CN106570916A - PH curve generation method used for highway three-dimensional linear design and apparatus thereof - Google Patents

Abstract

The invention relates to a PH curve generation method used for a highway three-dimensional linear design and an apparatus thereof. The method comprises the following steps of S1, selecting m-1 main control points between a starting point of a highway to be designed and a terminal; S2, constructing a PH curve taking t as a variable between each two adjacent main control points and converting into a quintic PH curve of a Bessel polynomial form; S3, according to 0-5 slave control points, determining the quintic PH curve between the two adjacent main control points; and S4, calculating curvature and torsion of each slave control point on the quintic PH curve between the two adjacent main control points, determining whether the quintic PH curve accords with a preset highway three-dimensional linear constraint condition, and if the quintic PH curve accords with the preset highway three-dimensional linear constraint condition, taking the quintic PH curve as the quintic PH curve used for designing a three-dimension line shape of a highway between the two adjacent main control points. By using the method and the apparatus of the invention, a disadvantage existing in a traditional-road flat and vertical separated line shape design method can be overcome and safety of road line shape design is increased.

Description

For the PH curves generation method and device of the design of highway three-dimensional linear

Technical field

The present invention relates to Road Design technical field, more particularly, to a kind of PH curves for the design of highway three-dimensional linear Generation method and device.

Background technology

Road traffic system be by people, car, road, environment structure complicated dynamical system, from the statistics of vehicle accident and Analysis is seen, although the reason for causing vehicle accident is many, but whether Alignment Design is rationally to be related to highway safety The root problem of sex chromosome mosaicism.Highway alignment as the key of whole Highway Design, be reflection design it is good and bad most intuitively Refraction.Road alignment design is the key of highway master-plan, total arrangement.Linear is the skeleton of highway, its it is reasonable in design with It is no, not only it is directly connected to that the quality of Highway Construction Project Based, mileage length, investment be how many, benefit height, more directly affect To road travel safety.By technical development of computer restriction and highway alignment 3 D analysis model complexity affected, it is existing Highway centrage generally projected to and be designed respectively on two dimensional surface by Alignment Design method, then by flat, ordinate shape group Conjunction obtains three-dimensional linear.This artificial fractionation and knockdown method for designing have ignored the interaction between flat, vertical design considerations and Coupling so that the quality of Alignment Design is heavily dependent on the correlation experience of designer so that some designs lack Fall into and careless omission is taken straight in later stage operation, easily cause vehicle accident.

The content of the invention

For disadvantages described above, the present invention provides a kind of PH curves generation method and dress for the design of highway three-dimensional linear Put, traditional road can be improved and equal the deficiency that the linear method for designing of vertical separate type is present, improve the safety of Correction in Road Alignment Design.

In a first aspect, including provided by the present invention for the PH curve generation methods of highway three-dimensional linear design：

S1, m-1 Master Node will be chosen between the starting point and terminal of highway to be designed, and using the starting point as the 0th Individual Master Node and using the terminal as m-th Master Node, wherein m is the integer more than 1；

S2, per the PH curves constructed between adjacent two Master Node with t as variable, and by the PH curves with t as variable Be converted to the five worms prescription of Bessel polynomial form；

S3, using per first Master Node in adjacent two Master Node as the five worms prescription the 0th from control Point, second Master Node as the five worms prescription the 5th from control point, the 0th from control point and the 5th from control point it Between select two control point as the 1st from control point and the 4th from control point, according to the described 0th from control point, the described 1st from control Point processed, the described 4th from control point and the described 5th from control point, it is determined that the described 1st from control point and the described 4th from control point Between the 2nd from control point and the 3rd from control point, and according to the 0th～5 from control point, determine between adjacent two Master Node Five worms prescription；

On S4, the five worms prescription for calculating between adjacent two Master Node each from the curvature and torsion at control point, and Judge whether the five worms prescription between adjacent two Master Node meets default highway according to the curvature and the torsion Three-dimensional linear constraints, if so, then using the five worms prescription between adjacent two Master Node as design this adjacent The five worms prescription of the three-dimensional linear of the highway between two Master Nodes.

Optionally, PH curves r (t) with t as variable as r (t)=[x (t), y (t), z (t)], the x (t), y in formula T the first derivative of () and z (t) meets x ' (t)²+y′(t)²+z′(t)²=σ (t)², x (t), y (t) and z (t) are represented with following formula：

Wherein, a (t)=1, GCD (b (t), c (t), d (t)) is constant, and b (t), c (t), d (t) are represented using following formula：

Wherein, b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂It is multinomial coefficient.

