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| author | David Thompson <dthompson2@worcester.edu> | 2023-12-28 11:23:49 -0500 |
|---|---|---|
| committer | David Thompson <dthompson2@worcester.edu> | 2023-12-28 11:23:49 -0500 |
| commit | 25c5eac5e6ca1035db1eddd7bea9ac78531da57e (patch) | |
| tree | 96377006bbfee75bcf0ce208c1ef89cbdfa5b803 /manuals/chickadee/Buffers.html | |
| parent | 5b2e467a7e5e2ffbb0cbbf2557283be891d8206b (diff) | |
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diff --git a/manuals/chickadee/Buffers.html b/manuals/chickadee/Buffers.html deleted file mode 100644 index ac5fb02..0000000 --- a/manuals/chickadee/Buffers.html +++ /dev/null @@ -1,482 +0,0 @@ -<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> -<html> -<!-- Copyright (C) 2017-2023 David Thompson dthompson2@worcester.edu - -Permission is granted to copy, distribute and/or modify this document -under the terms of the GNU Free Documentation License, Version 1.3 -or any later version published by the Free Software Foundation; -with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. -A copy of the license is included in the section entitled "GNU -Free Documentation License". - -A copy of the license is also available from the Free Software -Foundation Web site at http://www.gnu.org/licenses/fdl.html. - - -* Chickadee: (chickadee). Game programming toolkit for Guile. - -The document was typeset with -http://www.texinfo.org/ (GNU Texinfo). - --> -<!-- Created by GNU Texinfo 6.7, http://www.gnu.org/software/texinfo/ --> -<head> -<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> -<title>Buffers (The Chickadee Game Toolkit)</title> - -<meta name="description" content="Buffers (The Chickadee Game Toolkit)" /> -<meta name="keywords" content="Buffers (The Chickadee Game Toolkit)" /> -<meta name="resource-type" content="document" /> -<meta name="distribution" content="global" /> -<meta name="Generator" content="makeinfo" /> -<link href="index.html" rel="start" title="Top" /> -<link href="Index.html" rel="index" title="Index" /> -<link href="index.html#SEC_Contents" rel="contents" title="Table of Contents" /> -<link href="Graphics.html" rel="up" title="Graphics" /> -<link href="Shaders.html" rel="next" title="Shaders" /> -<link href="Meshes.html" rel="prev" title="Meshes" /> -<style type="text/css"> -<!-- -a.summary-letter {text-decoration: none} -blockquote.indentedblock {margin-right: 0em} -div.display {margin-left: 3.2em} -div.example {margin-left: 3.2em} -div.lisp {margin-left: 3.2em} -kbd {font-style: oblique} -pre.display {font-family: inherit} -pre.format {font-family: inherit} -pre.menu-comment {font-family: serif} -pre.menu-preformatted {font-family: serif} -span.nolinebreak {white-space: nowrap} -span.roman {font-family: initial; font-weight: normal} -span.sansserif {font-family: sans-serif; font-weight: normal} -ul.no-bullet {list-style: none} -@media (min-width: 1140px) { - body { - margin-left: 14rem; - margin-right: 4rem; - max-width: 52rem; - } -} - -@media (min-width: 800px) and (max-width: 1140px) { - body { - margin-left: 6rem; - margin-right: 4rem; - max-width: 52rem; - } -} - -@media (max-width: 800px) { - body { - margin: 1rem; - } -} - ---> -</style> -<link rel="stylesheet" type="text/css" href="https://dthompson.us/css/dthompson.css" /> - - -</head> - -<body lang="en"> -<span id="Buffers"></span><div class="header"> -<p> -Next: <a href="Shaders.html" accesskey="n" rel="next">Shaders</a>, Previous: <a href="Meshes.html" accesskey="p" rel="prev">Meshes</a>, Up: <a href="Graphics.html" accesskey="u" rel="up">Graphics</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Index.html" title="Index" rel="index">Index</a>]</p> -</div> -<hr /> -<span id="Buffers-1"></span><h4 class="subsection">5.3.12 Buffers</h4> - -<p>Alright, let’s brush aside all of those pretty high level abstractions -and discuss what is going on under the hood. The GPU exists as a -discrete piece of hardware