001 package com.croftsoft.core.math.axis;
002
003 import com.croftsoft.core.math.matrix.Matrix3x3Imp;
004 import com.croftsoft.core.math.matrix.Matrix3x3Mut;
005 import com.croftsoft.core.math.quat.QuatImp;
006 import com.croftsoft.core.math.quat.QuatMut;
007
008 /***********************************************************************
009 * A library of static methods to manipulate AxisAngle objects.
010 *
011 * @version
012 * $Id: AxisAngleLib.java,v 1.1 2008/05/09 18:35:55 croft Exp $
013 * @since
014 * 2008-05-09
015 * @author
016 * <a href="https://www.croftsoft.com/">David Wallace Croft</a>
017 ***********************************************************************/
018
019 public final class AxisAngleLib
020 ////////////////////////////////////////////////////////////////////////
021 ////////////////////////////////////////////////////////////////////////
022 {
023
024 public static double magnitude ( final AxisAngle axisAngle )
025 ////////////////////////////////////////////////////////////////////////
026 {
027 final double x = axisAngle.getX ( );
028
029 final double y = axisAngle.getY ( );
030
031 final double z = axisAngle.getZ ( );
032
033 return Math.sqrt ( x * x + y * y + z * z );
034 }
035
036 public static boolean matches (
037 final AxisAngle axisAngle0,
038 final AxisAngle axisAngle1 )
039 ////////////////////////////////////////////////////////////////////////
040 {
041 return axisAngle0.getDegrees ( ) == axisAngle1.getDegrees ( )
042 && axisAngle0.getX ( ) == axisAngle1.getX ( )
043 && axisAngle0.getY ( ) == axisAngle1.getY ( )
044 && axisAngle0.getZ ( ) == axisAngle1.getZ ( );
045 }
046
047 public static boolean matches (
048 final AxisAngle axisAngle0,
049 final AxisAngle axisAngle1,
050 final double tolerance )
051 ////////////////////////////////////////////////////////////////////////
052 {
053 if ( tolerance < 0 )
054 {
055 throw new IllegalArgumentException ( "tolerance < 0" );
056 }
057
058 return Math.abs (
059 axisAngle0.getDegrees ( ) - axisAngle1.getDegrees ( ) )
060 <= tolerance
061 && Math.abs ( axisAngle0.getX ( ) - axisAngle1.getX ( ) )
062 <= tolerance
063 && Math.abs ( axisAngle0.getY ( ) - axisAngle1.getY ( ) )
064 <= tolerance
065 && Math.abs ( axisAngle0.getZ ( ) - axisAngle1.getZ ( ) )
066 <= tolerance;
067 }
068
069 public static void normalize ( final AxisAngleMut axisAngleMut )
070 ////////////////////////////////////////////////////////////////////////
071 {
072 final double magnitude = axisAngleMut.magnitude ( );
073
074 axisAngleMut.setX ( axisAngleMut.getX ( ) / magnitude );
075
076 axisAngleMut.setY ( axisAngleMut.getY ( ) / magnitude );
077
078 axisAngleMut.setZ ( axisAngleMut.getZ ( ) / magnitude );
079 }
080
081 public static QuatMut toQuat ( final AxisAngle axisAngle )
082 ////////////////////////////////////////////////////////////////////////
083 {
084 final double halfRadians
085 = Math.toRadians ( axisAngle.getDegrees ( ) / 2 );
086
087 final double sinHalfRadians = Math.sin ( halfRadians );
088
089 return new QuatImp (
090 Math.cos ( halfRadians ),
091 sinHalfRadians * axisAngle.getX ( ),
092 sinHalfRadians * axisAngle.getY ( ),
093 sinHalfRadians * axisAngle.getZ ( ) );
094 }
095
096 public static Matrix3x3Mut toRotationMatrix (
097 final AxisAngle axisAngle )
098 ////////////////////////////////////////////////////////////////////////
099 {
100 // return toQuat ( axisAngle ).toRotationMatrix ( );
101
102 final double degrees = axisAngle.getDegrees ( );
103
104 final double x = axisAngle.getX ( );
105
106 final double y = axisAngle.getY ( );
107
108 final double z = axisAngle.getZ ( );
109
110 final double c = Math.cos ( Math.toRadians ( degrees ) );
111
112 final double s = Math.sin ( Math.toRadians ( degrees ) );
113
114 // Lengyel, "Mathematics for 3D Game Programming & Computer Graphics",
115 // Second Edition, p80, equation 3.22.
116
117 return new Matrix3x3Imp (
118 c + ( 1 - c ) * x * x,
119 ( 1 - c ) * x * y - s * z,
120 ( 1 - c ) * x * z + s * y,
121
122 ( 1 - c ) * x * y + s * z,
123 c + ( 1 - c ) * y * y,
124 ( 1 - c ) * y * z - s * x,
125
126 ( 1 - c ) * x * z - s * y,
127 ( 1 - c ) * y * z + s * x,
128 c + ( 1 - c ) * z * z );
129 }
130
131 public static String toString ( final AxisAngle axisAngle )
132 ////////////////////////////////////////////////////////////////////////
133 {
134 return String.format (
135 "%1$1.3f; %2$1.3f, %3$1.3f, %4$1.3f",
136 new Double ( axisAngle.getDegrees ( ) ),
137 new Double ( axisAngle.getX ( ) ),
138 new Double ( axisAngle.getY ( ) ),
139 new Double ( axisAngle.getZ ( ) ) );
140 }
141
142 ////////////////////////////////////////////////////////////////////////
143 // private methods
144 ////////////////////////////////////////////////////////////////////////
145
146 private AxisAngleLib ( )
147 ////////////////////////////////////////////////////////////////////////
148 {
149 // empty
150 }
151
152 ////////////////////////////////////////////////////////////////////////
153 ////////////////////////////////////////////////////////////////////////
154 }