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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: CastleQuaternions</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 CastleQuaternions</h1>
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<td><a class="section" href="#PasDoc-Description">Description</a></td><td><a class="section" href="#PasDoc-Uses">Uses</a></td><td><a class="section" href="#PasDoc-Classes">Classes, Interfaces, Objects and Records</a></td><td><a class="section" href="#PasDoc-FuncsProcs">Functions and Procedures</a></td><td>Types</td><td><a class="section" href="#PasDoc-Constants">Constants</a></td><td>Variables</td></tr></table>
<a name="PasDoc-Description"></a><h2 class="description">Description</h2>
<p>
Quaternions (in particular using them to express 3D rotations). </p>
<a name="PasDoc-Uses"></a><h2 class="uses">Uses</h2>
<ul class="useslist"><li><a href="CastleVectors.html">CastleVectors</a></li></ul><h2 class="overview">Overview</h2>
<a name="PasDoc-Classes"></a><h3 class="cio">Classes, Interfaces, Objects and Records</h3>
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<th class="itemname">Name</th>
<th class="itemdesc">Description</th>
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<td class="itemname">Object <a class="bold" href="CastleQuaternions.TQuaternion.html"><code>TQuaternion</code></a></td>
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<a name="PasDoc-FuncsProcs"></a><h3 class="summary">Functions and Procedures</h3>
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<td class="itemcode"><code>function <b><a href="CastleQuaternions.html#QuatFromAxisAngle">QuatFromAxisAngle</a></b>(const Axis: <a href="CastleVectors.html#TVector3Single">TVector3Single</a>; const AngleRad: Single; const NormalizeAxis: boolean = false): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<td class="itemcode"><code>function <b><a href="CastleQuaternions.html#QuatFromAxisAngle">QuatFromAxisAngle</a></b>(const AxisAngle: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>; const NormalizeAxis: boolean = false): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<td class="itemcode"><code>operator * (const Q1, Q2: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<td class="itemcode"><code>function <b><a href="CastleQuaternions.html#SLerp">SLerp</a></b>(const A: Single; const Q1, Q2: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<td class="itemcode"><code>function <b><a href="CastleQuaternions.html#SLerp">SLerp</a></b>(const A: Single; const Rot1, Rot2: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>): <a href="CastleVectors.html#TVector4Single">TVector4Single</a>;</code></td>
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<td class="itemcode"><code>function <b><a href="CastleQuaternions.html#NLerp">NLerp</a></b>(const A: Single; const Q1, Q2: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>; const ForceShortestPath: boolean = true): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<td class="itemcode"><code>function <b><a href="CastleQuaternions.html#NLerp">NLerp</a></b>(const A: Single; const Rot1, Rot2: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>; const ForceShortestPath: boolean = true): <a href="CastleVectors.html#TVector4Single">TVector4Single</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="CastleQuaternions.html#QuatIdentityRot">QuatIdentityRot</a></b>: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a> = (Data: (Vector: (0, 0, 0); Real: 1));</code></td>
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<h2 class="description">Description</h2>
<h3 class="detail">Functions and Procedures</h3>
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<td class="itemcode"><a name="QuatFromAxisAngle"></a><code>function <b>QuatFromAxisAngle</b>(const Axis: <a href="CastleVectors.html#TVector3Single">TVector3Single</a>; const AngleRad: Single; const NormalizeAxis: boolean = false): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<p>
Calculate unit quaternion representing rotation around Axis by AngleRad angle (in radians).
<p>Axis must be normalized, or you have to pass NormalizeAxis = true (then we'll normalize it ourselves inside). Otherwise you will get non-normalized quaternion that doesn't represent rotation, and is usually useless for us.</p>
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<td class="itemcode"><a name="QuatFromAxisAngle"></a><code>function <b>QuatFromAxisAngle</b>(const AxisAngle: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>; const NormalizeAxis: boolean = false): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<td class="itemcode"><a name="*"></a><code>operator * (const Q1, Q2: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<p>
Multiply two quaternions.
<p>Geometric interpretation: If these are unit quaternions representing rotations, multiplying them calculates one rotation that has the same effect as rotating by Q2 and then by Q1.
<p>Normal of result is equal to norm of Q1 * norm of Q2 (in particular, multiplying unit quaternions (used for rotations) yields another unit quaternion for sure).</p>
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<td class="itemcode"><a name="SLerp"></a><code>function <b>SLerp</b>(const A: Single; const Q1, Q2: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<p>
Interpolate between two rotations, along the shortest path on the unit sphere, with constant speed.
<p>The overloaded version that works with <a class="normal" href="CastleVectors.html#TVector4Single">TVector4Single</a> takes a rotation (not a quaternion) expressed as an axis (first 3 elements) and angle (in radians, 4th element). Axis does not have to be normalized (we'll normalize it). This is nice e.g. to interpolate VRML/X3D rotations.
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<td class="itemcode"><a name="SLerp"></a><code>function <b>SLerp</b>(const A: Single; const Rot1, Rot2: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>): <a href="CastleVectors.html#TVector4Single">TVector4Single</a>;</code></td>
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<td class="itemcode"><a name="NLerp"></a><code>function <b>NLerp</b>(const A: Single; const Q1, Q2: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>; const ForceShortestPath: boolean = true): <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a>;</code></td>
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<p>
Interpolate between two rotations, along the straightest path on the unit sphere.
<p>This is faster than <a class="normal" href="CastleQuaternions.html#SLerp">SLerp</a>, but does not guarantee the interpolated result travels with constant speed. Often it's not a noticeable / important problem (see <a href="http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/">http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/</a>)
<p>When ForceShortestPath = <code>False</code>, this doesn't guarantee choosing the shortest path. Although it goes through the <i>straightest</i> path, there are two such paths, it may go through the shorter or longer one. Use ForceShortestPath = <code>True</code> if you want to interpolate through the shortest.
<p>The overloaded version that works with <a class="normal" href="CastleVectors.html#TVector4Single">TVector4Single</a> takes a rotation (not a quaternion) expressed as an axis (first 3 elements) and angle (in radians, 4th element). Axis does not have to be normalized (we'll normalize it). This is nice e.g. to interpolate VRML/X3D rotations.
<p></p>
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<table class="detail wide_list">
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<td class="itemcode"><a name="NLerp"></a><code>function <b>NLerp</b>(const A: Single; const Rot1, Rot2: <a href="CastleVectors.html#TVector4Single">TVector4Single</a>; const ForceShortestPath: boolean = true): <a href="CastleVectors.html#TVector4Single">TVector4Single</a>;</code></td>
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<h3 class="detail">Constants</h3>
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<td class="itemcode"><a name="QuatIdentityRot"></a><code><b>QuatIdentityRot</b>: <a href="CastleQuaternions.TQuaternion.html">TQuaternion</a> = (Data: (Vector: (0, 0, 0); Real: 1));</code></td>
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