Optionally, five worms prescription r (t) of the Bessel polynomial form is：

Wherein, p_iFor the i-th control point, p_i=(x_i,y_i,z_i), i=0,1 ... 5, p₁～p₅Represented with following formula：

Optionally, it is described determine the described 1st from control point and the described 4th from the 2nd between control point from control point and 3rd from control point, including：

S31, according to the described 0th from control point, the described 1st from control point, the described 4th from control point and the described 5th from control It is processed, determine b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂, obtain：

In formula, Δ x_i=x_i+1-x_i, Δ y_i=y_i+1-y_i, Δ z_i=z_i+1-z_i, Δ p_i=p_i+1-p_i, | Δ p_i|=l_iRepresent The spacing at control point, e, f, g, h are represented with following formula：

S32, according to calculated b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂, the described 2nd is determined from control point and described 3 from control point each solve；

S33, with | | p₂-p₁||+||p₃-p₄| | minimum filters out optimal solution work as screening conditions in described each solution For the described 2nd from control point and the described 3rd from control point.

Optionally, it is described to calculate between adjacent two Master Node on Jing five worms prescriptions the curvature at each control point and scratch Rate, including：

The derivation of 1～3 time is carried out to Jing five worms prescriptions between adjacent two Master Node, represents that kth time is asked with following formula Lead：

In formula,

The result obtained after derivation is substituted into respectively in the computing formula of curvature and torsion, adjacent two Master Node is obtained Curvature and torsion.

Optionally, the computing formula of the curvature and torsion is：

Wherein, κ (t) is curvature, and τ (t) is torsion.

Optionally, the highway three-dimensional line that the five worms prescription between i-th Master Node and i+1 Master Node is adopted Shape constraints is：

Wherein, S_Δ012Three formed from control point for the 0th～2 between i-th Master Node and i+1 Master Node Angular area, S_Δ345For the triangle that the 3rd～5 between i-th Master Node and i+1 Master Node is formed from control point The area of shape, τ_maxFor maximum torsion, κ_maxFor maximum curvature, κ_max' be maximum curvature rate of change, p¹⁰、p²¹、p³⁰、p⁴³、p₅₂Point The 0th of five worms prescription that Wei be between i-th Master Node and i+1 Master Node is from control point and the 1st from control point The tangent vector of composition, the 1st from control point and the 2nd tangent vector constituted from control point, the 0th from control point and the 3rd from control point structure Into tangent vector, the 3rd from control point and the 4th from control point constitute tangent vector, the 2nd from control point and the 5th from control point constitute Tangent vector, κ_i(t)_T=1、κ_i+1(t)_T=0Five worms prescription between respectively i-th Master Node and i+1 Master Node Terminal curvature, the curvature of the starting point of five worms prescription between i+1 Master Node and the i-th+2 Master Nodes, τ_i (t)_T=1、τ_i+1(t)_T=0The terminal of the five worms prescription between respectively i-th Master Node and i+1 Master Node is scratched The torsion of the starting point of the five worms prescription between rate, i+1 Master Node and the i-th+2 Master Nodes, τ_iT () is i-th The torsion of any point on five worms prescription between Master Node and i+1 Master Node, the span of i is [0, m].

Optionally, methods described also includes：

If five worms prescription does not meet default highway three-dimensional linear constraints between adjacent two Master Node, adjust Save the 0th from control point and the 1st from the space length between control point and the 4th from control point and the 5th from the sky between control point Between distance, until adjust after after PH curves meet the highway three-dimensional linear constraints.

Second aspect, includes provided by the present invention for the PH curve generating means of highway three-dimensional linear design：

Insertion module, for inserting m-1 Master Node between the starting point and terminal by highway to be designed, and by described O'clock as the 0th Master Node and using the terminal as m Master Node, wherein m is the integer more than 1；

Curve builds module, for constructing the PH curves with t as variable between per adjacent two Master Node, and will be with t For variable PH Curve transforms for Bessel polynomial form five worms prescription；

Curve determining module, for first Master Node using in per adjacent two Master Node as five worms prescription 0th from control point, first Master Node as five worms prescription the 5th from control point, the 0th from control point and the 5th from control Two control point are selected between system point as the 1st from control point and the 4th from control point, according to the described 0th from control point, described the 1 from control point, the described 4th from control point and the described 5th from control point, it is determined that the described 1st from control point and the described 4th from control Between system point the 2nd determines adjacent two Master Node from control point and the 3rd from control point, and according to the 0th～5 from control point Between five worms prescription；

Judge module, for calculate on the five worms prescription between adjacent two Master Node curvature at each control point and Torsion, and whether the curvature at each control point is judged less than default maximum curvature, whether the torsion at each control point is less than pre- If maximum torsion, if so, then using the five worms prescription between adjacent two Master Node as designing adjacent two master The five worms prescription of the three-dimensional linear of the highway between control point.

