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Determining the shape of a conical curve |
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Conical curve parameters
The shape of the conical curve is determined by the value of the parameter Coefficient (k) or Height (h), see drawing.
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Taper curve parameter
The coefficient k (engineering discriminant) — is the ratio of a part of the triangle's median, located under the conical curve, to the full length of the median. The value of k is in the range of 0.0001–0.9999 and determines the shape of the curve:
•k = 0.5 — parabola,
•k <0.5 — ellipse,
•k > 0.5 — hyperbola.
Curve height is the distance from the intersection point of the conical curve with the median of the triangle to the side to which the median is drawn. The minimum and maximum values of h depend on the size of the triangle.
Obviously, each value of h corresponds to a single value of k (and vice versa), and, therefore, a certain shape of the curve.
How to set the shape for the conical curve
To set the shape of the conical curve as you build it, do the following.
1.Set the Coefficient/Curve height toggle switch to the desired position.
2.Enter the parameter value in the field Value.
The parameter value can also be set by pointing the point with the mouse in the graphics area. Wherein:
•When the toggle switch is set to Coefficient:
•if the point is specified inside the triangle with vertices at the points 1, 2, 3, then the curve passes directly through this point (figure a); the coefficient defining the resulting curve is calculated and entered in the field Coefficient,
•If a point is indicated outside the triangle, then the distance between it and segment 12 determines the height of the curve (fig. b); the coefficient corresponding to this height is calculated and entered into the field Coefficient.
•When the toggle switch is set to Curve height then, regardless of the position of the specified point, the distance between it and the segment 12 determines the height of the curve.
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a) |
b) |
Determining the position of a point on a curve:
a) the point is specified inside the triangle (switch Coefficient/Curve Height)
set to position Coefficient);
b) the point is specified outside the triangle
See Also
