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<!-- This example ilustrates the locus_defined_by_point_on_circle constraint
A cardioid is constructed as the pedal of a circle
See http://xahlee.org/SpecialPlaneCurves_dir/Cardioid_dir/cardioid.html
Description:
Let c be a circle and A a point on it
For every point P on the circle:
Let t be the tangent to c at P
Let X be the point on t such that AX is perpendicular to PX
-->
<construction>
<elements>
<point id="C">
<homogeneous_coordinates>
<double>0</double>
<double>0</double>
<double>1</double>
</homogeneous_coordinates>
</point>
<point id="A">
<homogeneous_coordinates>
<double>0</double>
<double>5</double>
<double>1</double>
</homogeneous_coordinates>
</point>
<point id="P">
<homogeneous_coordinates>
<double>5</double>
<double>0</double>
<double>1</double>
</homogeneous_coordinates>
</point>
<point id="X">
<homogeneous_coordinates>
<double>5</double>
<double>5</double>
<double>1</double>
</homogeneous_coordinates>
</point>
<line id="r">
<homogeneous_coordinates>
<double>0</double>
<double>1</double>
<double>0</double>
</homogeneous_coordinates>
</line>
<line id="t">
<homogeneous_coordinates>
<double>1</double>
<double>0</double>
<double>-5</double>
</homogeneous_coordinates>
</line>
<line id="l">
<homogeneous_coordinates>
<double>0</double>
<double>1</double>
<double>-5</double>
</homogeneous_coordinates>
</line>
<circle id="c">
<matrix>
<double>1</double>
<double>0</double>
<double>0</double>
<double>0</double>
<double>1</double>
<double>0</double>
<double>0</double>
<double>0</double>
<double>-25</double>
</matrix>
</circle>
<locus id="L">
</locus>
</elements>
<constraints>
<circle_by_center_and_point>
<circle out="true">c</circle>
<point>C</point>
<point>A</point>
</circle_by_center_and_point>
<point_on_circle>
<point out="true">P</point>
<circle>c</circle>
</point_on_circle>
<line_through_two_points>
<line out="true">r</line>
<point>C</point>
<point>P</point>
</line_through_two_points>
<line_perpendicular_to_line_through_point>
<line out="true">t</line>
<line>r</line>
<point>P</point>
</line_perpendicular_to_line_through_point>
<line_perpendicular_to_line_through_point>
<line out="true">l</line>
<line>t</line>
<point>A</point>
</line_perpendicular_to_line_through_point>
<point_intersection_of_two_lines>
<point out="true">X</point>
<line>t</line>
<line>l</line>
</point_intersection_of_two_lines>
<locus_defined_by_point_on_circle>
<locus out="true">L</locus>
<point>X</point>
<point>P</point>
<circle>c</circle>
</locus_defined_by_point_on_circle>
</constraints>
</construction>
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