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<title>Castle Game Engine: CastleTerrain: Class TTerrainNoise</title>
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<h2>Castle Game Engine</h2><p><a href="introduction.html" class="navigation">Introduction</a></p><p><a href="AllUnits.html" class="navigation">Units</a></p><p><a href="ClassHierarchy.html" class="navigation">Class Hierarchy</a></p><p><a href="AllClasses.html" class="navigation">Classes, Interfaces, Objects and Records</a></p><p><a href="AllTypes.html" class="navigation">Types</a></p><p><a href="AllVariables.html" class="navigation">Variables</a></p><p><a href="AllConstants.html" class="navigation">Constants</a></p><p><a href="AllFunctions.html" class="navigation">Functions and Procedures</a></p><p><a href="AllIdentifiers.html" class="navigation">Identifiers</a></p></td><td class="content">
<a name="TTerrainNoise"></a><h1 class="cio">Class TTerrainNoise</h1>
<table class="sections wide_list">
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<td><a class="section" href="#PasDoc-Description">Description</a></td><td><a class="section" href="#PasDoc-Hierarchy">Hierarchy</a></td><td>Fields</td><td><a class="section" href="#PasDoc-Methods">Methods</a></td><td><a class="section" href="#PasDoc-Properties">Properties</a></td></tr></table>
<a name="PasDoc-Description"></a><h2 class="unit">Unit</h2>
<p class="unitlink">
<a href="CastleTerrain.html">CastleTerrain</a></p>
<h2 class="declaration">Declaration</h2>
<p class="declaration">
<code>type TTerrainNoise = class(<a class="normal" href="CastleTerrain.TTerrainImage.html">TTerrainImage</a>)</code></p>
<h2 class="description">Description</h2>
<p>
Procedural terrain: data from a procedural noise.
<p>"Synthesized noise" means it's not simply something random. We take the noise (integer noise, i.e. hash), smooth it (how well, and how fast — see <a class="normal" href="CastleTerrain.TTerrainNoise.html#Interpolation">Interpolation</a> and <a class="normal" href="CastleTerrain.TTerrainNoise.html#Blur">Blur</a>), and add several functions ("<a class="normal" href="CastleTerrain.TTerrainNoise.html#Octaves">octaves</a>") of such noise (with varying <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">frequency</a> and <a class="normal" href="CastleTerrain.TTerrainNoise.html#Amplitude">amplitude</a>) together. This is the kind of noise used to synthesize textures, terrains and all other procedural stuff.
<p>For more info about math inside:
<p></p>
<ul class="paragraph_spacing">
<li><p>[<a href="http://en.wikipedia.org/wiki/Fractional_Brownian_motion">http://en.wikipedia.org/wiki/Fractional_Brownian_motion</a>]. This is the idea of summing up <a class="normal" href="CastleTerrain.TTerrainNoise.html#Octaves">octaves</a> of noise. Ken Musgrave's dissertation has a lot of info and interesting references: [<a href="http://www.kenmusgrave.com/dissertation.html">http://www.kenmusgrave.com/dissertation.html</a>]</p></li>
<li><p>Blender's source code is informative, interesting file is blender/source/blender/blenlib/intern/noise.c</p></li>
<li><p>The simplest practical <a class="normal" href="introduction.html">introduction</a> to the idea is on [<a href="http://freespace.virgin.net/hugo.elias/models/m_perlin.htm">http://freespace.virgin.net/hugo.elias/models/m_perlin.htm</a>]. It describes how to get nice noise very easily, and my approach follows theirs.</p></li>
</ul>
<p>
<p>This descends from <a class="normal" href="CastleTerrain.TTerrainImage.html">TTerrainImage</a>, so you add an image to your function result.</p>
<a name="PasDoc-Hierarchy"></a><h2 class="hierarchy">Hierarchy</h2>
<ul class="hierarchy"><li class="ancestor">TObject</li>
<li class="ancestor"><a class="normal" href="CastleTerrain.TTerrain.html">TTerrain</a></li>
<li class="ancestor"><a class="normal" href="CastleTerrain.TTerrainImage.html">TTerrainImage</a></li>
<li class="thisitem">TTerrainNoise</li></ul><h2 class="overview">Overview</h2>
<a name="PasDoc-Methods"></a><h3 class="summary">Methods</h3>
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<td class="itemcode"><code>constructor <b><a href="CastleTerrain.TTerrainNoise.html#Create">Create</a></b>;</code></td>
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<td class="itemcode"><code>function <b><a href="CastleTerrain.TTerrainNoise.html#Height">Height</a></b>(const X, Y: Single): Single; override;</code></td>
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<a name="PasDoc-Properties"></a><h3 class="summary">Properties</h3>
