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</pre><pre class='rust '>
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>fmt</span>;
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::{<span class='ident'>Add</span>, <span class='ident'>Sub</span>, <span class='ident'>Mul</span>, <span class='ident'>Neg</span>, <span class='ident'>MulAssign</span>};
<span class='kw'>use</span> <span class='ident'>rand</span>::{<span class='ident'>Rand</span>, <span class='ident'>Rng</span>};
<span class='kw'>use</span> <span class='ident'>num</span>::<span class='ident'>One</span>;
<span class='kw'>use</span> <span class='ident'>structs</span>::<span class='ident'>matrix</span>::{<span class='ident'>Matrix3</span>, <span class='ident'>Matrix4</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>structure</span>::{<span class='ident'>Cast</span>, <span class='ident'>Dimension</span>, <span class='ident'>Column</span>, <span class='ident'>BaseFloat</span>, <span class='ident'>BaseNum</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>operations</span>::{<span class='ident'>Inverse</span>, <span class='ident'>ApproxEq</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>geometry</span>::{<span class='ident'>RotationMatrix</span>, <span class='ident'>Rotation</span>, <span class='ident'>Rotate</span>, <span class='ident'>AbsoluteRotate</span>, <span class='ident'>Transform</span>, <span class='ident'>Transformation</span>,
<span class='ident'>Translate</span>, <span class='ident'>Translation</span>, <span class='ident'>ToHomogeneous</span>};
<span class='kw'>use</span> <span class='ident'>structs</span>::<span class='ident'>vector</span>::{<span class='ident'>Vector1</span>, <span class='ident'>Vector2</span>, <span class='ident'>Vector3</span>};
<span class='kw'>use</span> <span class='ident'>structs</span>::<span class='ident'>point</span>::{<span class='ident'>Point2</span>, <span class='ident'>Point3</span>};
<span class='kw'>use</span> <span class='ident'>structs</span>::<span class='ident'>rotation</span>::{<span class='ident'>Rotation2</span>, <span class='ident'>Rotation3</span>};
<span class='attribute'>#[<span class='ident'>cfg</span>(<span class='ident'>feature</span><span class='op'>=</span><span class='string'>"arbitrary"</span>)]</span>
<span class='kw'>use</span> <span class='ident'>quickcheck</span>::{<span class='ident'>Arbitrary</span>, <span class='ident'>Gen</span>};
<span class='doccomment'>/// Two dimensional **direct** isometry.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This is the composition of a rotation followed by a translation. Vectors `Vector2` are not</span>
<span class='doccomment'>/// affected by the translational component of this transformation while points `Point2` are.</span>
<span class='doccomment'>/// Isometries conserve angles and distances, hence do not allow shearing nor scaling.</span>
<span class='attribute'>#[<span class='ident'>repr</span>(<span class='ident'>C</span>)]</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Eq</span>, <span class='ident'>PartialEq</span>, <span class='ident'>RustcEncodable</span>, <span class='ident'>RustcDecodable</span>, <span class='ident'>Clone</span>, <span class='ident'>Debug</span>, <span class='ident'>Copy</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>Isometry2</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// The rotation applicable by this isometry.</span>
<span class='kw'>pub</span> <span class='ident'>rotation</span>: <span class='ident'>Rotation2</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>,
<span class='doccomment'>/// The translation applicable by this isometry.</span>
<span class='kw'>pub</span> <span class='ident'>translation</span>: <span class='ident'>Vector2</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>
}
<span class='doccomment'>/// Three dimensional **direct** isometry.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This is the composition of a rotation followed by a translation. Vectors `Vector3` are not</span>
<span class='doccomment'>/// affected by the translational component of this transformation while points `Point3` are.</span>
<span class='doccomment'>/// Isometries conserve angles and distances, hence do not allow shearing nor scaling.</span>
<span class='attribute'>#[<span class='ident'>repr</span>(<span class='ident'>C</span>)]</span>
<span class='attribute'>#[<span class='ident'>derive</span>(<span class='ident'>Eq</span>, <span class='ident'>PartialEq</span>, <span class='ident'>RustcEncodable</span>, <span class='ident'>RustcDecodable</span>, <span class='ident'>Clone</span>, <span class='ident'>Debug</span>, <span class='ident'>Copy</span>)]</span>
<span class='kw'>pub</span> <span class='kw'>struct</span> <span class='ident'>Isometry3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// The rotation applicable by this isometry.</span>
<span class='kw'>pub</span> <span class='ident'>rotation</span>: <span class='ident'>Rotation3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>,
<span class='doccomment'>/// The translation applicable by this isometry.</span>
