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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/1999/REC-html401-19991224/loose.dtd">
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<title>Castle Game Engine: CastleSphericalHarmonics</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">
<h1 class="unit">Unit CastleSphericalHarmonics</h1>
<table class="sections wide_list">
<tr>
<td><a class="section" href="#PasDoc-Description">Description</a></td><td><a class="section" href="#PasDoc-Uses">Uses</a></td><td>Classes, Interfaces, Objects and Records</td><td><a class="section" href="#PasDoc-FuncsProcs">Functions and Procedures</a></td><td><a class="section" href="#PasDoc-Types">Types</a></td><td><a class="section" href="#PasDoc-Constants">Constants</a></td><td><a class="section" href="#PasDoc-Variables">Variables</a></td></tr></table>
<a name="PasDoc-Description"></a><h2 class="description">Description</h2>
<p>
Spherical harmonic basis functions.</p>
<a name="PasDoc-Uses"></a><h2 class="uses">Uses</h2>
<ul class="useslist"><li><a  href="CastleVectors.html">CastleVectors</a></li><li><a  href="CastleUtils.html">CastleUtils</a></li><li>Math</li><li><a  href="CastleCubeMaps.html">CastleCubeMaps</a></li></ul><h2 class="overview">Overview</h2>
<a name="PasDoc-FuncsProcs"></a><h3 class="summary">Functions and Procedures</h3>
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<td class="itemcode"><code>function <b><a  href="CastleSphericalHarmonics.html#SHBasis">SHBasis</a></b>(const LM: Cardinal; const PhiTheta: <a  href="CastleVectors.html#TVector2Single">TVector2Single</a>): <a  href="CastleUtils.html#Float">Float</a>;</code></td>
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<td class="itemcode"><code>procedure <b><a  href="CastleSphericalHarmonics.html#LMDecode">LMDecode</a></b>(const LM: Cardinal; out L: Cardinal; out M: Integer);</code></td>
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<td class="itemcode"><code>procedure <b><a  href="CastleSphericalHarmonics.html#InitializeSHBasisMap">InitializeSHBasisMap</a></b>;</code></td>
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<td class="itemcode"><code>procedure <b><a  href="CastleSphericalHarmonics.html#SHVectorFromCubeMap">SHVectorFromCubeMap</a></b>(var SHVector: array of Single; const Map: <a  href="CastleCubeMaps.html#TCubeMapByte">TCubeMapByte</a>);</code></td>
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<a name="PasDoc-Types"></a><h3 class="summary">Types</h3>
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<td class="itemcode"><code><b><a  href="CastleSphericalHarmonics.html#TSHVectorSingle">TSHVectorSingle</a></b> = array [0..<a  href="CastleSphericalHarmonics.html#MaxSHBasis">MaxSHBasis</a> - 1] of Single;</code></td>
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<td class="itemcode"><code><b><a  href="CastleSphericalHarmonics.html#PSHVectorSingle">PSHVectorSingle</a></b> = &circ;<a  href="CastleSphericalHarmonics.html#TSHVectorSingle">TSHVectorSingle</a>;</code></td>
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<a name="PasDoc-Constants"></a><h3 class="summary">Constants</h3>
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<td class="itemcode"><code><b><a  href="CastleSphericalHarmonics.html#MaxSHBasis">MaxSHBasis</a></b> = 25;</code></td>
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<td class="itemcode"><code><b><a  href="CastleSphericalHarmonics.html#SHBasis0">SHBasis0</a></b> = 1 / (2 * Sqrt(Pi));</code></td>
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<a name="PasDoc-Variables"></a><h3 class="summary">Variables</h3>
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<td class="itemcode"><code><b><a  href="CastleSphericalHarmonics.html#SHBasisMap">SHBasisMap</a></b>: array [0..<a  href="CastleSphericalHarmonics.html#MaxSHBasis">MaxSHBasis</a> - 1] of <a  href="CastleCubeMaps.html#TCubeMapFloat">TCubeMapFloat</a>;</code></td>
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<h2 class="description">Description</h2>
<h3 class="detail">Functions and Procedures</h3>
<table class="detail wide_list">
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<td class="itemcode"><a name="SHBasis"></a><code>function <b>SHBasis</b>(const LM: Cardinal; const PhiTheta: <a  href="CastleVectors.html#TVector2Single">TVector2Single</a>): <a  href="CastleUtils.html#Float">Float</a>;</code></td>
</tr>
<tr><td colspan="1">
<p>
Calculate spherical harmonic basis function for given arguments.

