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Continuous transition curve constitution method based on quintic Bezier curve

A transition curve and construction method technology, applied in special data processing applications, instruments, electrical digital data processing, etc., can solve problems such as interactive design of difficult models, large storage space, and curve oscillation

Inactive Publication Date: 2014-03-19
BEIHANG UNIV
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  • Application Information

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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.

Method used

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  • Continuous transition curve constitution method based on quintic Bezier curve
  • Continuous transition curve constitution method based on quintic Bezier curve
  • Continuous transition curve constitution method based on quintic Bezier curve

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Embodiment Construction

[0029] See figure 1 — Figure 4 , a kind of G3 continuous transition curve construction method based on 5th degree Bezier curve of the present invention, the concrete implementation steps of this method are as follows:

[0030] Step 1: Find the first-order derivative and second-order derivative of the original curve at the connection, Represents the first and second derivatives of the connection point between curve 0 and the transition curve and the first and second derivatives of the connection point between curve 1 and the transition curve, "point" means derivation of the original curve, "prime" means derivation of the transition curve;

[0031] Step 2: Curves 0, 1 and the transition curve satisfy G2 continuity, and the expression that satisfies this condition is: r′′=λv 1 +ω 2 v 2 , where ω and λ are arbitrary coefficients; in this step, we can make Among them, α, β are unit vectors, and there are α⊥β,v 2 for exist The projected vector in the vertical directio...

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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 method for constructing a G3 continuous transition curve based on a fifth-order Bezier curve, and belongs to the technical field of CAD. Background technique [0002] G3 Continuous is sometimes useful in CAD modeling, such as: rounded curves for the leading and trailing edges of blades, iPhone casings, car designs, etc. G3 continuous belongs to the continuous curvature rate of change. This continuous level not only has the characteristics of the continuous level of G0, G1, and G2, but also the curvature rate of change at the connection point is continuous, which makes the curvature change smoother. This continuous level of surface Has smoother visuals than G2. At present, some CAD software have the ability to construct G3 continuous curves and surfaces. For example, Autodesk Alias2011Essentials uses 7th degree polynomials to construct G3 continuous curves. However, the 7th-degree polynomial curve has a high degree, and the ...

Claims

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Application Information

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IPC IPC(8): G06F17/50
Inventor 宁涛陈志同席平
Owner BEIHANG UNIV
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