CN106294928A - A kind of method identifying the surface of revolution expressed with rational B-spline surface form - Google Patents

Abstract

The present invention relates to part machining features recognition field, a kind of method identifying the surface of revolution expressed with rational B-spline surface form.Comprise the steps: step 1: input rational B-spline surface；Step 2: according to the rational B-spline surface of input, investigate that the single argument B-spline curves in independent u direction and v direction indicate whether is all circular arc, if being not all circular arc, then writes down the single argument B-spline curves on u direction and v direction；Step 3: ask the center of circle of all circular arcs respectively, and judge whether the center of circle is to write down this straight line on same straight line；Step 4: judge that the straight line at place, all centers of circle is the most vertical with the plane at each circular arc place, if vertical, illustrates that this curved surface is surface of revolution；Step 5: output " this curved surface is surface of revolution ".The present invention is compared with the existing technology, it can be determined that whether rational B-spline surface is surface of revolution, and analyzes bus and the rotary shaft of its surface of revolution further, facilitates follow-up display, processes and process.

Description

A kind of method identifying the surface of revolution expressed with rational B-spline surface form

Technical field

The present invention relates to part machining features recognition field, specifically one identifies with rational B-spline surface form The method of the surface of revolution expressed.

Background technology

Different CAD/CAM system is carried out during data exchange, multiple different data form to be used, as IGES, STEP etc., these data forms there may be multiple different expression, need these parts to express same 3 d part Carry out feature identification and just can restore the part of three-dimensional.

Mathematically the definition for " surface of revolution " is: rotate one with plane curve straight line in its plane Week, formed curved surface was surface of revolution；Straight line as the center rotated is referred to as rotary shaft, and another plane curve is referred to as Bus.

Usually can be by piece surface that reality is " surface of revolution " with the shape of " rational B-spline surface " in CAD/CAM software Formula carries out recording, express and exporting.Accordingly, it would be desirable to one may determine that whether these rational B-spline surface are surface of revolutions, if It is to obtain the bus of this surface of revolution and the method for axis further.The most domestic CAD/CAM software also cannot be by this With rational B-spline surface form express surface of revolution correct be identified as surface of revolution.

Summary of the invention

The present invention, for overcoming the deficiencies in the prior art, designs the rotation that a kind of identification is expressed with rational B-spline surface form The method of curved surface, what the method can interpolate that whether rational B-spline surface express is a surface of revolution, if dividing the most further Separate out bus and the rotary shaft of its surface of revolution, carry out follow-up display to facilitate, process and process.

For achieving the above object, the method designing the surface of revolution that a kind of identification is expressed with rational B-spline surface form, its It is characterised by comprising the steps:

(1) step 1: input rational B-spline surface；

(2) step 2: according to the rational B-spline surface of input, investigate the single argument B-spline curves whether table of independent u direction Show is all circular arc, and investigate that the single argument B-spline curves in independent v direction indicate whether is all circular arc simultaneously, if the u side obtained To not being the most circular arc with the single argument B-spline surface on v direction, then output " not being surface of revolution ", otherwise writes down u direction and v Single argument B-spline curves on direction, and go to step 3；

(3) step 3: if the single argument B-spline curves on u direction and v direction are all circular arcs, seek all circular arcs the most respectively The center of circle, and judge that this straight line, the most all on same straight line, if the center of circle is on same straight line, is write down in all centers of circle, and Go to step 4, otherwise output " not being surface of revolution "；

(4) step 4: judge that the straight line at place, all centers of circle is the most vertical with the plane at each circular arc place, if not hanging down Straight then output " not being surface of revolution "；If vertical, illustrate that this curved surface is surface of revolution, go to step 5；

(5) step 5: output " this curved surface is surface of revolution ", and in step 3, place, center of circle straight line is the rotation of the surfaces of revolution Axle, in step 2, the single argument B-spline curves on non-circular arc direction are its buses.

The present invention is compared with the existing technology, it can be determined that whether rational B-spline surface is surface of revolution, and judging is In the case of surface of revolution, analyze further bus and the rotary shaft of its surface of revolution, thus conveniently carry out follow-up display, place Reason and processing.

Accompanying drawing explanation

Fig. 1 is the flow chart of the present invention.

Fig. 2 is the control node schematic diagram of embodiment in the present invention.

Fig. 3 is the surface modeling figure of embodiment in the present invention.

Detailed description of the invention

Below according to accompanying drawing, the present invention is described further.

