Perlin Noise Results Range

Question

Problem

I was going to using the Perlin Noise Reference implementation .

The algorithm code does not mention the range of values ​​that it will produce. From what I read about Perlin Noise, the result should be in the range [0,1]. This is not for this algorithm. Therefore, I played, showed the result on the diagram and realized that the result should be from -0.5 to 0.5.

Well, that is not the case either. Until you set the parameter x to any value and leave y and z equal to 0.

As soon as you e. g. have x and y, the result is one outside of -0.5 and 0.5.

Question

Does anyone know how to use this algorithm? In what range are the result values?

the code

I wrote a sample program in JavaFX using Perlin noise code :

import javafx.application.Application; import javafx.scene.Scene; import javafx.scene.chart.LineChart; import javafx.scene.chart.NumberAxis; import javafx.scene.chart.XYChart; import javafx.stage.Stage; public class NoiseChart extends Application { @Override public void start(Stage stage) { // defining the axes final NumberAxis xAxis = new NumberAxis(); final NumberAxis yAxis = new NumberAxis(); // creating the chart final LineChart<Number, Number> lineChart = new LineChart<Number, Number>(xAxis, yAxis); lineChart.setCreateSymbols(false); // defining a series XYChart.Series series1 = new XYChart.Series(); series1.setName("Perlin Noise"); // populating the series with data from trhe perlin noise algorithm double tx = 0; double ty = 10000; for (int i = 0; i < 256; i++) { double x = ImprovedNoise.noise(tx, ty, 0); series1.getData().add(new XYChart.Data(tx, x)); tx += 0.02; ty += 0.02; // output if we cross the [-0.5,0.5] range if( Double.compare(x, -0.5) < 0 || Double.compare( x, 0.5) > 0) { System.err.println( "tx=" + tx + ", ty=" + ty + ", perlin noise: " + x); } } // show chart Scene scene = new Scene(lineChart, 800, 600); lineChart.getData().addAll(series1); stage.setScene(scene); stage.show(); } public static void main(String[] args) { launch(args); } // JAVA REFERENCE IMPLEMENTATION OF IMPROVED NOISE - COPYRIGHT 2002 KEN PERLIN. // http://mrl.nyu.edu/~perlin/paper445.pdf // http://mrl.nyu.edu/~perlin/noise/ public final static class ImprovedNoise { static public double noise(double x, double y, double z) { int X = (int)Math.floor(x) & 255, // FIND UNIT CUBE THAT Y = (int)Math.floor(y) & 255, // CONTAINS POINT. Z = (int)Math.floor(z) & 255; x -= Math.floor(x); // FIND RELATIVE X,Y,Z y -= Math.floor(y); // OF POINT IN CUBE. z -= Math.floor(z); double u = fade(x), // COMPUTE FADE CURVES v = fade(y), // FOR EACH OF X,Y,Z. w = fade(z); int A = p[X ]+Y, AA = p[A]+Z, AB = p[A+1]+Z, // HASH COORDINATES OF B = p[X+1]+Y, BA = p[B]+Z, BB = p[B+1]+Z; // THE 8 CUBE CORNERS, return lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ), // AND ADD grad(p[BA ], x-1, y , z )), // BLENDED lerp(u, grad(p[AB ], x , y-1, z ), // RESULTS grad(p[BB ], x-1, y-1, z ))),// FROM 8 lerp(v, lerp(u, grad(p[AA+1], x , y , z-1 ), // CORNERS grad(p[BA+1], x-1, y , z-1 )), // OF CUBE lerp(u, grad(p[AB+1], x , y-1, z-1 ), grad(p[BB+1], x-1, y-1, z-1 )))); } static double fade(double t) { return t * t * t * (t * (t * 6 - 15) + 10); } static double lerp(double t, double a, double b) { return a + t * (b - a); } static double grad(int hash, double x, double y, double z) { int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS. v = h<4 ? y : h==12||h==14 ? x : z; return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v); } static final int p[] = new int[512], permutation[] = { 151,160,137,91,90,15, 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180 }; static { for (int i=0; i < 256 ; i++) p[256+i] = p[i] = permutation[i]; } } } 

Values ​​in which the range [-0,5,0,5] is exceeded:

 tx=0.5200000000000001, ty=10000.520000000011, perlin noise: -0.5000000000027285 tx=0.5400000000000001, ty=10000.540000000012, perlin noise: -0.5084454691119766 tx=0.5600000000000002, ty=10000.560000000012, perlin noise: -0.5135793753147445 tx=0.5800000000000002, ty=10000.580000000013, perlin noise: -0.515139185394058 tx=0.6000000000000002, ty=10000.600000000013, perlin noise: -0.512927358018701 tx=0.6200000000000002, ty=10000.620000000014, perlin noise: -0.5068223692749664 

And the chart:

