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3.7.4 Texts and Snap – the Bézier subdivision example

Now that you can create and transform objects, use snap and create TeX texts, you are ready for a more sophisticated example. We will create this picture:

The Be'zier subdivision example.

First, create four circles. Then create four TeX texts with the TeX source codes $X_1$, $X_2$, $X_3$, $X_4$, and snap them to the center points of the circles. If you keep the texts' default properties unchanged, the texts will overlap the center points. To avoid that, modify the absolute-shift-x property in the Property editor (the meaning of the absolute-shift-x property is quite obvious). Set the values so that in the Anchor rehang mode you do not see the center point hangers being overlapped by the texts.

Four circles with labelled center points.

Now create segments connecting the points mathmanual0 and mathmanual1, mathmanual2 and mathmanual3, mathmanual4 and mathmanual5 so that the end points of the segments are snapped to he circle center points.

Create a quadratic Bézier curve with the control points mathmanual6, mathmanual7, mathmanual8, mathmanual9:

The four circles connected by segments and a Be'zier curve.

Create parametric points in the middle of the Bézier curve and the segments (switch on the line snapping mode, choose the “Points, decorations” category in the left toolbar and click the “New point” icon in the right toolbar) and click on the line. The parametric point is created, now change its property “parameter” in the Property window (see Modifying the properties) to value “0.5”. Repeat that for each segment and also for the Bézier curve. Describe these points with TeX labels: mathmanual10, mathmanual11 and mathmanual12 for the center points of the segments, and mathmanual13 for the Bézier curve's parametric point (with the source code $X_{1,2}$, $X_{1,2,3,4}$ and similar).

Now create segments connecting the parametric points, create parametric points in their middles and link them by a segment (the middle label of this segment is mathmanual14). The resulting image is displayed in the following picture:

The resulting Be'zier subdivision example.

To see how the created dependencies work, try to move some of the circles and watch the rest of the image.