A Construction Method of G3 Continuous Transition Curve Based on 5th Bezier Curve

Abstract

The invention discloses a G3 continuous transition curve constitution method based on a quintic Bezier curve. The method comprises the following steps: step 1, working out the first-order steering vector and the second-order steering vector at the end point of a primitive curve; step 2, enabling the primitive curve and a transition curve to satisfy a G2 continuity condition at the connection point; step 3, on the basis of the step 2, enabling the primitive curve and the transition curve to satisfy G3 continuity at the connection point; step 4, inversely calculating the reference mark of a quintic Bezier transition curve; step 5, normally calculating the quintic Bezier transition curve according to the control peak in the step 4. According to the invention, a Bezier curve is adopt to construct the transition curve, so that the advantages of controlling the shape of the curve easily and visually and providing convenience for interactive design can be achieved; besides, the few the parameters are, the few the orders are, so that the calculation frequency is low, and the memory space occupied in a computer is relatively small; the invention can be applied to construction of transition curves in CAD modeling.

Description

technical field [0001] The invention relates to a construction method of a G3 continuous transition curve based on a 5-degree Bezier curve, which belongs to the technical field of CAD. Background technique [0002] G3 continuous is sometimes useful in CAD modeling, such as: the fillet curve of the front and rear edges of the blade, iphone mobile phone shell, car design, etc. G3 continuous belongs to the continuous rate of curvature change. This continuous level not only has the characteristics of G0, G1, and G2 continuous levels, but also the curvature change rate at the connection point is continuous, which makes the curvature change smoother. The surface of this continuous level Has smoother visuals than the G2. At present, some CAD software has the ability to construct G3 continuous curves and surfaces. For example, Autodesk Alias ​​2011 Essentials constructs G3 continuous curves with polynomials of degree 7. However, the degree of polynomial curve of degree 7 is high, ...

AI Technical Summary

Problems solved by technology

However, the order of the 7th degree polynomial curve is high, and the curve is prone to "oscillation", which makes it difficult to interactively design the model, and the higher the order of the curve, the more calculation times are required, and the larger the storage space is.

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