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</pre><pre class='rust '>
<span class='doccomment'>//! Traits of operations having a well-known or explicit geometric meaning.</span>
<span class='kw'>use</span> <span class='ident'>std</span>::<span class='ident'>ops</span>::{<span class='ident'>Neg</span>, <span class='ident'>Mul</span>};
<span class='kw'>use</span> <span class='ident'>traits</span>::<span class='ident'>structure</span>::{<span class='ident'>BaseFloat</span>, <span class='ident'>SquareMatrix</span>};
<span class='doccomment'>/// Trait of object which represent a translation, and to wich new translation</span>
<span class='doccomment'>/// can be appended.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Translation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='comment'>// FIXME: add a "from translation: translantion(V) -> Self ?</span>
<span class='doccomment'>/// Gets the translation associated with this object.</span>
<span class='kw'>fn</span> <span class='ident'>translation</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>V</span>;
<span class='doccomment'>/// Gets the inverse translation associated with this object.</span>
<span class='kw'>fn</span> <span class='ident'>inverse_translation</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>V</span>;
<span class='doccomment'>/// Appends a translation to this object.</span>
<span class='kw'>fn</span> <span class='ident'>append_translation_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>V</span>);
<span class='doccomment'>/// Appends the translation `amount` to a copy of `t`.</span>
<span class='kw'>fn</span> <span class='ident'>append_translation</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Prepends a translation to this object.</span>
<span class='kw'>fn</span> <span class='ident'>prepend_translation_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>V</span>);
<span class='doccomment'>/// Prepends the translation `amount` to a copy of `t`.</span>
<span class='kw'>fn</span> <span class='ident'>prepend_translation</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Sets the translation.</span>
<span class='kw'>fn</span> <span class='ident'>set_translation</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>V</span>);
}
<span class='doccomment'>/// Trait of objects able to translate other objects. This is typically</span>
<span class='doccomment'>/// implemented by vectors to translate points.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Translate</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='doccomment'>/// Apply a translation to an object.</span>
<span class='kw'>fn</span> <span class='ident'>translate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>;
<span class='doccomment'>/// Apply an inverse translation to an object.</span>
<span class='kw'>fn</span> <span class='ident'>inverse_translate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>;
}
<span class='doccomment'>/// Trait of object which can represent a rotation, and to which new rotations can be appended. A</span>
<span class='doccomment'>/// rotation is assumed to be an isometry without translation and without reflexion.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='doccomment'>/// Gets the rotation associated with `self`.</span>
<span class='kw'>fn</span> <span class='ident'>rotation</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>V</span>;
<span class='doccomment'>/// Gets the inverse rotation associated with `self`.</span>
<span class='kw'>fn</span> <span class='ident'>inverse_rotation</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>V</span>;
<span class='doccomment'>/// Appends a rotation to this object.</span>
<span class='kw'>fn</span> <span class='ident'>append_rotation_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>V</span>);
<span class='doccomment'>/// Appends the rotation `amount` to a copy of `t`.</span>
<span class='kw'>fn</span> <span class='ident'>append_rotation</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Prepends a rotation to this object.</span>
<span class='kw'>fn</span> <span class='ident'>prepend_rotation_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>V</span>);
<span class='doccomment'>/// Prepends the rotation `amount` to a copy of `t`.</span>
<span class='kw'>fn</span> <span class='ident'>prepend_rotation</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Sets the rotation of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>set_rotation</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>V</span>);
}
<span class='doccomment'>/// Trait of object that can be rotated to be superimposed with another one of the same nature.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>RotationTo</span> {
<span class='doccomment'>/// Type of the angle between two elements.</span>
<span class='kw'>type</span> <span class='ident'>AngleType</span>;
<span class='doccomment'>/// Type of the rotation between two elements.</span>
<span class='kw'>type</span> <span class='ident'>DeltaRotationType</span>;
<span class='doccomment'>/// Computes an angle nedded to transform the first element to the second one using a</span>
<span class='doccomment'>/// rotation.</span>
<span class='kw'>fn</span> <span class='ident'>angle_to</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='self'>Self</span>) <span class='op'>-></span> <span class='self'>Self</span>::<span class='ident'>AngleType</span>;
<span class='doccomment'>/// Computes the smallest rotation needed to transform the first element to the second one.</span>
<span class='kw'>fn</span> <span class='ident'>rotation_to</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='self'>Self</span>) <span class='op'>-></span> <span class='self'>Self</span>::<span class='ident'>DeltaRotationType</span>;
}
<span class='doccomment'>/// Trait of objects able to rotate other objects.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This is typically implemented by matrices which rotate vectors.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Rotate</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='doccomment'>/// Applies a rotation to `v`.</span>
<span class='kw'>fn</span> <span class='ident'>rotate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>;
<span class='doccomment'>/// Applies an inverse rotation to `v`.</span>
