreepen.com/2017/06/20/range-perlin-noise.html
-sqrt(N/4), sqrt(N/4)
With N being the amount of dimensions. 2 in your case.
Octaves, persistence and amplitude add on top of that:
double range = 0.0;
double _amplitude = parameters.;
for (int k = 0; k < parameters.octaves; k++) {
range += sqrt(N/4) * _amplitude;
_amplitude *= parameters.persistence;
}
return range;
There might be some way to do this as a single mathematical expression. Involving pow(), but by brain fails me right now.

This is not a problem with octaves and frequency affecting amplitude, not directly at least. It is a problem with integer overflow. Because you introduce your random seed by adding it to the the x and y co-ordinates (which is unusual, I don't think this is the usual implimentation)
t += GetValue(j * freq + parameters.randomseed, i * freq + parameters.randomseed)* _amplitude;
And random seed could be huge (possibly the near full size of the int) because
this.randomseed = 2 + randomseed * randomseed;
So if you input large values for j and i you end up with the doubles that are passed through at GetValue(double x, double y) being larger than the maximum size of int, at that point when you call
int Xint = (int) x;
int Yint = (int) y;
Xint and YInt won't be anything like x and y (because x and y could be huge!) and so
double Xfrac = x - Xint;
double Yfrac = y - Yint;
could be much much larger that 1, allowing values not between -1 and 1 to be returned.
Using reasonable and small values my ranges using your code are between -1 and 1 (for amplitude 1)
As an asside, in java usually method names are methodName, not MethodName
If its useful please find annother java implimentation of perlin noise here:
http://mrl.nyu.edu/~perlin/noise/