<span class='kw'>pub</span> <span class='ident'>translation</span>: <span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>Clone</span> <span class='op'>+</span> <span class='ident'>BaseFloat</span><span class='op'>></span> <span class='ident'>Isometry3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Creates an isometry that corresponds to the local frame of an observer standing at the</span>
<span class='doccomment'>/// point `eye` and looking toward `target`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// It maps the view direction `target - eye` to the positive `z` axis and the origin to the</span>
<span class='doccomment'>/// `eye`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Arguments</span>
<span class='doccomment'>/// * eye - The observer position.</span>
<span class='doccomment'>/// * target - The target position.</span>
<span class='doccomment'>/// * up - Vertical direction. The only requirement of this parameter is to not be collinear</span>
<span class='doccomment'>/// to `eye - at`. Non-collinearity is not checked.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>new_observer_frame</span>(<span class='ident'>eye</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>target</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>up</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Isometry3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>new_rotation_matrix</span> <span class='op'>=</span> <span class='ident'>Rotation3</span>::<span class='ident'>new_observer_frame</span>(<span class='kw-2'>&</span>(<span class='op'>*</span><span class='ident'>target</span> <span class='op'>-</span> <span class='op'>*</span><span class='ident'>eye</span>), <span class='ident'>up</span>);
<span class='ident'>Isometry3</span>::<span class='ident'>new_with_rotation_matrix</span>(<span class='ident'>eye</span>.<span class='ident'>as_vector</span>().<span class='ident'>clone</span>(), <span class='ident'>new_rotation_matrix</span>)
}
<span class='doccomment'>/// Builds a right-handed look-at view matrix.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This conforms to the common notion of right handed look-at matrix from the computer</span>
<span class='doccomment'>/// graphics community.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Arguments</span>
<span class='doccomment'>/// * eye - The eye position.</span>
<span class='doccomment'>/// * target - The target position.</span>
<span class='doccomment'>/// * up - A vector approximately aligned with required the vertical axis. The only</span>
<span class='doccomment'>/// requirement of this parameter is to not be collinear to `target - eye`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>look_at_rh</span>(<span class='ident'>eye</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>target</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>up</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Isometry3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>rotation</span> <span class='op'>=</span> <span class='ident'>Rotation3</span>::<span class='ident'>look_at_rh</span>(<span class='kw-2'>&</span>(<span class='op'>*</span><span class='ident'>target</span> <span class='op'>-</span> <span class='op'>*</span><span class='ident'>eye</span>), <span class='ident'>up</span>);
<span class='kw'>let</span> <span class='ident'>trans</span> <span class='op'>=</span> <span class='ident'>rotation</span> <span class='op'>*</span> (<span class='op'>-</span><span class='op'>*</span><span class='ident'>eye</span>);
<span class='ident'>Isometry3</span>::<span class='ident'>new_with_rotation_matrix</span>(<span class='ident'>trans</span>.<span class='ident'>to_vector</span>(), <span class='ident'>rotation</span>)
}
<span class='doccomment'>/// Builds a left-handed look-at view matrix.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This conforms to the common notion of left handed look-at matrix from the computer</span>
<span class='doccomment'>/// graphics community.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Arguments</span>
<span class='doccomment'>/// * eye - The eye position.</span>
<span class='doccomment'>/// * target - The target position.</span>
<span class='doccomment'>/// * up - A vector approximately aligned with required the vertical axis. The only</span>
<span class='doccomment'>/// requirement of this parameter is to not be collinear to `target - eye`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>pub</span> <span class='kw'>fn</span> <span class='ident'>look_at_lh</span>(<span class='ident'>eye</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>target</span>: <span class='kw-2'>&</span><span class='ident'>Point3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>, <span class='ident'>up</span>: <span class='kw-2'>&</span><span class='ident'>Vector3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span>) <span class='op'>-></span> <span class='ident'>Isometry3</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='kw'>let</span> <span class='ident'>rotation</span> <span class='op'>=</span> <span class='ident'>Rotation3</span>::<span class='ident'>look_at_lh</span>(<span class='kw-2'>&</span>(<span class='op'>*</span><span class='ident'>target</span> <span class='op'>-</span> <span class='op'>*</span><span class='ident'>eye</span>), <span class='ident'>up</span>);