It is multinomial using Bezier provided by the present invention for the PH curves generation method and device of the design of highway three-dimensional linear The five worms prescription model of formula form, then determining each control point by way of determine the five worms prescription, and by sentencing Whether PH curves determined by disconnected meet highway engineering constraints so that the three-dimensional linear of final design is a continual curvature And the wheeled path of traffic safety is can guarantee that, and with unified mathematical expression form, method simplicity is easy to calculate, and is improving Traditional road equals the deficiency that the linear method for designing of vertical separate type is present, and improves the safety of Correction in Road Alignment Design.

Description of the drawings

In order to be illustrated more clearly that the embodiment of the present disclosure or technical scheme of the prior art, below will be to embodiment or existing The accompanying drawing to be used needed for having technology description is briefly described, it should be apparent that, drawings in the following description are only this Disclosed some embodiments, for those of ordinary skill in the art, on the premise of not paying creative work, can be with Other accompanying drawings are obtained according to these figures.

Fig. 1 shows that the flow process of the PH curve generation methods for being used for the design of highway three-dimensional linear in one embodiment of the invention is shown It is intended to；

Fig. 2 shows that the flow process of the PH curve generation methods for being used for the design of highway three-dimensional linear in one embodiment of the invention is shown It is intended to.

Specific embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present disclosure, the technical scheme in the embodiment of the present disclosure is carried out clear, complete Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than the embodiment of whole.It is based on Embodiment in the disclosure, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made Embodiment, belongs to the scope of disclosure protection.

The present invention provides a kind of PH curve generation methods for the design of highway three-dimensional linear, as shown in figure 1, the method bag Include：

S1, m-1 Master Node will be chosen between the starting point and terminal of highway to be designed, and using the starting point as the 0th Individual Master Node and using the terminal as m-th Master Node, wherein m is the integer more than 1；

For example, when needing to build a highway and B ground between in A, multiple positions are selected and B ground between in A Put a little as Master Node, for example using A and C ground between B ground, D ground, E and F as Master Node.It will be appreciated that The starting point A ground of the highway, the Master Node for also serving as the highway terminal B.

S2, per the PH curves constructed between adjacent two Master Node with t as variable, and by the PH curves with t as variable Be converted to the five worms prescription of Bessel polynomial form；

Wherein, PH curves refer to Pythagoras hodograph, the five worms prescription of so-called Bessel polynomial form That is the Pythagoras hodograph of Bezier polynomial forms.

It will be appreciated that per between two adjacent Master Nodes can constructing PH curves by way of determine this two Highway between individual Master Node three-dimensional linear design, such as in above-mentioned B and C ground between construct a PH with t as variable Curve, then by the PH Curve transforms for Bessel polynomial form five worms prescription.Here it is only to set up a curve Model, the parameters in model have not determined.

S3, using per first Master Node in adjacent two Master Node as five worms prescription the 0th from control point, the Two Master Nodes as five worms prescription the 5th from control point, the 0th from control point and the 5th from selecting two between control point Individual control point as the 1st from control point and the 4th from control point, according to the described 0th from control point, the described 1st from control point, described 4th from control point and the described 5th from control point, it is determined that the described 1st from control point and the described 4th from the 2nd between control point From control point and the 3rd from control point, and determine five PH songs between adjacent two Master Node from control point according to the 0th～5 Line；

For example, two control point are chosen as the 1st from control point and the 4th from control point and C ground between in B, and Using B this Master Node of ground as the 0th from control point, using this Master Node of C as the 5th from control point, then according to the 0th, 1st, 4,5 from Master Node, just can determine the 1st between control point and the 4th control point the 2nd from control point and the 3rd from control It is processed, so according to this six from control point, the parameters with just can determine B and in the five worms prescription between C ground, i.e., Five worms prescription with determining B and between C ground.It will be appreciated that five PH between arbitrarily per two adjacent Master Nodes The determination mode of five worms prescription and C ground between is obtained curve with being referred to B.

On S4, the five worms prescription for calculating between adjacent two Master Node each from the curvature and torsion at control point, and Judge whether the five worms prescription between adjacent two Master Node meets default highway according to the curvature and the torsion Three-dimensional linear constraints, if so, then using the five worms prescription between adjacent two Master Node as design this adjacent The five worms prescription of the three-dimensional linear of the highway between two Master Nodes.

