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# Bezier cross section

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# Bezier cross section

The shape of a Bezier cross-section is described by a Bezier curve.

One half of the shape of the cross-section is described using a 4th degree Bezier polynomial. Points 0 and 4 are the end points and cannot be changed. Point 1 can be moved along a straight line which corresponds to the cone angle of the cross-section (0° for a rectangle type, δ for a trapezoid type). Point 3 can only be moved in the horizontal direction in order to guarantee a smooth transition between the two symmetrical halves. The intersection of the two lines which points 1 and 3 are on is designated by the letter S and plays an important role in the positioning of Bezier points 1 and 3. Point 2 can be moved freely and therefore he has the major influence on the shape of the cross-section. In the first design, point 2 is identical with point S.

Two basic shapes of the cross-section can be selected, rectangular or trapezoid. Only the end cross-section of the volute is designed, all other cross-sections result from this. Under the heading Inner point position, you can select whether positioning of the inner points 1 and 3 should be relative (0..1; 0=point 0/4; 1=point S) or absolute (distance from point S). The numeric values of the positions can be changed by right-clicking on points 1 or 3. If the option Show all points under the heading Options is selected, the different positioning methods become apparent.

The minimum curvature radius of the designed contour is shown in the box to the bottom right.