separate from the CPU. In order to make it -draw things, we must ship lots of data out of our memory space and -into the GPU. The <code>(chickadee graphics buffer</code>) module provides an -API for manipulating GPU buffers. -</p> -<p>In OpenGL terminology, a chunk of data allocated on the GPU is a -“vertex buffer object” or VBO. For example, here is a bytevector -that could be transformed into a GPU buffer that packs together vertex -position and texture coordinates: -</p> -<div class="lisp"> -<pre class="lisp"><span class="syntax-open">(</span><span class="syntax-symbol">use-modules</span> <span class="syntax-open">(</span><span class="syntax-symbol">chickadee</span> <span class="syntax-symbol">graphics</span> <span class="syntax-symbol">buffer</span><span class="syntax-close">)</span> <span class="syntax-open">(</span><span class="syntax-symbol">srfi</span> <span class="syntax-symbol">srfi-4</span><span class="syntax-close">)</span><span class="syntax-close">)</span> -<span class="syntax-open">(</span><span class="syntax-special">define</span> <span class="syntax-symbol">data</span> - <span class="syntax-open">(</span><span class="syntax-symbol">f32vector</span> <span class="syntax-symbol">-8.0</span> <span class="syntax-symbol">-8.0</span> <span class="syntax-comment">; 2D vertex -</span> <span class="syntax-symbol">0.0</span> <span class="syntax-symbol">0.0</span> <span class="syntax-comment">; 2D texture coordinate -</span> <span class="syntax-symbol">8.0</span> <span class="syntax-symbol">-8.0</span> <span class="syntax-comment">; 2D vertex -</span> <span class="syntax-symbol">1.0</span> <span class="syntax-symbol">0.0</span> <span class="syntax-comment">; 2D texture coordinate -</span> <span class="syntax-symbol">8.0</span> <span class="syntax-symbol">8.0</span> <span class="syntax-comment">; 2D vertex -</span> <span class="syntax-symbol">1.0</span> <span class="syntax-symbol">1.0</span> <span class="syntax-comment">; 2D texture coordinate -</span> <span class="syntax-symbol">-8.0</span> <span class="syntax-symbol">8.0</span> <span class="syntax-comment">; 2D vertex -</span> <span class="syntax-symbol">0.0</span> <span class="syntax-symbol">1.0</span><span class="syntax-close">)</span><span class="syntax-close">)</span> <span class="syntax-comment">; 2D texture coordinate -</span></pre></div> - -<p>This data represents a textured 16x16 square centered on the -origin. To send this data to the GPU, the <code>make-buffer</code> procedure -is needed: -</p> -<div class="lisp"> -<pre class="lisp"><span class="syntax-open">(</span><span class="syntax-special">define</span> <span class="syntax-symbol">buffer</span> <span class="syntax-open">(</span><span class="syntax-symbol">make-buffer</span> <span class="syntax-symbol">data</span> <span class="syntax-keyword">#:stride</span> <span class="syntax-symbol">16</span><span class="syntax-close">)</span><span class="syntax-close">)</span> -</pre></div> - -<p>The <code>#:stride</code> keyword argument indicates how many bytes make up -each element of the buffer. In this case, there are 4 floats per -element: 2 for the vertex, and 2 for the texture coordinate. A 32-bit -float is 4 bytes in length, so the buffer’s stride is 16. -</p> -<p>Within a VBO, one or more “attributes”, as OpenGL calls them, may be -present. Attributes are subregions within the buffer that have a -particular data type. In this case, there are two attributes packed -into the buffer. To define vertex attributes, the -<code>make-vertex-attribute</code> procedure is needed: -</p> -<div class="lisp"> -<pre class="lisp"><span class="syntax-open">(</span><span class="syntax-special">define</span> <span class="syntax-symbol">vertices</span> - <span class="syntax-open">(</span><span class="syntax-symbol">make-vertex-attribute</span> <span class="syntax-keyword">#:buffer</span> <span class="syntax-symbol">buffer</span> - <span class="syntax-keyword">#:type</span> <span