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43 <tr><td>
44 \ref Rotation2D "2D rotation" from an angle</td><td>\code
45 Rotation2D<float> rot2(angle_in_radian);\endcode</td></tr>
46 <tr class="alt"><td>
47 3D rotation as an \ref AngleAxis "angle + axis"</td><td>\code
49 <span class="note">The axis vector must be normalized.</span></td></tr>
50 <tr><td>
51 3D rotation as a \ref Quaternion "quaternion"</td><td>\code
52 Quaternion<float> q; q = AngleAxis<float>(angle_in_radian, axis);\endcode</td></tr>
53 <tr class="alt"><td>
54 N-D Scaling</td><td>\code
58 Scaling(vecN)\endcode</td></tr>
59 <tr><td>
60 N-D Translation</td><td>\code
64 Translation<float,N>(vecN)\endcode</td></tr>
65 <tr class="alt"><td>
66 N-D \ref TutorialGeoTransform "Affine transformation"</td><td>\code
68 Transform<float,3,Affine> t = Translation3f(p) * AngleAxisf(a,axis) * Scaling(s);\endcode</td></tr>
69 <tr><td>
71 <em class=note>(pure rotations, \n scaling, etc.)</em></td><td>\code
74 Matrix<float,3> t = AngleAxisf(a,axis) * Scaling(s);\endcode</td></tr>
91 <tr><td>\code
99 \endcode</td></tr>
108 <tr><td>
109 Concatenation of two transformations</td><td>\code
110 gen1 * gen2;\endcode</td></tr>
111 <tr class="alt"><td>Apply the transformation to a vector</td><td>\code
112 vec2 = gen1 * vec1;\endcode</td></tr>
113 <tr><td>Get the inverse of the transformation</td><td>\code
114 gen2 = gen1.inverse();\endcode</td></tr>
115 <tr class="alt"><td>Spherical interpolation \n (Rotation2D and Quaternion only)</td><td>\code
116 rot3 = rot1.slerp(alpha,rot2);\endcode</td></tr>
128 <tr><td>
129 Apply the transformation to a \b point </td><td>\code
131 p2 = t * p1;\endcode</td></tr>
132 <tr class="alt"><td>
133 Apply the transformation to a \b vector </td><td>\code
135 vec2 = t.linear() * vec1;\endcode</td></tr>
136 <tr><td>
138 (<a href="http://www.cgafaq.info/wiki/Transforming_normals">explanations</a>)</td><td>\code
141 n2 = (normalMatrix * n1).normalized();\endcode</td></tr>
142 <tr class="alt"><td>
144 (no scaling, no shear)</td><td>\code
145 n2 = t.linear() * n1;\endcode</td></tr>
146 <tr><td>
147 OpenGL compatibility \b 3D </td><td>\code
148 glLoadMatrixf(t.data());\endcode</td></tr>
149 <tr class="alt"><td>
150 OpenGL compatibility \b 2D </td><td>\code
154 glLoadMatrixf(aux.data());\endcode</td></tr>
159 <tr><td>
160 full read-write access to the internal matrix</td><td>\code
163 \endcode</td></tr>
164 <tr class="alt"><td>
165 coefficient accessors</td><td>\code
168 \endcode</td></tr>
169 <tr><td>
170 translation part</td><td>\code
173 \endcode</td></tr>
174 <tr class="alt"><td>
175 linear part</td><td>\code
178 \endcode</td></tr>
179 <tr><td>
180 extract the rotation matrix</td><td>\code
182 \endcode</td></tr>
191 <tr><td>Translation</td><td>\code
194 \endcode</td><td>\code
197 \endcode</td></tr>
198 …lass="alt"><td>\b Rotation \n <em class="note">In 2D and for the procedural API, any_rotation can …
201 \endcode</td><td>\code
204 \endcode</td></tr>
205 <tr><td>Scaling</td><td>\code
210 \endcode</td><td>\code
215 \endcode</td></tr>
216 <tr class="alt"><td>Shear transformation \n ( \b 2D \b only ! )</td><td>\code
219 \endcode</td><td></td></tr>
224 <tr><td>\code
226 \endcode</td></tr>
227 <tr><td>\code
229 \endcode</td></tr>
236 <tr><td style="max-width:30em;">
239 to create a rotation matrix according to the 2-1-2 convention.</td><td>\code
244 \endcode</td></tr>