It will be appreciated that being not that any highway three-dimensional linear according to five worms prescription design meets actual safety Require, be the driving safety for ensureing driver on designed highway, the curvature of highway can not be too big, and the rate of change of curvature is not Can be too big, the longitudinal gradient of highway can not the torsion of Tai great Ji highways can not be too big etc., just can determine public affairs according to these requirements Road three-dimensional linear constraints.The five worms prescription for only meeting highway three-dimensional linear constraints could be used as being eventually used for this The PH curves of the three-dimensional linear of the highway between adjacent two Master Node.

Provided by the present invention for the PH curve generation methods of highway three-dimensional linear design, using Bezier polynomial forms Five worms prescription model, then determining each control point by way of determine the five worms prescription, and by judging institute really Whether fixed PH curves meet highway engineering constraints so that the three-dimensional linear of final design is a continual curvature and can protect The wheeled path of card traffic safety, and with unified mathematical expression form, method simplicity is easy to calculate, and is improving traditional road The deficiency that the linear method for designing of vertical separate type is present is equalled on road, improves the safety of Correction in Road Alignment Design.

In the specific implementation, PH curves r (t) with t as variable of construction can be in S2：

R (t)=[x (t), y (t), z (t)] (1)

In formula, the first derivative of x (t), y (t) and z (t) meets x ' (t)²+y′(t)²+z′(t)²=σ (t)².Wherein t, σ T () is the parameter without physical significance.

X (t) therein, y (t) and z (t) are represented with following formula：

Wherein, a (t)=1, GCD (b (t), c (t), d (t)) is constant.

B (t), c (t), d (t) are represented using following formula：

Wherein, b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂It is multinomial coefficient.

Here b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂It is unknown coefficient to be asked.

In the specific implementation, five worms prescription r (t) of the Bessel polynomial form being converted in S2 can use following formula Represent：

Wherein, p_iFor the i-th control point, p_i=(x_i,y_i,z_i), i=0,1 ... 5.

P therein₁～p₅Can be represented using following formula：

As long as can be seen that obtaining b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂, just can obtain five worms prescription.

In the specific implementation, the 0th it is to determine from control point from control point and the 5th, the 1st from control point and the 4th from control Point can be it is voluntarily selected, the 2nd from control point and the 3rd from control point can four control point determination according to more than, specifically Can be：

S31, according to the described 0th from control point, the described 1st from control point, the described 4th from control point and the described 5th from control It is processed, determine b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂, obtain：

In formula, Δ x_i=x_i+1-x_i, Δ y_i=y_i+1-y_i, Δ z_i=z_i+1-z_i, Δ p_i=p_i+1-p_i, | Δ p_i|=l_iRepresent The spacing at control point, e, f, g, h are represented with following formula：

S32, according to calculated b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂, the described 2nd is determined from control point and described 3 from control point each solve；

S33, with | | p₂-p₁||+||p₃-p₄| | minimum filters out optimal solution work as screening conditions in described each solution For the described 2nd from control point and the described 3rd from control point.

In the specific implementation, the direction azimuth of the border free vector at each Master NodeRepresent, master control System point with close to use l respectively from the space length at control point in front and back_i4And l_(i+1)1Represent.For the i-th -1 Master Node and Four between i Master Node are expressed as follows from control point (including the i-th -1 Master Node and i-th Master Node)：

In formula, θ_i,1、For the starting point of the five worms prescription between i-th Master Node and i+1 Master Node Boundary vector (the 0th i.e. between two Master Nodes is from control point and the 1st from the connecting line between control point) is put down with xoy and xoz The angle in face, θ_i,5、Swear on destination county border for the five worms prescription between i-th Master Node and i+1 Master Node The folder of amount (the 4th i.e. between two Master Nodes is from control point and the 5th from the connecting line between control point) and xoy and xoz planes Angle.

It can be seen that, the 0th is the i-th -1 Master Node q from control point_i-1, the 5th is i-th Master Node from control point q_i, the 1st is Master Node q from control point_i-1Position and the 1st from control point and Master Node q_i-1Apart from sum, the 4th from Control point is from control point p₅Position and the 4th from control point with from control point p₅Between distance difference.

In the specific implementation, the song at each control point on Jing five worms prescriptions between adjacent two Master Node is calculated in S4 The process of rate and torsion can include：

The derivation of 1～3 time is carried out to Jing five worms prescriptions between adjacent two Master Node, represents that kth time is asked with following formula Lead：

In formula,

The result obtained after derivation is substituted into respectively in the computing formula of curvature and torsion, adjacent two Master Node is obtained Curvature and torsion.

Wherein, the computing formula of the curvature and torsion can be：

Wherein, κ (t) is curvature, and τ (t) is torsion.

