1. Field of the Invention
This invention relates to a curved surface creation method and, more particularly, to a curved surface creation method suitable for use in creating two curved surfaces for coarse and finishing machining.
2. Description of the Related Art
As illustrated in FIG. 4, one method of creating a free curved surface entails obtaining two, i.e., first and second, space curves (base curves) 11a, 11b [FIG. 4(a)], dividing each of the base curves 11a, 11b into N segments [FIG. 4(b)], and connecting corresponding dividing points by straight lines, thereby forming a curved surface CS [FIG. 4(c)].
In this curved surface creation method, the base curves 11a, 11b are specified by discrete point sequences P.sub.li (x.sub.i,y.sub.i,z.sub.i) (i=1, 2, . . . ) and P.sub.2j (x.sub.j,y.sub.j,z.sub.j) (j=1, 2, . . . ), respectively, as shown in FIG. 4(d). In order to obtain these sequences of points (base curves), a predetermined curved surface is generated in advance and curves in the XY plane are projected onto this curved surface.
FIGS. 5 and 6 are views for describing the processing for obtaining a sequence of points which specify a base curve. As shown in FIG. 5, let L.sub.c (j) express an intermediate section curve containing a j-th dividing point on a base curve BSCl of a curved surface 10, and let L.sub.r (i) express a curve obtained by connecting an i-th dividing point on each of the intermediate section curves L.sub.c (j) (j=1, 2, 3, . . . n). A quadrilateral bounded by curves L.sub.c (j), L.sub.c (j+1), L.sub.r (i) and L.sub.r (1+1) shall be referred to as a "patch" PT (i,j). The four vertices Q1, Q2, Q3, Q4 of the patch PT (i,j) are stored in memory.
As shown in FIG. 6, points of intersection are where a curve CV in the X-Y plane intersects the sides of each projection patch obtained by projecting each patch onto the X-Y plane, and the coordinates of the points on the curved surface 10 corresponding to these points of intersection are computed. For example, four sides i.sub.a, i.sub.b, j.sub.a, j.sub.b are obtained by projecting a predetermined patch P (m,n) on a three-dimensional curved surface onto the X-Y plane. Let P.sub.1 i, P.sub.2i represent the points of intersection between the curve CV and a predetermined two of these four sides, and let (x.sub.li, y.sub.li), (x.sub.2i, y.sub.2i) represent the coordinates of these points of intersection. Further, let Q.sub.1 ', Q.sub.2 ' denote the end points of the side i.sub.a intersected by the curve CV, let Q.sub.3 ', Q.sub.4 ' denote the end points of the side i.sub.b intersected by curve CV, let Q.sub.i (i=1-4) represent the points on the three-dimensional curved surface that correspond to the points Q.sub.i ' (i=1-4), and let (x.sub.i, y.sub.i, z.sub.i) denote the coordinates of each of the points Q.sub.i. Then, the Z coordinates z.sub.li, z.sub.2i of the points P.sub.li ', P.sub.2i ' on the curved surface that correspond to the points of intersection P.sub.li, P.sub.2i are calculated in accordance with the following equations: EQU z.sub.li =z.sub.1 +(z.sub.2 -z.sub.1)(x.sub.li -x.sub.1)/(x.sub.2 -x.sub.1) EQU z.sub.2i =z.sub.3 +(z.sub.4 -z.sub.3)(x.sub.2i -x.sub.3)/(x.sub.4 -x.sub.3)
Thus, the coordinates of the points P.sub.li ', P.sub.2i ' on the curved surface are, respectively, (x.sub.li, y.sub.li, z.sub.li), (x.sub.2i, y.sub.2i, z.sub.2i). The set of points P.sub.li ', P.sub.2i ' (i=1, 2, . . . ) on the curved surface represent the sequence of points defining the base curve.
Since numerical control (NC) machining ordinarily includes coarse machining and finishing machining, it is necessary to create a curved surface for coarse machining and a curved surface for finishing machining. When creating a curved surface for coarse machining in the prior art, the curved surface, namely the NC data, for coarse machining is prepared by obtaining the base curves 11a, 11b (FIG. 4) through the above-mentioned method upon enlarging the length of each side of the patch PT of the curved surface 10 (FIG. 5). When creating a curved surface for finishing machining in the prior art, the curved surface, namely the NC data, for finishing machining is similarly prepared by obtaining the base curves 11a, 11b through the foregoing method upon reducing the length of each side of the patch.
However, the processing for specifying the space curves that are the base curves requires a very long period of time. For this reason, considerable time is required to obtain the two curved surfaces, namely for coarse and finishing machining.