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<td class="itemcode"><code>property <b><a href="CastleTerrain.TTerrainNoise.html#Octaves">Octaves</a></b>: Single read FOctaves write FOctaves default 4.0;</code></td>
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<td class="itemcode"><code>property <b><a href="CastleTerrain.TTerrainNoise.html#Smoothness">Smoothness</a></b>: Single read FSmoothness write FSmoothness default 2.0;</code></td>
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<td class="itemcode"><code>property <b><a href="CastleTerrain.TTerrainNoise.html#Amplitude">Amplitude</a></b>: Single read FAmplitude write FAmplitude default 1.0;</code></td>
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<td class="itemcode"><code>property <b><a href="CastleTerrain.TTerrainNoise.html#Frequency">Frequency</a></b>: Single read FFrequency write FFrequency default 1.0;</code></td>
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<td class="itemcode"><code>property <b><a href="CastleTerrain.TTerrainNoise.html#Interpolation">Interpolation</a></b>: <a href="CastleTerrain.html#TNoiseInterpolation">TNoiseInterpolation</a>
read FInterpolation write SetInterpolation default niCosine;</code></td>
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<td class="itemcode"><code>property <b><a href="CastleTerrain.TTerrainNoise.html#Blur">Blur</a></b>: boolean read FBlur write SetBlur default false;</code></td>
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<td class="itemcode"><code>property <b><a href="CastleTerrain.TTerrainNoise.html#Seed">Seed</a></b>: Cardinal read FSeed write FSeed default 0;</code></td>
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<td class="itemcode"><code>property <b><a href="CastleTerrain.TTerrainNoise.html#Heterogeneous">Heterogeneous</a></b>: Single
read FHeterogeneous write FHeterogeneous default 0.0;</code></td>
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<h2 class="description">Description</h2>
<h3 class="detail">Methods</h3>
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<td class="itemcode"><a name="Create"></a><code>constructor <b>Create</b>;</code></td>
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<td class="itemcode"><a name="Height"></a><code>function <b>Height</b>(const X, Y: Single): Single; override;</code></td>
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<h3 class="detail">Properties</h3>
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<td class="itemcode"><a name="Octaves"></a><code>property <b>Octaves</b>: Single read FOctaves write FOctaves default 4.0;</code></td>
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<p>
Number of noise functions to sum. This linearly affects the time for Height call, so don't make it too much. Usually ˜a few are Ok.
<p>(The fact that it's a float is just a simple trick to allow smooth transitions from x to x+1. In fact, it's executed like Trunc(<code>Octaves</code>) * some noises + Frac(<code>Octaves</code>) * some last noise.)</p>
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<td class="itemcode"><a name="Smoothness"></a><code>property <b>Smoothness</b>: Single read FSmoothness write FSmoothness default 2.0;</code></td>
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<tr><td colspan="2">
<p>
How noise <a class="normal" href="CastleTerrain.TTerrainNoise.html#Amplitude">amplitude</a> changes, when <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">frequency</a> doubles. When we double <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">frequency</a>, <a class="normal" href="CastleTerrain.TTerrainNoise.html#Amplitude">amplitude</a> is divided by this. Smaller values <=> larger <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">frequency</a> noise is more visible, so terrain is less smooth (more noisy).
<p>This is elsewhere called fractal increment, fractal dimension parameter, "H", spectral exponent (see e.g. Blender sources, Musgrave's dissertation). Do not confuse this with "lacunarity" (how <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">frequency</a> changes in each octave), that is simply hardcoded to 2.0 in our code currently. In [<a href="http://freespace.virgin.net/hugo.elias/models/m_perlin.htm">http://freespace.virgin.net/hugo.elias/models/m_perlin.htm</a>], the inverse of this 1/<code>Smoothness</code> is called "Persistence".
<p>I decided to call it "<code>Smoothness</code>", since this is the practical intuitive meaning.
