C-Hook Name: asphere.dll/.scr/.txt Date: January 12, 2001 Programmer: CNC Software, Inc. Description: Using a fixed formula (with user defined coefficients) for aspheres, creates points, lines, arc or a spline that passes through points on the asphere. The asphere formula is: z = c * x^2 / [1 + sqrt(1-(k+1) * c^2 * x^2)] + a1 * x^4 + a2 * x^6 + a3 * x^8 + a4 * x^10 + a5 * x^12 + a6 * x^14 + a7 * x^16 + a8 * x^18 + a9 * x^20 + a10 * x^22 + a11 * x^24 + a12 * x^26 + a13 * x^28 + a14 * x^30 + a15 * x^32 + a16 * x^34 + a17 * x^36 + a18 * x^38 + a19 * x^40 + a20 * x^42 where k = conic constant = -e^2 e = eccentricity r = radius of curvature = 1 / c c = curvature a1-a20 = coefficients The x and z coordinates are mirrored. A positive radius, representing a convex asphere, will cause the curve to slope downward. A negative radius, representing a concave asphere, will cause the curve to slope upward. The following variables are also used: x start = starting x coordinate x finish = final x coordinate x step = x step size value. New points, lines or spline nodes are created at this step amount. The default value for x start is zero. Positive values should be used for x finish and x increment. Additional options for curve generation: 1. Chordal deviation. This parameter is enabled only when arcs are created. It represent the maximum between the arcs that are generated and a spline that goes through generated points. It does NOT represent the maximum error between the theoretical asphere curve and the arcs (total error). Total error is an indirect function of x increment and chordal deviation. Compatibility with previous versions of asphere: The new version of asphere uses 20 coefficients. They are written to parameters 101 through 120 in the [asphere] section of the .prm file. The previous version of asphere used 9 coefficients. They were written to parameters 1-9 of the .prm file. The new version of asphere can read old asphere .prm files, but the old version of asphere cannot read new .prm files. Modifications: jds 02/04/97 initial version jds 04/21/97 added chordal deviation, create curve in cplane / xz, start curve at origin and mirror curve about x jds 05/06/97 deleted create curve in cplane / xz, start curve at origin and mirror curve about x jds 07/08/97 checked into version 7 $lgb$ 1.0 jds 01/15/01 expanded number of coefficients from 9 to 20 $lge$ Distributor: CNC Software 671 Old Post Road Tolland, CT 06084 Contact: CNC Software Phone: (860) 875-5006
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