It is illustrated in figure 1 the flow process of the present invention, comprises the steps:

(1) step 1: input rational B-spline surface；

(2) step 2: according to the rational B-spline surface of input, investigate the single argument B-spline curves whether table of independent u direction Show is all circular arc, and investigate that the single argument B-spline curves in independent v direction indicate whether is all circular arc simultaneously, if the u side obtained To not being the most circular arc with the single argument B-spline surface on v direction, then output " not being surface of revolution ", otherwise writes down u direction and v Single argument B-spline curves on direction, and go to step 3；

(3) step 3: if the single argument B-spline curves on u direction and v direction are all circular arcs, seek all circular arcs the most respectively The center of circle, and judge that this straight line, the most all on same straight line, if the center of circle is on same straight line, is write down in all centers of circle, and Go to step 4, otherwise output " not being surface of revolution "；

(4) step 4: judge that the straight line at place, all centers of circle is the most vertical with the plane at each circular arc place, if not hanging down Straight then output " not being surface of revolution "；If vertical, illustrate that this curved surface is surface of revolution, go to step 5；

(5) step 5: output " this curved surface is surface of revolution ", and in step 3, place, center of circle straight line is the rotation of the surfaces of revolution Axle, in step 2, the single argument B-spline curves on non-circular arc direction are its buses.

Embodiment:

Rational B-spline surface is by the Control point mesh of both direction, two knot vectors and single argument B-spline base letter thereof The product of number defines, and its expression formula is:

$S(u,v)=\frac{{\mathrm{\Σ}}_{i=0}^n{\mathrm{\Σ}}_{j=0}^m{N}_{i,p}\left(u\right)N_{j,q}\left(v\right)w_{i,j}{P}_{i,j}}{{\mathrm{\Σ}}_{i=0}^n{\mathrm{\Σ}}_{j=0}^m{N}_{i,p}\left(u\right)N_{j,q}\left(v\right)w_{i,j}}$

Wherein, P_{I, j}For the individual point range of (m+1) × (n+1) in given space, constitute one and control grid, w_{I, j}For weight factor, N_{I, p}(u) and N_{J, q}(v) be respectively along u to p time and along v to the B-spline basic function of q time.Control point mesh P_{I, j}May decide that curved surface Shape.Determine parameter (u, v) can be obtained by curved surface a unique corresponding point, if only determining parameter u, in v, Then obtain B-spline curves corresponding on curved surface.

As shown in Figures 2 and 3, defined can be obtained by rational B-spline surface, when in the rotary shaft and XYZ axle of rotary body A certain axle parallel time, what rational B-spline surface represented is that the sufficient and necessary condition of a surfaces of revolution is: a) u of curved surface, In v both direction, the b SPL in some direction is entirely circular arc；B) center of circle of these circular arcs is the most point-blank； C) this straight line is vertical with the plane at all circular arc places.

Claims (2)

1. the method identifying the surface of revolution expressed with rational B-spline surface form, it is characterised in that comprise the steps:

(1) step 1: input rational B-spline surface；

(2) step 2: according to the rational B-spline surface of input, investigates what the single argument B-spline curves of independent u direction indicated whether Being all circular arc, investigate that the single argument B-spline curves in independent v direction indicate whether is all circular arc simultaneously, if the u direction obtained and Single argument B-spline surface on v direction is not the most circular arc, then output " not being surface of revolution ", otherwise writes down u direction and v direction On single argument B-spline curves, and go to step 3；

(3) step 3: if the single argument B-spline curves on u direction and v direction are all circular arcs, seek the circle of all circular arcs the most respectively The heart, and judge that all centers of circle, the most all on same straight line, if the center of circle is on same straight line, is write down this straight line, and turned Step 4, otherwise output " not being surface of revolution "；

(4) step 4: judge that the straight line at place, all centers of circle is the most vertical with the plane at each circular arc place, if out of plumb, Output " not being surface of revolution "；If vertical, illustrate that this curved surface is surface of revolution, go to step 5；

(5) step 5: output " this curved surface is surface of revolution ", and in step 3, place, center of circle straight line is the rotary shaft of the surfaces of revolution, In step 2, the single argument B-spline curves on non-circular arc direction are its buses.

A kind of method identifying the surface of revolution expressed with rational B-spline surface form the most as claimed in claim 1, its feature It is: the rational B-spline surface in described step 1 is by the Control point mesh of both direction, two knot vectors and single argument B-spline The product of basic function defines, and its expression formula is

$S(u,v)=\frac{{\mathrm{\Σ}}_{i=0}^n{\mathrm{\Σ}}_{j=0}^m{N}_{i,p}\left(u\right)N_{j,q}\left(v\right)w_{i,j}{P}_{i,j}}{{\mathrm{\Σ}}_{i=0}^n{\mathrm{\Σ}}_{j=0}^m{N}_{i,p}\left(u\right)N_{j,q}\left(v\right)w_{i,j}}.$