<span class='kw'>let</span> <span class='ident'>trans</span> <span class='op'>=</span> <span class='ident'>rotation</span> <span class='op'>*</span> (<span class='op'>-</span><span class='op'>*</span><span class='ident'>eye</span>);
<span class='ident'>Isometry3</span>::<span class='ident'>new_with_rotation_matrix</span>(<span class='ident'>trans</span>.<span class='ident'>to_vector</span>(), <span class='ident'>rotation</span>)
}
}
<span class='macro'>isometry_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Rotation2</span>, <span class='ident'>Vector2</span>, <span class='ident'>Vector1</span>);
<span class='macro'>rotation_matrix_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Rotation2</span>, <span class='ident'>Vector2</span>, <span class='ident'>Vector1</span>);
<span class='macro'>rotation_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Rotation2</span>, <span class='ident'>Vector1</span>);
<span class='macro'>dim_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='number'>2</span>);
<span class='macro'>one_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>);
<span class='macro'>absolute_rotate_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Vector2</span>);
<span class='macro'>rand_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>);
<span class='macro'>approx_eq_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>);
<span class='macro'>to_homogeneous_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Matrix3</span>);
<span class='macro'>inverse_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>);
<span class='macro'>transform_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Point2</span>);
<span class='macro'>transformation_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>);
<span class='macro'>rotate_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Vector2</span>);
<span class='macro'>translation_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Vector2</span>);
<span class='macro'>translate_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Point2</span>);
<span class='macro'>isometry_mul_isometry_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>);
<span class='macro'>isometry_mul_rotation_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Rotation2</span>);
<span class='macro'>isometry_mul_point_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Point2</span>);
<span class='macro'>isometry_mul_vec_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>, <span class='ident'>Vector2</span>);
<span class='macro'>arbitrary_isometry_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>);
<span class='macro'>isometry_display_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry2</span>);
<span class='macro'>isometry_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Rotation3</span>, <span class='ident'>Vector3</span>, <span class='ident'>Vector3</span>);
<span class='macro'>rotation_matrix_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Rotation3</span>, <span class='ident'>Vector3</span>, <span class='ident'>Vector3</span>);
<span class='macro'>rotation_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Rotation3</span>, <span class='ident'>Vector3</span>);
<span class='macro'>dim_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='number'>3</span>);
<span class='macro'>one_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>);
<span class='macro'>absolute_rotate_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Vector3</span>);
<span class='macro'>rand_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>);
<span class='macro'>approx_eq_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>);
<span class='macro'>to_homogeneous_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Matrix4</span>);
<span class='macro'>inverse_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>);
<span class='macro'>transform_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Point3</span>);
<span class='macro'>transformation_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>);
<span class='macro'>rotate_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Vector3</span>);
<span class='macro'>translation_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Vector3</span>);
<span class='macro'>translate_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Point3</span>);
<span class='macro'>isometry_mul_isometry_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>);
<span class='macro'>isometry_mul_rotation_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Rotation3</span>);
<span class='macro'>isometry_mul_point_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Point3</span>);
<span class='macro'>isometry_mul_vec_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>, <span class='ident'>Vector3</span>);
<span class='macro'>arbitrary_isometry_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>);
<span class='macro'>isometry_display_impl</span><span class='macro'>!</span>(<span class='ident'>Isometry3</span>);
</pre>
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