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Checking of curves continuity |
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Checking of curves continuity is used to analyze precision and smoothness of joints of the curves. The place of the curves connection is defined as a juncture if the distance between ending points of these curves in this place does not exceed the threshold value (Radius of juncture).
If the curves form a juncture, checks are performed for this juncture based on the G0 (Precision of juncture), G1 (Tangency) and G2 (Smoothness) criteria. Permissible values are set for the continuity criteria. Depending on which criteria the juncture meets, the following types of continuity can be defined for it:
•G0 — curves are connected at end points with a gap which does not exceed the G0 threshold value (Joint Accuracy). If the gap value exceeds the permissible value, a break is defined in the juncture, and no subsequent calculations are performed for this juncture,
•G1 — the juncture meets the G0 criterion and the angle between tangent vectors does not exceed the threshold value of the angular deviation set for the G1 (Tangency) criterion.
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Note that the G1 criterion is also met for junctures where tangent vectors are directed in the opposite directions. In this case, comparison with the threshold value considers the angle between the tangent vector of one curve and the vector opposite to the tangent vector of the other curve. |
If the G1 criterion is not met, the angle between the tangent vectors is fixed and no subsequent calculations are performed for this juncture.
•G2 — the juncture meets the G0 and G1 criteria and the relative deviation of curvature does not exceed the threshold value set for the G2 (Smoothness) criterion.
The relative deviation of curvature is calculated using the formula |k1/k2-1|*100%, where k1 is the minimum curvature at the point of connection, and k2 is the maximum curvature at the point of connection. During the command operation, the type of continuity is displayed in the place of the curves connection.
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Type of continuity when joining curves (for clarity shown Curvature plot)
a) G0, b) G1, c) G2