It will be appreciated that formula (9) is substituted into into formula (10), just can obtain：

In formula：S_Δ012For first three control point p₀、p₁And p₂The area of the triangle of composition, S_Δ345For rear three control point p³、p₄And p₅The area of the triangle of composition.

In the specific implementation, the highway that the five worms prescription between i-th Master Node and i+1 Master Node is adopted Three-dimensional linear constraints is：

Wherein, S_Δ012Three formed from control point for the 0th～2 between i-th Master Node and i+1 Master Node Angular area, S_Δ345For the triangle that the 3rd～5 between i-th Master Node and i+1 Master Node is formed from control point The area of shape, τ_maxFor maximum torsion, κ_maxFor maximum curvature, κ_max' be maximum curvature rate of change, p₁₀、p₂₁、p₃₀、p₄₃、p₅₂Point The 0th of five worms prescription that Wei be between i-th Master Node and i+1 Master Node is from control point and the 1st from control point The tangent vector of composition, the 1st from control point and the 2nd tangent vector constituted from control point, the 0th from control point and the 3rd from control point structure Into tangent vector, the 3rd from control point and the 4th from control point constitute tangent vector, the 2nd from control point and the 5th from control point constitute Tangent vector, κ_i(t)_T=1、κ_i+1(t)_T=0Five worms prescription between respectively i-th Master Node and i+1 Master Node Terminal curvature, the curvature of the starting point of five worms prescription between i+1 Master Node and the i-th+2 Master Nodes, τ_i (t)_T=1、τ_i+1(t)_T=0The terminal of the five worms prescription between respectively i-th Master Node and i+1 Master Node is scratched The torsion of the starting point of the five worms prescription between rate, i+1 Master Node and the i-th+2 Master Nodes, τ_iT () is i-th The torsion of any point on five worms prescription between Master Node and i+1 Master Node, the span of i is [0, m].

Certainly, if as shown in Fig. 2 Jing judges to learn that five worms prescription does not meet between adjacent two Master Node in S4 Default highway three-dimensional linear constraints, can adjust the 0th from control point and the 1st from the space length between control point and 4th from control point and the 5th from the space length between control point, until the PH curves after after adjusting meet the highway three-dimensional line Shape constraints.

Based on identical inventive concept, the present invention also provides a kind of PH curves for the design of highway three-dimensional linear and generates dress Put, the device includes：

Insertion module, for inserting m-1 Master Node between the starting point and terminal by highway to be designed, and by described O'clock as the 0th Master Node and using the terminal as m Master Node, wherein m is the integer more than 1；

Curve builds module, for constructing the PH curves with t as variable between per adjacent two Master Node, and will be with t For variable PH Curve transforms for Bessel polynomial form five worms prescription；

Curve determining module, for using per first Master Node in adjacent two Master Node as the 0th of PH curves From control point, first Master Node as five worms prescription the 5th from control point, the 0th from control point and the 5th from control point Between select two control point as the 1st from control point and the 4th from control point, according to the described 0th from control point, the described 1st from Control point, the described 4th from control point and the described 5th from control point, it is determined that the described 1st from control point and the described 4th from control Between point the 2nd from control point and the 3rd from control point, and according to the 0th～5 from control point, determine adjacent two Master Node it Between five worms prescription；

Judge module, for calculate on the five worms prescription between adjacent two Master Node curvature at each control point and Torsion, and whether the curvature at each control point is judged less than default maximum curvature, whether the torsion at each control point is less than pre- If maximum torsion, if so, then using the five worms prescription between adjacent two Master Node as designing adjacent two master The five worms prescription of the three-dimensional linear of the highway between control point.

The function structure mould of the PH curve generation methods that the PH curves generating means that the present invention is provided are provided for the present invention Block, it may be referred to the PH curves generation side of present invention offer about the content such as explanation, explanation, citing, beneficial effect of content Appropriate section in method, repeats no more here.

In the description of the present invention, a large amount of details are illustrated.It is to be appreciated, however, that embodiments of the invention can be with Put into practice in the case of without these details.In some instances, known method, structure and skill is not been shown in detail Art, so as not to obscure the understanding of this description.

Above example only to illustrate technical scheme, rather than a limitation；Although with reference to the foregoing embodiments The present invention has been described in detail, it will be understood by those within the art that；It still can be to aforementioned each enforcement Technical scheme described in example is modified, or carries out equivalent to which part technical characteristic；And these modification or Replace, do not make the spirit and scope of the essence disengaging various embodiments of the present invention technical scheme of appropriate technical solution.