<p>LM indicates (L, M) that specify which SH basis to use. LM determines a pair (L, M) in the natural order: for each L, take for each M from -L to L. That is, LM = (0, 1, 2, 3, ...) indicate </p>

<pre class="preformatted">
    (L, M) =
  ( (0, 0),
    (1, -1), (1, 0), (1, 1),
    (2, -2), (2, -1), (2, 0), (2, 1), (2, 2),
    ... )
</pre>

<p> )</p>
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<td class="itemcode"><a name="LMDecode"></a><code>procedure <b>LMDecode</b>(const LM: Cardinal; out L: Cardinal; out M: Integer);</code></td>
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&nbsp;</td></tr>
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<td class="itemcode"><a name="InitializeSHBasisMap"></a><code>procedure <b>InitializeSHBasisMap</b>;</code></td>
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&nbsp;</td></tr>
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<table class="detail wide_list">
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<td class="itemcode"><a name="SHVectorFromCubeMap"></a><code>procedure <b>SHVectorFromCubeMap</b>(var SHVector: array of Single; const Map: <a  href="CastleCubeMaps.html#TCubeMapByte">TCubeMapByte</a>);</code></td>
</tr>
<tr><td colspan="1">
<p>
Calculate SH basis coefficients that approximate function in Map. This uses <a class="normal" href="CastleSphericalHarmonics.html#SHBasisMap">SHBasisMap</a>, so be sure to initialize it first.</p>
</td></tr>
</table>
<h3 class="detail">Types</h3>
<table class="detail wide_list">
<tr class="list">
<td class="itemcode"><a name="TSHVectorSingle"></a><code><b>TSHVectorSingle</b> = array [0..<a  href="CastleSphericalHarmonics.html#MaxSHBasis">MaxSHBasis</a> - 1] of Single;</code></td>
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&nbsp;</td></tr>
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<table class="detail wide_list">
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<td class="itemcode"><a name="PSHVectorSingle"></a><code><b>PSHVectorSingle</b> = &circ;<a  href="CastleSphericalHarmonics.html#TSHVectorSingle">TSHVectorSingle</a>;</code></td>
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<tr><td colspan="1">
&nbsp;</td></tr>
</table>
<h3 class="detail">Constants</h3>
<table class="detail wide_list">
<tr class="list">
<td class="itemcode"><a name="MaxSHBasis"></a><code><b>MaxSHBasis</b> = 25;</code></td>
</tr>
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<p>
How many basis can <a class="normal" href="CastleSphericalHarmonics.html#SHBasis">SHBasis</a> calculate. LM for <a class="normal" href="CastleSphericalHarmonics.html#SHBasis">SHBasis</a> must be within 0 .. SHBasesCount - 1.</p>
</td></tr>
</table>
<table class="detail wide_list">
<tr class="list">
<td class="itemcode"><a name="SHBasis0"></a><code><b>SHBasis0</b> = 1 / (2 * Sqrt(Pi));</code></td>
</tr>
<tr><td colspan="1">
<p>
The first SH basis function is actually constant. This is sometimes useful.</p>
</td></tr>
</table>
<h3 class="detail">Variables</h3>
<table class="detail wide_list">
<tr class="list">
<td class="itemcode"><a name="SHBasisMap"></a><code><b>SHBasisMap</b>: array [0..<a  href="CastleSphericalHarmonics.html#MaxSHBasis">MaxSHBasis</a> - 1] of <a  href="CastleCubeMaps.html#TCubeMapFloat">TCubeMapFloat</a>;</code></td>
</tr>
<tr><td colspan="1">
<p>
For each <a class="normal" href="CastleSphericalHarmonics.html#SHBasis">SHBasis</a> function (first index of the array is LM of this function), a precalculated results of basic spherical harmonic functions. Multiplied by solid angle of this cube map pixel, since this is what you usually need.

<p>For each side of the cube, and for each pixel on this side (pixels are arranged same as in <a class="normal" href="CastleImages.TGrayscaleImage.html">TGrayscaleImage</a>, that is row-by-row from lower to higher, from left to right) this gives the result of <a class="normal" href="CastleSphericalHarmonics.html#SHBasis">SHBasis</a> for this direction. Multiplied by solid angle.

<p>You have to initialize this (once, like at the beginning of your program) by <a class="normal" href="CastleSphericalHarmonics.html#InitializeSHBasisMap">InitializeSHBasisMap</a>.

<p>This is useful for calculating sh basis vector from given cube map: since you can just project any function on any basis, so if you have a particular cube map you can project it on each SH basis function. See <a class="normal" href="CastleSphericalHarmonics.html#SHVectorFromCubeMap">SHVectorFromCubeMap</a> implementation for code how to use <code>SHBasisMap</code> for this, and in simple cases you can just call <a class="normal" href="CastleSphericalHarmonics.html#SHVectorFromCubeMap">SHVectorFromCubeMap</a>.</p>
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