<span class='kw'>fn</span> <span class='ident'>inverse_rotate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>;
}
<span class='doccomment'>/// Various composition of rotation and translation.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Utilities to make rotations with regard to a point different than the origin. All those</span>
<span class='doccomment'>/// operations are the composition of rotations and translations.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Those operations are automatically implemented in term of the `Rotation` and `Translation`</span>
<span class='doccomment'>/// traits.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>RotationWithTranslation</span><span class='op'><</span><span class='ident'>LV</span>: <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>LV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Copy</span>, <span class='ident'>AV</span><span class='op'>></span>: <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>AV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Translation</span><span class='op'><</span><span class='ident'>LV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Sized</span> {
<span class='doccomment'>/// Applies a rotation centered on a specific point.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Arguments</span>
<span class='doccomment'>/// * `t` - the object to be rotated.</span>
<span class='doccomment'>/// * `amount` - the rotation to apply.</span>
<span class='doccomment'>/// * `point` - the center of rotation.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>append_rotation_wrt_point</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>AV</span>, <span class='ident'>center</span>: <span class='kw-2'>&</span><span class='ident'>LV</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='kw'>let</span> <span class='kw-2'>mut</span> <span class='ident'>res</span> <span class='op'>=</span> <span class='ident'>Translation</span>::<span class='ident'>append_translation</span>(<span class='self'>self</span>, <span class='kw-2'>&</span><span class='op'>-</span><span class='op'>*</span><span class='ident'>center</span>);
<span class='ident'>res</span>.<span class='ident'>append_rotation_mut</span>(<span class='ident'>amount</span>);
<span class='ident'>res</span>.<span class='ident'>append_translation_mut</span>(<span class='ident'>center</span>);
<span class='ident'>res</span>
}
<span class='doccomment'>/// Rotates `self` using a specific center of rotation.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The rotation is applied in-place.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Arguments</span>
<span class='doccomment'>/// * `amount` - the rotation to be applied</span>
<span class='doccomment'>/// * `center` - the new center of rotation</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>append_rotation_wrt_point_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>AV</span>, <span class='ident'>center</span>: <span class='kw-2'>&</span><span class='ident'>LV</span>) {
<span class='self'>self</span>.<span class='ident'>append_translation_mut</span>(<span class='kw-2'>&</span><span class='op'>-</span><span class='op'>*</span><span class='ident'>center</span>);
<span class='self'>self</span>.<span class='ident'>append_rotation_mut</span>(<span class='ident'>amount</span>);
<span class='self'>self</span>.<span class='ident'>append_translation_mut</span>(<span class='ident'>center</span>);
}
<span class='doccomment'>/// Applies a rotation centered on the translation of `m`.</span>
<span class='doccomment'>/// </span>
<span class='doccomment'>/// # Arguments</span>
<span class='doccomment'>/// * `t` - the object to be rotated.</span>
<span class='doccomment'>/// * `amount` - the rotation to apply.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>append_rotation_wrt_center</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>AV</span>) <span class='op'>-></span> <span class='self'>Self</span> {
<span class='ident'>RotationWithTranslation</span>::<span class='ident'>append_rotation_wrt_point</span>(<span class='self'>self</span>, <span class='ident'>amount</span>, <span class='kw-2'>&</span><span class='self'>self</span>.<span class='ident'>translation</span>())
}
<span class='doccomment'>/// Applies a rotation centered on the translation of `m`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The rotation os applied on-place.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// # Arguments</span>
<span class='doccomment'>/// * `amount` - the rotation to apply.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>append_rotation_wrt_center_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>AV</span>) {
<span class='kw'>let</span> <span class='ident'>center</span> <span class='op'>=</span> <span class='self'>self</span>.<span class='ident'>translation</span>();
<span class='self'>self</span>.<span class='ident'>append_rotation_wrt_point_mut</span>(<span class='ident'>amount</span>, <span class='kw-2'>&</span><span class='ident'>center</span>)
}
}
<span class='kw'>impl</span><span class='op'><</span><span class='ident'>LV</span>: <span class='ident'>Neg</span><span class='op'><</span><span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>LV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Copy</span>, <span class='ident'>AV</span>, <span class='ident'>M</span>: <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>AV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Translation</span><span class='op'><</span><span class='ident'>LV</span><span class='op'>>></span> <span class='ident'>RotationWithTranslation</span><span class='op'><</span><span class='ident'>LV</span>, <span class='ident'>AV</span><span class='op'>></span> <span class='kw'>for</span> <span class='ident'>M</span> {
}
<span class='doccomment'>/// Trait of transformation having a rotation extractable as a rotation matrix. This can typically</span>
<span class='doccomment'>/// be implemented by quaternions to convert them to a rotation matrix.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>RotationMatrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>LV</span>: <span class='ident'>Mul</span><span class='op'><</span><span class='self'>Self</span>::<span class='ident'>Output</span>, <span class='ident'>Output</span> <span class='op'>=</span> <span class='ident'>LV</span><span class='op'>></span>, <span class='ident'>AV</span><span class='op'>></span> : <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>AV</span><span class='op'>></span> {