Claims (9)

1. it is a kind of for highway three-dimensional linear design PH curve generation methods, it is characterised in that include：

S1, m-1 Master Node will be chosen between the starting point and terminal of highway to be designed, and using the starting point as the 0th master Control point and using the terminal as m-th Master Node, wherein m is the integer more than 1；

S2, per the PH curves constructed between adjacent two Master Node with t as variable, and by the PH Curve transforms with t as variable For the five worms prescription of Bessel polynomial form；

S3, using per first Master Node in adjacent two Master Node as the five worms prescription the 0th from control point, the Two Master Nodes the 5th from control point, are selected from control point and the 5th the 0th as the five worms prescription between control point Fixed two control point as the 1st from control point and the 4th from control point, according to the described 0th from control point, the described 1st from control point, Described 4th from control point and the described 5th from control point, it is determined that the described 1st from control point and the described 4th between control point 2nd from control point and the 3rd from control point, and determines five times between adjacent two Master Node from control point according to the 0th～5 PH curves；

On S4, the five worms prescription for calculating between adjacent two Master Node each from the curvature and torsion at control point, and according to It is three-dimensional that the curvature and the torsion judge whether the five worms prescription between adjacent two Master Node meets default highway Linear constraints condition, if so, then using the five worms prescription between adjacent two Master Node as designing adjacent two master The five worms prescription of the three-dimensional linear of the highway between control point.

2. method according to claim 1, it is characterised in that PH curves r (t) with t as variable (t)=[x as r (t), y (t), z (t)], the first derivative of the x (t), y (t) in formula and z (t) meets x ' (t)²+y′(t)²+z′(t)²=σ (t)², X (t), y (t) and z (t) are represented with following formula：

$\left\{\begin{array}{c}{x}^{\′}\left(t\right)=a\left(t\right)(b{\left(t\right)}^2-c{\left(t\right)}^2-d{\left(t\right)}^2)\\ y^{\′}\left(t\right)=2a\left(t\right)b\left(t\right)c\left(t\right)\\ z^{\′}\left(t\right)=2a\left(t\right)b\left(t\right)d\left(t\right)\end{array}\right.$

Wherein, a (t)=1, GCD (b (t), c (t), d (t)) is constant, and b (t), c (t), d (t) are represented using following formula：

$\left\{\begin{array}{c}b\left(t\right)=b_0(1-t^2)+2b_{1}t(1-t^2)+b_2{t}^2\\ c\left(t\right)=c_0(1-t^2)+2c_{1}t(1-t^2)+c_2{t}^2\\ d\left(t\right)=d_0(1-t^2)+2d_{1}t(1-t^2)+d_2{t}^2\end{array}\right.$

Wherein, b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂It is multinomial coefficient.

3. method according to claim 2, it is characterised in that five worms prescription r (t) of the Bessel polynomial form For：

$r\left(t\right)=\underset{i=0}{\overset{5}{\Σ}}{p}_i\frac{5!}{i!(5-i)!}{t}^i{(1-t)}^{5-i}$

Wherein, p_iFor the i-th control point, p_i=(x_i,y_i,z_i), i=0,1 ... 5, p₁～p₅Represented with following formula：

$\left\{\begin{array}{c}{p}_1=p_0+\frac{1}{5}(2b_0{c}_0,2b_0{d}_0,{b_0}^2-{c_0}^2-{d_0}^2)\\ p_2=p_1+\frac{1}{5}(b_0{c}_1+b_1{c}_0,b_0{d}_1+b_1{d}_0,b_0{b}_1-c_0{c}_1-d_0{d}_1)\\ p_3=p_2+\frac{2}{15}(2b_1{c}_1,2b_1{d}_1,{b_1}^2-{c_1}^2-{d_1}^2)\\ +\frac{1}{15}(b_0{c}_2+b_2{c}_0,b_0{d}_2+b_2{d}_0,b_0{b}_2-c_0{c}_2-d_0{d}_2)\\ p_4=p_3+\frac{1}{5}(b_1{c}_2+b_2{c}_1,b_1{d}_2+b_2{d}_1,b_1{b}_2-c_1{c}_2-d_1{d}_2)\\ p_5=p_4+\frac{1}{5}(2b_2{c}_2,2b_2{d}_2,{b_2}^2-{c_2}^2-{d_2}^2)\end{array}\right..$

4. method according to claim 3, it is characterised in that the determination the described 1st from control point and the described 4th from Between control point the 2nd from control point and the 3rd from control point, including：

S31, according to the described 0th from control point, the described 1st from control point, the described 4th from control point and the described 5th from control point, Determine b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂, obtain：