class="syntax-symbol">'vec2</span> - <span class="syntax-keyword">#:component-type</span> <span class="syntax-symbol">'float</span> - <span class="syntax-keyword">#:length</span> <span class="syntax-symbol">4</span><span class="syntax-close">)</span><span class="syntax-close">)</span> -<span class="syntax-open">(</span><span class="syntax-special">define</span> <span class="syntax-symbol">texcoords</span> - <span class="syntax-open">(</span><span class="syntax-symbol">make-vertex-attribute</span> <span class="syntax-keyword">#:buffer</span> <span class="syntax-symbol">buffer</span> - <span class="syntax-keyword">#:type</span> <span class="syntax-symbol">'vec2</span> - <span class="syntax-keyword">#:component-type</span> <span class="syntax-symbol">'float</span> - <span class="syntax-keyword">#:length</span> <span class="syntax-symbol">4</span> - <span class="syntax-keyword">#:offset</span> <span class="syntax-symbol">8</span><span class="syntax-close">)</span><span class="syntax-close">)</span> -</pre></div> - -<p>To render a square, the GPU needs to draw two triangles, which means -we need 6 vertices in total. However, the above buffer only contains -data for 4 vertices. This is because there are only 4 unique vertices -for a square, but 2 of them must be repeated for each triangle. To -work with deduplicated vertex data, an “index buffer” must be -created. -</p> -<div class="lisp"> -<pre class="lisp"><span class="syntax-open">(</span><span class="syntax-special">define</span> <span class="syntax-symbol">index-buffer</span> - <span class="syntax-open">(</span><span class="syntax-symbol">make-buffer</span> <span class="syntax-open">(</span><span class="syntax-symbol">u32vector</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">3</span> <span class="syntax-symbol">2</span> <span class="syntax-symbol">0</span> <span class="syntax-symbol">2</span> <span class="syntax-symbol">1</span><span class="syntax-close">)</span> - <span class="syntax-keyword">#:target</span> <span class="syntax-symbol">'index</span><span class="syntax-close">)</span> -<span class="syntax-open">(</span><span class="syntax-special">define</span> <span class="syntax-symbol">indices</span> - <span class="syntax-open">(</span><span class="syntax-symbol">make-vertex-attribute</span> <span class="syntax-keyword">#:type</span> <span class="syntax-symbol">'scalar</span> - <span class="syntax-keyword">#:component-type</span> <span class="syntax-symbol">'unsigned-int</span> - <span class="syntax-keyword">#:buffer</span> <span class="syntax-symbol">index-buffer</span><span class="syntax-close">)</span><span class="syntax-close">)</span> -</pre></div> - -<p>Note the use of the <code>#:target</code> keyword argument. It is required -because the GPU treats index data in a special way and must be told -which data is index data. -</p> -<p>Now that the vertex attributes have been created, all that’s left is -to bind them all together in a vertex array. Vertex arrays associate -each vertex attribute with an attribute index on the GPU. The indices -that are chosen must correspond with the indices that the shader -(see <a href="Shaders.html">Shaders</a>) expects for each attribute. -</p> -<div class="lisp"> -<pre class="lisp"><span class="syntax-open">(</span><span class="syntax-special">define</span> <span class="syntax-symbol">vertex-array</span> - <span class="syntax-open">(</span><span class="syntax-symbol">make-vertex-array</span> <span class="syntax-keyword">#:indices</span> <span class="syntax-symbol">indices</span> - <span class="syntax-keyword">#:attributes</span> <span class="syntax-symbol">`</span><span class="syntax-open">(</span><span class="syntax-open">(</span><span class="syntax-symbol">0</span> <span class="syntax-symbol">.</span> <span class="syntax-symbol">,vertices</span><span class="syntax-close">)</span> - <span class="syntax-open">(</span><span class="syntax-symbol">1</span> <span class="syntax-symbol">.