<span class='doccomment'>/// The output rotation matrix type.</span>
<span class='kw'>type</span> <span class='ident'>Output</span>: <span class='ident'>SquareMatrix</span><span class='op'><</span><span class='ident'>N</span>, <span class='ident'>LV</span><span class='op'>></span> <span class='op'>+</span> <span class='ident'>Rotation</span><span class='op'><</span><span class='ident'>AV</span><span class='op'>></span>;
<span class='doccomment'>/// Gets the rotation matrix represented by `self`.</span>
<span class='kw'>fn</span> <span class='ident'>to_rotation_matrix</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span>::<span class='ident'>Output</span>;
}
<span class='doccomment'>/// Composition of a rotation and an absolute value.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The operation is accessible using the `RotationMatrix`, `Absolute`, and `RMul` traits, but</span>
<span class='doccomment'>/// doing so is not easy in generic code as it can be a cause of type over-parametrization.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>AbsoluteRotate</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='doccomment'>/// This is the same as:</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// ```.ignore</span>
<span class='doccomment'>/// self.rotation_matrix().absolute().rmul(v)</span>
<span class='doccomment'>/// ```</span>
<span class='kw'>fn</span> <span class='ident'>absolute_rotate</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>v</span>: <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>;
}
<span class='doccomment'>/// Trait of object which represent a transformation, and to which new transformations can</span>
<span class='doccomment'>/// be appended.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// A transformation is assumed to be an isometry without reflexion.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Transformation</span><span class='op'><</span><span class='ident'>M</span><span class='op'>></span> {
<span class='doccomment'>/// Gets the transformation of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>transformation</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>M</span>;
<span class='doccomment'>/// Gets the inverse transformation of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>inverse_transformation</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>M</span>;
<span class='doccomment'>/// Appends a transformation to this object.</span>
<span class='kw'>fn</span> <span class='ident'>append_transformation_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>M</span>);
<span class='doccomment'>/// Appends the transformation `amount` to a copy of `t`.</span>
<span class='kw'>fn</span> <span class='ident'>append_transformation</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Prepends a transformation to this object.</span>
<span class='kw'>fn</span> <span class='ident'>prepend_transformation_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>M</span>);
<span class='doccomment'>/// Prepends the transformation `amount` to a copy of `t`.</span>
<span class='kw'>fn</span> <span class='ident'>prepend_transformation</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>amount</span>: <span class='kw-2'>&</span><span class='ident'>M</span>) <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Sets the transformation of `self`.</span>
<span class='kw'>fn</span> <span class='ident'>set_transformation</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>, <span class='ident'>M</span>);
}
<span class='doccomment'>/// Trait of objects able to transform other objects.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This is typically implemented by matrices which transform vectors.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Transform</span><span class='op'><</span><span class='ident'>V</span><span class='op'>></span> {
<span class='doccomment'>/// Applies a transformation to `v`.</span>
<span class='kw'>fn</span> <span class='ident'>transform</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>;
<span class='doccomment'>/// Applies an inverse transformation to `v`.</span>
<span class='kw'>fn</span> <span class='ident'>inverse_transform</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='kw-2'>&</span><span class='ident'>V</span>) <span class='op'>-></span> <span class='ident'>V</span>;
}
<span class='doccomment'>/// Traits of objects having a dot product.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Dot</span><span class='op'><</span><span class='ident'>N</span><span class='op'>></span> {
<span class='doccomment'>/// Computes the dot (inner) product of two vectors.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>dot</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='self'>Self</span>) <span class='op'>-></span> <span class='ident'>N</span>;
}
<span class='doccomment'>/// Traits of objects having an euclidian norm.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Norm</span><span class='op'><</span><span class='ident'>N</span>: <span class='ident'>BaseFloat</span><span class='op'>></span> {
<span class='doccomment'>/// Computes the norm of `self`.</span>
<span class='attribute'>#[<span class='ident'>inline</span>]</span>
<span class='kw'>fn</span> <span class='ident'>norm</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>N</span> {
<span class='self'>self</span>.<span class='ident'>norm_squared</span>().<span class='ident'>sqrt</span>()
}
<span class='doccomment'>/// Computes the squared norm of `self`.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// This is usually faster than computing the norm itself.</span>
<span class='kw'>fn</span> <span class='ident'>norm_squared</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>N</span>;
<span class='doccomment'>/// Gets the normalized version of a copy of `v`.</span>
<span class='kw'>fn</span> <span class='ident'>normalize</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Normalizes `self`.</span>
<span class='kw'>fn</span> <span class='ident'>normalize_mut</span>(<span class='kw-2'>&</span><span class='kw-2'>mut</span> <span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>N</span>;
}
<span class='doccomment'>/**
* Trait of elements having a cross product.