<p>Value equal 1.0 means that <a class="normal" href="CastleTerrain.TTerrainNoise.html#Amplitude">amplitude</a> doesn't change at all, each noise <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">frequency</a> is visible the same, so in effect you will just see a lot of noise. And values < 1.0 are really nonsense, they make more <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">frequency</a> noise even more visible, which means that the terrain is dominated by noise.</p>
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<td class="itemcode"><a name="Amplitude"></a><code>property <b>Amplitude</b>: Single read FAmplitude write FAmplitude default 1.0;</code></td>
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<tr><td colspan="2">
<p>
<code>Amplitude</code> and <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">frequency</a> of the first noise octave. <code>Amplitude</code> scales the height of the result, and <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">Frequency</a> scales the size of the bumps. </p>
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<td class="itemcode"><a name="Frequency"></a><code>property <b>Frequency</b>: Single read FFrequency write FFrequency default 1.0;</code></td>
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<td class="itemcode"><a name="Interpolation"></a><code>property <b>Interpolation</b>: <a href="CastleTerrain.html#TNoiseInterpolation">TNoiseInterpolation</a>
read FInterpolation write SetInterpolation default niCosine;</code></td>
</tr>
<tr><td colspan="2">
<p>
How integer noise is interpolated to get smooth float noise.
<p>Setting this to niNone turns off <code>interpolation</code>, which means that your terrain is a sum of a couple of blocky noises — ugly.
<p>Using niLinear (means "bilinear", since this is 2D case) is also usually bad. Unless you use <a class="normal" href="CastleTerrain.TTerrainNoise.html#Octaves">octaves</a> of really high frequencies, usually sharp edges / flat in-betweens will be visible.
<p>Using niCosine in right now the best.
<p>Using niSpline is even better looking (usese Catmull-Rom splines, which are special case of cubic Hermite spline, see <a href="http://en.wikipedia.org/wiki/Cubic_Hermite_spline">http://en.wikipedia.org/wiki/Cubic_Hermite_spline</a>, <a href="http://en.wikipedia.org/wiki/Bicubic_interpolation">http://en.wikipedia.org/wiki/Bicubic_interpolation</a>). But it's more time consuming under current implementation.</p>
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<td class="itemcode"><a name="Blur"></a><code>property <b>Blur</b>: boolean read FBlur write SetBlur default false;</code></td>
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<p>
Resulting noise <a class="normal" href="CastleTerrain.TTerrainNoise.html#Octaves">octaves</a> may be blurred. This helps to remove the inherent vertical/horizontal directionality in our 2D noise (it also makes it more smooth, since that's what blurring is about; you may want to increase <a class="normal" href="CastleTerrain.TTerrainNoise.html#Frequency">Frequency</a> * 2 to balance this).
<p>This is independent from <a class="normal" href="CastleTerrain.TTerrainNoise.html#Interpolation">Interpolation</a>. Although the need for <code>Blur</code> is most obvious in poor/none <a class="normal" href="CastleTerrain.TTerrainNoise.html#Interpolation">interpolation</a> methods (none, linear), it also helps for the nicer <a class="normal" href="CastleTerrain.TTerrainNoise.html#Interpolation">interpolation</a> methods (cosine, cubic).
<p>Note about [<a href="http://freespace.virgin.net/hugo.elias/models/m_perlin.htm">http://freespace.virgin.net/hugo.elias/models/m_perlin.htm</a>]: this "blurring" is called "smoothing" there. I call it blurring, as it seems more precise to me.</p>
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<td class="itemcode"><a name="Seed"></a><code>property <b>Seed</b>: Cardinal read FSeed write FSeed default 0;</code></td>
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<p>
Determines the random seeds used when generating the terrain.</p>
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<td class="itemcode"><a name="Heterogeneous"></a><code>property <b>Heterogeneous</b>: Single
read FHeterogeneous write FHeterogeneous default 0.0;</code></td>
</tr>
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<p>
If non-zero, then we generate terrain using <code>heterogeneous</code> fBm. Intuitively, the idea is that the terrain details (from higher <a class="normal" href="CastleTerrain.TTerrainNoise.html#Octaves">octaves</a>) are more noisy when ground is higher. This is realistic (debris gathers in lower terrain, smoothing it more).
<p>More precisely, this means that we accumulate multiplied previous noise, at each step dividing this accumulated result by <code>Heterogeneous</code>, and clamping at 1.0. So when <code>Heterogeneous</code> is very small, this always ends up 1.0, and we get normal (homogeneous) generation. When <code>Heterogeneous</code> is larger, the details (at lower ground) are scaled down (terrain is smoother).
<p>This is called "threshold" in Musgrave's dissertation (see algorithm in section 2.3.2.5 "A Large Scale Terrain Model").</p>
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