Patent GB-1386435-A (GB)
Title: Apparatus for approximating with linear segments a curvature on a threedimensional surface
IPC: G06F17/17
Filed: 1972-07-07
Abstract: 1386435 Approximating three dimensional surface CINCINNATI MILACRON Inc 7 July 1972 [21 July 1971] 32023/72 Heading G4A Apparatus for approximating the curvature of a three dimensional surface includes a scanning device producing a series of sample points on the surface and a computer programmed to determine a series of linear segments extending between pairs of the sample points, each succeeding segment being defined by the end point of the preceding segment and the sample point which immediately precedes the first sample point which lies at a distance from an extension of the preceding segment greater than a predetermined distance. Apparatus.-The surface of a three dimensional body is traced by a scanning apparatus which generates a series of samples along the surface which are fed to a programmed computer. A tape punching unit is provided to store data defining the linear segments. Reference is made to Specification 1,341,714. Operation.-The operation utilizes vector algebra and is as follows. The cartesian coordinates of the first two sample points p 0  and p 1  are stored and a reference vector u extending between the points is calculated. This vector is tested (tolerance check) to ensure that it is larger than a fixed magnitude (in particular to ensure it is non zero) and if satisfactory a first linear segment is defined between the two samples. If the vector is not satisfactory a third sample point is substituted for the second and the process repeated. The first (reference) segment defines the longitudinal axis 38 of a cylindrical boundary 40 of a radius corresponding to the resolution required in tracing the surface. The next sample point p n  is stored, no tolerance check being performed since this point represents the best resolution attainable, and a further sample point p n+1  is then stored. The magnitude of the vector w (which is a perpendicular to axis 38 passing through p n+1 ) is then compared with the radius of cylinder 40 to determine whether point p n+1  is within the approximation tolerance for a linear segment. If p n+1  lies outside the cylinder 40, i.e. |#w| is greater than the radius of cylinder 40, a second linear segment is defined between p 1  and p n , the reference segment is replaced by the second segment after a check to ensure that the second segment is non-zero, and the process repeated with further samples. If p n+1  lies within the cylinder a further point p n+2  is sampled, the co-ordinates of p n  are replaced by p n+1  and the process repeated with p n+2 , the only difference being that if p n+2  lies outside the cylinder the second segment is defined from p 1  to p n+1 . The process results in a series of linear segments being defined which approximate to a predetermined degree (viz. the radius of cylinder 40) the curvature of the surface being sampled. Further details.-The Specification gives the vector theory of the process in full together with a flow chart giving the vector algebra in terms of cartesian co-ordinates and a program written in assembler language for a particular computer.