*/</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Cross</span> {
<span class='doccomment'>/// The cross product output.</span>
<span class='kw'>type</span> <span class='ident'>CrossProductType</span>;
<span class='doccomment'>/// Computes the cross product between two elements (usually vectors).</span>
<span class='kw'>fn</span> <span class='ident'>cross</span>(<span class='kw-2'>&</span><span class='self'>self</span>, <span class='ident'>other</span>: <span class='kw-2'>&</span><span class='self'>Self</span>) <span class='op'>-></span> <span class='self'>Self</span>::<span class='ident'>CrossProductType</span>;
}
<span class='doccomment'>/**
* Trait of elements having a cross product operation which can be expressed as a matrix.
*/</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>CrossMatrix</span><span class='op'><</span><span class='ident'>M</span><span class='op'>></span> {
<span class='doccomment'>/// The matrix associated to any cross product with this vector. I.e. `v.cross(anything)` =</span>
<span class='doccomment'>/// `v.cross_matrix().rmul(anything)`.</span>
<span class='kw'>fn</span> <span class='ident'>cross_matrix</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>M</span>;
}
<span class='doccomment'>/// Traits of objects which can be put in homogeneous coordinates form.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>ToHomogeneous</span><span class='op'><</span><span class='ident'>U</span><span class='op'>></span> {
<span class='doccomment'>/// Gets the homogeneous coordinates form of this object.</span>
<span class='kw'>fn</span> <span class='ident'>to_homogeneous</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>U</span>;
}
<span class='doccomment'>/// Traits of objects which can be build from an homogeneous coordinate form.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>FromHomogeneous</span><span class='op'><</span><span class='ident'>U</span><span class='op'>></span> {
<span class='doccomment'>/// Builds an object from its homogeneous coordinate form.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// Note that this this is not required that `from` is the inverse of `to_homogeneous`.</span>
<span class='doccomment'>/// Typically, `from` will remove some informations unrecoverable by `to_homogeneous`.</span>
<span class='kw'>fn</span> <span class='ident'>from</span>(<span class='kw-2'>&</span><span class='ident'>U</span>) <span class='op'>-></span> <span class='self'>Self</span>;
}
<span class='doccomment'>/// Trait of vectors able to sample a unit sphere.</span>
<span class='doccomment'>///</span>
<span class='doccomment'>/// The number of sample must be sufficient to approximate a sphere using a support mapping</span>
<span class='doccomment'>/// function.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>UniformSphereSample</span> : <span class='ident'>Sized</span> {
<span class='doccomment'>/// Iterate through the samples.</span>
<span class='kw'>fn</span> <span class='ident'>sample</span><span class='op'><</span><span class='ident'>F</span>: <span class='ident'>FnMut</span>(<span class='self'>Self</span>)<span class='op'>></span>(<span class='ident'>F</span>);
}
<span class='doccomment'>/// The zero element of a vector space, seen as an element of its embeding affine space.</span>
<span class='comment'>// XXX: once associated types are suported, move this to the `AnyPoint` trait.</span>
<span class='kw'>pub</span> <span class='kw'>trait</span> <span class='ident'>Origin</span> {
<span class='doccomment'>/// The trivial origin.</span>
<span class='kw'>fn</span> <span class='ident'>origin</span>() <span class='op'>-></span> <span class='self'>Self</span>;
<span class='doccomment'>/// Returns true if this points is exactly the trivial origin.</span>
<span class='kw'>fn</span> <span class='ident'>is_origin</span>(<span class='kw-2'>&</span><span class='self'>self</span>) <span class='op'>-></span> <span class='ident'>bool</span>;
}
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