</span> <span class="syntax-symbol">,texcoords</span><span class="syntax-close">)</span><span class="syntax-close">)</span><span class="syntax-close">)</span><span class="syntax-close">)</span> -</pre></div> - -<p>With the vertex array created, the GPU is now fully aware of how to -interpret the data that it has been given in the original buffer. -Actually rendering this square is left as an exercise to the reader. -See the <a href="Shaders.html">Shaders</a> section and the <code>shader-apply</code> procedure in -<a href="Rendering-Engine.html">Rendering Engine</a> for the remaining pieces of a successful draw -call. Additionally, consider reading the source code for sprites, -shapes, or particles to see GPU buffers in action. -</p> -<p>Without further ado, the API reference: -</p> -<dl> -<dt id="index-make_002dbuffer">Procedure: <strong>make-buffer</strong> <em>data [#:name "anonymous"] [#:length] [#:offset 0] [#:stride 0] [#:target <code>vertex</code>] [#:usage <code>static</code>]</em></dt> -<dd> -<p>Upload <var>data</var>, a bytevector, to the GPU. By default, the entire -bytevector is uploaded. A subset of the data may be uploaded by -specifying the <var>offset</var>, the index of the first byte to be -uploaded, and <var>length</var>, the number of bytes to upload. -</p> -<p>If <var>data</var> is <code>#f</code>, allocate <var>length</var> bytes of fresh GPU -memory instead. -</p> -<p><var>target</var> and <var>usage</var> are hints that tell the GPU how the -buffer is intended to be used. -</p> -<p><var>target</var> may be: -</p> -<ul> -<li> <code>vertex</code> -Vertex attribute data. - -</li><li> <code>index</code> -Index buffer data. - -</li></ul> - -<p><var>usage</var> may be: -</p> -<ul> -<li> <code>static</code> -The buffer data will not be modified after creation. - -</li><li> <code>stream</code> -The buffer data will be modified frequently. - -</li></ul> - -<p><var>name</var> is simply an arbitrary string for debugging purposes that -is never sent to the GPU. -</p></dd></dl> - -<dl> -<dt id="index-buffer_003f">Procedure: <strong>buffer?</strong> <em>obj</em></dt> -<dd><p>Return <code>#t</code> if <var>obj</var> is a GPU buffer. -</p></dd></dl> - -<dl> -<dt id="index-index_002dbuffer_003f">Procedure: <strong>index-buffer?</strong> <em>buffer</em></dt> -<dd><p>Return <code>#t</code> if <var>buffer</var> is an index buffer. -</p></dd></dl> - -<dl> -<dt id="index-null_002dbuffer">Variable: <strong>null-buffer</strong></dt> -<dd><p>Represents the absence of a buffer. -</p></dd></dl> - -<dl> -<dt id="index-buffer_002dname">Procedure: <strong>buffer-name</strong> <em>buffer</em></dt> -<dd><p>Return the name of <var>buffer</var>. -</p></dd></dl> - -<dl> -<dt id="index-buffer_002dlength">Procedure: <strong>buffer-length</strong> <em>buffer</em></dt> -<dd><p>Return the length of <var>buffer</var>. -</p></dd></dl> - -<dl> -<dt id="index-buffer_002dstride">Procedure: <strong>buffer-stride</strong> <em>buffer</em></dt> -<dd><p>Return the amount of space, in bytes, between each element in -<var>buffer</var>. -</p></dd></dl> - -<dl> -<dt id="index-buffer_002dtarget">Procedure: <strong>buffer-target</strong> <em>buffer</em></dt> -<dd><p>Return the the intended usage of <var>buffer</var>, either <code>vertex</code> or -<code>index</code>. -</p></dd></dl> - -<dl> -<dt id="index-buffer_002dusage">Procedure: <strong>buffer-usage</strong> <em>buffer</em></dt> -<dd><p>Return the intended usage of <var>buffer</var>, either <code>static</code> for -buffer data that will not change once sent to the GPU, or -<code>stream</code> for buffer data that will be frequently updated from the -client-side. -</p></dd></dl> - -<dl> -<dt id="index-buffer_002ddata">Procedure: <strong>buffer-data</strong> <em>buffer</em></dt> -<dd><p>Return a bytevector containing all the data within <var>buffer</var>. If -<var>buffer</var> has not been mapped (see <code>with-mapped-buffer</code>) then -this procedure will return <code>#f</code>. -</p></dd></dl> - -<dl> -<dt id="index-with_002dmapped_002dbuffer">Syntax: <strong>with-mapped-buffer</strong> <em>buffer body …</em></dt> -<dd><p>Evaluate <var>body</var> in the context of <var>buffer</var> having its data -synced from GPU memory to RAM. In this context, <code>buffer-data</code> -will return a bytevector of all the data stored in <var>buffer</var>. When -program execution exits this form, the data (including any -modifications) is synced back to the GPU. -</p> -<dl> -<dt id="index-current_002dbuffer">Procedure: <strong>current-buffer</strong></dt> -<dd><p>Return the current buffer. -</p></dd></dl> - -<dl> -<dt id="index-g_003abuffer">Variable: <strong>g:buffer</strong></dt> -<dd><p>Render state for buffers (see <a href="Rendering-Engine.html">Rendering Engine</a>.) -</p></dd></dl> - -<p>This form is useful for streaming buffers that need to update their -contents dynamically, such as a sprite batch. -</p></dd></dl> - -<dl> -<dt id="index-make_002dvertex_002dattribute">Procedure: <strong>make-vertex-attribute</strong> <em>#:buffer #:type #:component-type #:length [#:offset <code>0</code>] [#:divisor <code>1</code>] [#:name <code>"anonymous"</code>]</em></dt> -<dd> -<p>Return a new vertex attribute for <var>buffer</var> starting at byte index -<var>offset</var> of <var>length</var> elements, where each element is of -<var>type</var> and composed of <var>component-type</var> values. -</p> -<p>Valid values for <var>type</var> are: -</p> -<ul> -<li> <code>scalar</code> -single number - -</li><li> <code>vec2</code> -2D vector - -</li><li> <code>vec3</code> -3D vector - -</li><li> <code>vec4</code> -4D vector - -</li><li> <code>mat2</code> -2x2 matrix - -</li><li> <code>mat3</code> -3x3 matrix - -</li><li> <code>mat4</code> -4x4 matrix -</li></ul> - -<p>Valid values for <var>component-type</var> are: -</p> -<ul> -<li> <code>byte</code> -</li><li> <code>unsigned-byte</code> -</li><li> <code>short</code> -</li><li> <code>unsigned-short</code> -</li><li> <code>int</code> -</li><li> <code>unsigned-int</code> -</li><li> <code>float</code> -</li><li> <code>double</code> - -</li></ul> - -<p><var>divisor</var> is only needed for instanced rendering applications (see -<code>shader-apply/instanced</code> in <a href="Rendering-Engine.html">Rendering Engine</a>) and represents -how many instances each vertex element applies to. A divisor of 0 -means that a single element is used for every instance and is used for -the data being instanced. A divisor of 1 means that each element is -used for 1 instance. A divisor of 2 means that each element is used -for 2 instances, and so on. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002dattribute_003f">Procedure: <strong>vertex-attribute?</strong> <em>obj</em></dt> -<dd><p>Return <code>#t</code> if <var>obj</var> is a vertex attribute. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002dattribute_002d_003ebuffer">Procedure: <strong>vertex-attribute->buffer</strong> <em>vertex-attribute</em></dt> -<dd><p>Return the buffer that <var>vertex-attribute</var> is using. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002dattribute_002dname">Procedure: <strong>vertex-attribute-name</strong> <em>vertex-attribute</em></dt> -<dd><p>Return the name of <var>vertex-attribute</var>. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002dattribute_002doffset">Procedure: <strong>vertex-attribute-offset</strong> <em>vertex-attribute</em></dt> -<dd><p>Return the byte offset of <var>vertex-attribute</var>. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002dattribute_002dtype">Procedure: <strong>vertex-attribute-type</strong> <em>vertex-attribute</em></dt> -<dd><p>Return the data type of <var>vertex-attribute</var>. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002dattribute_002dcomponent_002dtype">Procedure: <strong>vertex-attribute-component-type</strong> <em>vertex-attribute</em></dt> -<dd><p>Return the component data type of <var>vertex-attribute</var> -</p></dd></dl> - -<dl> -<dt id="index-vertex_002dattribute_002ddivisor">Procedure: <strong>vertex-attribute-divisor</strong> <em>vertex-attribute</em></dt> -<dd><p>Return the instance divisor for <var>vertex-attribute</var>. -</p></dd></dl> - -<dl> -<dt id="index-with_002dmapped_002dvertex_002dattribute">Syntax: <strong>with-mapped-vertex-attribute</strong> <em>vertex-attribute body …</em></dt> -<dd> -<p>Evaluate <var>body</var> in the context of <var>vertex-attribute</var> having -its data synced from GPU memory to RAM. See <code>with-mapped-buffer</code> -for more information. -</p></dd></dl> - -<dl> -<dt id="index-make_002dvertex_002darray">Procedure: <strong>make-vertex-array</strong> <em>#:indices #:attributes [#:mode <code>triangles</code>]</em></dt> -<dd> -<p>Return a new vertex array using the index data within the vertex -attributes <var>indices</var> and the vertex attribute data within -<var>attributes</var>. -</p> -<p><var>attributes</var> is an alist mapping shader attribute indices to -vertex attributes: -</p> -<div class="lisp"> -<pre class="lisp"><span class="syntax-symbol">`</span><span class="syntax-open">(</span><span class="syntax-open">(</span><span class="syntax-symbol">1</span> <span class="syntax-symbol">.</span> <span class="syntax-symbol">,vertex-attribute-a</span><span class="syntax-close">)</span> - <span class="syntax-open">(</span><span class="syntax-symbol">2</span> <span class="syntax-symbol">.</span> <span class="syntax-symbol">,vertex-attribute-b</span><span class="syntax-close">)</span> - <span class="syntax-symbol">...</span><span class="syntax-close">)</span> -</pre></div> - -<p>By default, the vertex array is interpreted as containing a series of -triangles. If another primtive type is desired, the <var>mode</var> -keyword argument may be overridden. The following values are -supported: -</p> -<ul> -<li> <code>points</code> -</li><li> <code>lines</code> -</li><li> <code>line-loop</code> -</li><li> <code>line-strip</code> -</li><li> <code>triangles</code> -</li><li> <code>triangle-strip</code> -</li><li> <code>triangle-fan</code> -</li></ul> - -</dd></dl> - -<dl> -<dt id="index-null_002dvertex_002darray">Variable: <strong>null-vertex-array</strong></dt> -<dd><p>Represents the absence of a vertex array. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002darray_003f">Procedure: <strong>vertex-array?</strong> <em>obj</em></dt> -<dd><p>Return <code>#t</code> if <var>obj</var> is a vertex array. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002darray_002dindices">Procedure: <strong>vertex-array-indices</strong> <em>vertex-array</em></dt> -<dd><p>Return the buffer view containing index data for <var>vertex-array</var>. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002darray_002dattributes">Procedure: <strong>vertex-array-attributes</strong> <em>vertex-array</em></dt> -<dd><p>Return the attribute index -> buffer view mapping of vertex attribute -data for <var>vertex-array</var>. -</p></dd></dl> - -<dl> -<dt id="index-vertex_002darray_002dmode">Procedure: <strong>vertex-array-mode</strong> <em>vertex-array</em></dt> -<dd><p>Return the primitive rendering mode for <var>vertex-array</var>. -</p></dd></dl> - -<dl> -<dt id="index-current_002dvertex_002darray">Procedure: <strong>current-vertex-array</strong></dt> -<dd><p>Return the current vertex array. -</p></dd></dl> - -<dl> -<dt id="index-g_003avertex_002darray">Variable: <strong>g:vertex-array</strong></dt> -<dd><p>Render state for vertex arrays (see <a href="Rendering-Engine.html">Rendering Engine</a>.) -</p></dd></dl> - -<hr /> -<div class="header"> -<p> -Next: <a href="Shaders.html" accesskey="n" rel="next">Shaders</a>, Previous: <a href="Meshes.html" accesskey="p" rel="prev">Meshes</a>, Up: <a href="Graphics.html" accesskey="u" rel="up">Graphics</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Index.html" title="Index" rel="index">Index</a>]</p> -</div> - - - -</body> -</html> |