Or as a more suitable use case in an image in which the result of Perlin Noise is mapped to color values:

 import javafx.application.Application; import javafx.beans.property.DoubleProperty; import javafx.beans.property.SimpleDoubleProperty; import javafx.beans.value.ChangeListener; import javafx.beans.value.ObservableValue; import javafx.scene.Scene; import javafx.scene.control.Label; import javafx.scene.control.Slider; import javafx.scene.image.Image; import javafx.scene.image.ImageView; import javafx.scene.image.PixelWriter; import javafx.scene.image.WritableImage; import javafx.scene.layout.BorderPane; import javafx.scene.layout.HBox; import javafx.scene.paint.Color; import javafx.stage.Stage; public class NoiseImage extends Application { DoubleProperty frequencyProperty = new SimpleDoubleProperty( 5); @Override public void start(Stage stage) { BorderPane root = new BorderPane(); ImageView imageView = new ImageView(createImage()); root.setCenter(imageView); HBox toolbar = new HBox(); Label frequencyLabel = new Label( "Frequency"); Slider frequencySlider = new Slider(0, 50, 5); frequencySlider.setPrefWidth(200); frequencySlider.setShowTickLabels(true); frequencySlider.setShowTickMarks(true); frequencySlider.valueProperty().bindBidirectional(frequencyProperty); frequencyProperty.addListener(new ChangeListener<Number>() { @Override public void changed(ObservableValue<? extends Number> observable, Number oldValue, Number newValue) { imageView.setImage(createImage()); } }); Label frequencyValueLabel = new Label( "Frequency"); frequencyValueLabel.textProperty().bind(frequencyProperty.asString()); toolbar.getChildren().addAll(frequencyLabel, frequencySlider, frequencyValueLabel); root.setTop(toolbar); Scene scene = new Scene(root, 800, 600); stage.setScene(scene); stage.show(); } /** * For each pixel in the image create the perlin noise and set the gray color accordingly * @return */ public Image createImage() { double noise; int width = 256; int height = 256; WritableImage wr = new WritableImage(width, height); PixelWriter pw = wr.getPixelWriter(); for (int x = 0; x < width; x++) { for (int y = 0; y < height; y++) { double frequency = frequencyProperty.get() / (double) width; double tx = x * frequency; double ty = y * frequency; noise = ImprovedNoise.noise(tx, ty, 0); double gray = normalizeValue(noise, -.5, .5, 0., 1.); // output if we cross the [-0.5,0.5] range if( Double.compare(gray, 0) < 0 || Double.compare( gray, 1) > 0) { System.err.println( "tx=" + x + ", ty=" + y + ", perlin noise: " + noise); } // TODO: this shouldn't be necessary // question: what range does the noise method return values? currently they can be larger than .5 gray = clamp(gray, 0, 1); pw.setColor(x, y, Color.gray(gray)); } } return wr; } public static double normalizeValue( double value, double min, double max, double newMin, double newMax) { return (value - min) * (newMax - newMin) / (max - min) + newMin; } public static double clamp( double value, double min, double max) { if( Double.compare(value, min) < 0) return min; if( Double.compare(value, max) > 0) return max; return value; } public static void main(String[] args) { launch(args); } // JAVA REFERENCE IMPLEMENTATION OF IMPROVED NOISE - COPYRIGHT 2002 KEN PERLIN. // http://mrl.nyu.edu/~perlin/paper445.pdf // http://mrl.nyu.edu/~perlin/noise/ public final static class ImprovedNoise { static public double noise(double x, double y, double z) { int X = (int)Math.floor(x) & 255, // FIND UNIT CUBE THAT Y = (int)Math.floor(y) & 255, // CONTAINS POINT. Z = (int)Math.floor(z) & 255; x -= Math.floor(x); // FIND RELATIVE X,Y,Z y -= Math.floor(y); // OF POINT IN CUBE. z -= Math.floor(z); double u = fade(x), // COMPUTE FADE CURVES v = fade(y), // FOR EACH OF X,Y,Z. w = fade(z); int A = p[X ]+Y, AA = p[A]+Z, AB = p[A+1]+Z, // HASH COORDINATES OF B = p[X+1]+Y, BA = p[B]+Z, BB = p[B+1]+Z; // THE 8 CUBE CORNERS, return lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ), // AND ADD grad(p[BA ], x-1, y , z )), // BLENDED lerp(u, grad(p[AB ], x , y-1, z ), // RESULTS grad(p[BB ], x-1, y-1, z ))),// FROM 8 lerp(v, lerp(u, grad(p[AA+1], x , y , z-1 ), // CORNERS grad(p[BA+1], x-1, y , z-1 )), // OF CUBE lerp(u, grad(p[AB+1], x , y-1, z-1 ), grad(p[BB+1], x-1, y-1, z-1 )))); } static double fade(double t) { return t * t * t * (t * (t * 6 - 15) + 10); } static double lerp(double t, double a, double b) { return a + t * (b - a); } static double grad(int hash, double x, double y, double z) { int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS. v = h<4 ? y : h==12||h==14 ? x : z; return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v); } static final int p[] = new int[512], permutation[] = { 151,160,137,91,90,15, 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180 }; static { for (int i=0; i < 256 ; i++) p[256+i] = p[i] = permutation[i]; } } } 

Values ​​where [-0,5,0,5] are exceeded:

 ... tx=250, ty=131, perlin noise: -0.5221718771387314 tx=250, ty=132, perlin noise: -0.5026623324564983 tx=251, ty=124, perlin noise: -0.5021001248099309 tx=251, ty=125, perlin noise: -0.5193524233279807 tx=251, ty=126, perlin noise: -0.5312601268638136 tx=251, ty=127, perlin noise: -0.5375809523803251 tx=251, ty=128, perlin noise: -0.5382082635276979 tx=251, ty=129, perlin noise: -0.5331735730625967 tx=251, ty=130, perlin noise: -0.5226452480286591 tx=251, ty=131, perlin noise: -0.5069234176982861 tx=252, ty=125, perlin noise: -0.509547880806866 tx=252, ty=126, perlin noise: -0.5202072536185804 ... 

Screenshot:

Thank you for help!