$\left\{\begin{array}{c}(b_0,c_0,d_0)=\±\sqrt{\frac{5}{2}}(\sqrt{{\mathrm{\Δz}}_0+\left|{\mathrm{\Δp}}_0\right|},\frac{{\mathrm{\Δx}}_0}{\sqrt{{\mathrm{\Δz}}_0+\left|{\mathrm{\Δp}}_0\right|}},\frac{{\mathrm{\Δy}}_0}{\sqrt{{\mathrm{\Δz}}_0+\left|{\mathrm{\Δp}}_0\right|}})\\ (b_2,c_2,d_2)=\±\sqrt{\frac{5}{2}}(\sqrt{{\mathrm{\Δz}}_4+\left|{\mathrm{\Δp}}_4\right|},\frac{{\mathrm{\Δx}}_4}{\sqrt{{\mathrm{\Δz}}_4+\left|{\mathrm{\Δp}}_4\right|}},\frac{{\mathrm{\Δy}}_4}{\sqrt{{\mathrm{\Δz}}_4+\left|{\mathrm{\Δp}}_4\right|}})\\ (b_1,c_1,d_1)=-\frac{3}{4}(b_0+b_2,c_0+c_2,d_0+d_2)\±\sqrt{\frac{1}{2}}(\sqrt{g+h},\frac{e}{\sqrt{g+h}},\frac{f}{\sqrt{g+h}})\end{array}\right.$

In formula, Δ x_i=x_i+1-x_i, Δ y_i=y_i+1-y_i, Δ z_i=z_i+1-z_i, Δ p_i=p_i+1-p_i, | Δ p_i|=l_iRepresent control point Spacing, e, f, g, h are represented with following formula：

$\left\{\begin{array}{c}e=\frac{15}{2}(x_4-x_1)+\frac{9}{8}(b_0{c}_0+b_2{c}_2)+\frac{5}{8}(b_0{c}_2+b_2{c}_0)\\ f=\frac{15}{2}(y_4-y_1)+\frac{9}{8}(b_0{d}_0+b_2{d}_2)+\frac{5}{8}(b_0{d}_2+b_2{d}_0)\\ g=\frac{15}{2}(z_4-z_1)+\frac{9}{16}({b_0}^2-{c_0}^2-{d_0}^2+{b_2}^2-{c_2}^2-{d_2}^2)+\frac{5}{8}(b_0{b}_2-c_0{c}_2-d_0{d}_2)\\ h=\sqrt{e^2+f^2+g^2}\end{array}\right.;$

S32, according to calculated b₀、b₁、b₂、c₀、c₁、c₂、d₀、d₁、d₂, determine the described 2nd from control point and the described 3rd from Each solution at control point；

S33, with | | p₂-p₁||+||p₃-p₄| | minimum filters out optimal solution as institute as screening conditions in described each solution The 2nd is stated from control point and the described 3rd from control point.

5. method according to claim 4, it is characterised in that five PH of Jing between the calculating adjacent two Master Node The curvature and torsion at each control point on curve, including：

The derivation of 1～3 time is carried out to Jing five worms prescriptions between adjacent two Master Node, with following formula kth time derivation is represented：

$\frac{d^{k}r\left(t\right)}{{\mathrm{dt}}^k}=\frac{5!}{(5-k)!}\underset{m=0}{\overset{5-k}{\Σ}}{\mathrm{\Δ}}^k{B}_m\frac{(5-k)!}{m!(5-k-m)!}{t}^m{(1-t)}^{5-k-m}$

In formula,

The result obtained after derivation is substituted into respectively in the computing formula of curvature and torsion, the song of adjacent two Master Node is obtained Rate and torsion.

6. method according to claim 5, it is characterised in that the computing formula of the curvature and torsion is：

$\left\{\begin{array}{c}\mathrm{\κ}\left(t\right)=\frac{|r^{\′}\left(t\right)\×r^{\′\′}\left(t\right)|}{|r^{\′}\left(t\right){|}^3}\\ \mathrm{\τ}\left(t\right)=\frac{\left(r^{\′}\right(t)\×r^{\′\′}(t\left)\right)\·r^{\′\′\′}\left(t\right)}{|r^{\′}\left(t\right)\×r^{\′\′}\left(t\right){|}^2}\end{array}\right.$

Wherein, κ (t) is curvature, and τ (t) is torsion.

7. method according to claim 6, it is characterised in that between i-th Master Node and i+1 Master Node The highway three-dimensional linear constraints that five worms prescription is adopted for：

$\left\{\begin{array}{c}\frac{{\left(S_{\mathrm{\Δ}345}\right)}_i}{{{\left(\right|p_{54}\left|\right)}_i}^3}=\frac{{\left(S_{\mathrm{\Δ}012}\right)}_{i+1}}{{{\left(\right|p_{10}\left|\right)}_{i+1}}^3}\\ {\mathrm{\κ}}_i{\left(t\right)}_{t=1}=\frac{8S_{\mathrm{\Δ}345}}{5|p_{54}{|}^3}\≤{\mathrm{\κ}}_{\max }\\ {\mathrm{\κ}}_{i+1}{\left(t\right)}_{t=0}=\frac{8S_{\mathrm{\Δ}012}}{5|p_{10}{|}^3}\≤{\mathrm{\κ}}_{\max }\\ {\mathrm{\κ}}_i\left(t\right)\≤{\mathrm{\κ}}_{\max }\\ {\mathrm{\κ}}_i{\left(t\right)}^{\′}\≤{{\mathrm{\κ}}_{\max }}^{\′}\\ \left|{\mathrm{\τ}}_i{\left(t\right)}_{t=1}\right|=\left|\frac{3(p_{54}\×(p_{54}-p_{43}\left)\right)\·(p_{52}-3p_{43})}{20{S_{\mathrm{\Δ}345}}^2}\right|\≤{\mathrm{\τ}}_{\max }\\ \left|{\mathrm{\τ}}_{i+1}{\left(t\right)}_{t=0}\right|=\left|\frac{3(p_{10}\×(p_{21}-p_{10}\left)\right)\·(p_{30}-3p_{21})}{20{S_{\mathrm{\Δ}012}}^2}\right|\≤{\mathrm{\τ}}_{\max }\\ \left|{\mathrm{\τ}}_i\left(t\right)\right|\≤{\mathrm{\τ}}_{\max }\end{array}\right.$

Wherein, S_Δ012For the triangle that the 0th～2 between i-th Master Node and i+1 Master Node is formed from control point Area, S_Δ345The triangle formed from control point for the 3rd～5 between i-th Master Node and i+1 Master Node Area, τ_maxFor maximum torsion, κ_maxFor maximum curvature, κ_max' be maximum curvature rate of change, p₁₀、p₂₁、p₃₀、p₄₃、p₅₂Respectively The 0th of five worms prescription between i-th Master Node and i+1 Master Node is constituted from control point and the 1st from control point Tangent vector, the 1st from control point and the 2nd from control point constitute tangent vector, the 0th from control point and the 3rd from control point constitute Tangent vector, the 3rd from control point and the 4th from control point constitute tangent vector, the 2nd from control point and the 5th from control point constitute cutting Vector, κ_i(t)_T=1、κ_i+1(t)_T=0The end of the five worms prescription between respectively i-th Master Node and i+1 Master Node The curvature of the curvature of point, the starting point of the five worms prescription between i+1 Master Node and the i-th+2 Master Nodes, τ_i (t)_T=1、τ_i+1(t)_T=0The terminal of the five worms prescription between respectively i-th Master Node and i+1 Master Node is scratched The torsion of the starting point of the five worms prescription between rate, i+1 Master Node and the i-th+2 Master Nodes, τ_iT () is i-th The torsion of any point on five worms prescription between Master Node and i+1 Master Node, the span of i is [0, m].

8. method according to claim 7, it is characterised in that also include：

If five worms prescription does not meet default highway three-dimensional linear constraints between adjacent two Master Node, is adjusted 0 from control point and the 1st from the space length between control point and the 4th from control point and the 5th from the space between control point away from From until the PH curves after after adjusting meet the highway three-dimensional linear constraints.

9. it is a kind of for highway three-dimensional linear design PH curve generating means, it is characterised in that include：

Insertion module, for inserting m-1 Master Node between the starting point and terminal by highway to be designed, and the starting point is made For the 0th Master Node and using the terminal as m Master Node, wherein m is the integer more than 1；

Curve builds module, for constructing the PH curves with t as variable between per adjacent two Master Node, and will be with t to become The PH Curve transforms of amount are the five worms prescription of Bessel polynomial form；

Curve determining module, for using per first Master Node in adjacent two Master Node as the 0th of five worms prescription From control point, first Master Node as five worms prescription the 5th from control point, the 0th from control point and the 5th from control point Between select two control point as the 1st from control point and the 4th from control point, according to the described 0th from control point, the described 1st from Control point, the described 4th from control point and the described 5th from control point, it is determined that the described 1st from control point and the described 4th from control Between point the 2nd from control point and the 3rd from control point, and according to the 0th～5 from control point, determine adjacent two Master Node it Between five worms prescription；

Judge module, for calculating on the five worms prescription between adjacent two Master Node curvature at each control point and scratching Rate, and whether the curvature at each control point is judged less than default maximum curvature, whether the torsion at each control point is less than default Maximum torsion, if so, then using the five worms prescription between adjacent two Master Node as designing adjacent two master control The five worms prescription of the three-dimensional linear of the highway between system point.