Geodesic Math
01-02-2017, 10:51 PM
Post: #1
 SlideRule Senior Member Posts: 1,312 Joined: Dec 2013
Geodesic Math
Loquitor

Does anyone have or have access to the HP-65 User Library programs referenced in Hugh Kenner's book Geodesic Math? ie:
Code:
GEODESICS I: Icosa Coordinates (02487A) GEODESICS II: Chord Factors (02486A) GEODESICS Ill: Superellipsoid Radii (02693A) GEODESICS IV: Face & Dihedral Angles - Spheres (02694A) GEODESICS V: Dihedral & Axial Angles: Non-spheres GEODESICS VI: Octahedron Coordinates (02691) GEODESICS VII: Icosa Class I Second Triangle (02692) GEODESICS VIII: Class II Icosa Triangles 2, 3, 4, 5 (02701A) GEODESICS IX: Triacon Coordinates (02734A) GEODESICS X: \$pherical Coordinate Rotation (02700A)
I own a copy of the book & have the listings for the two 65 routines included in the text. I'm referring to the references cited in Appendix III, pages 169-170.
BEST!
SlideRule
01-09-2017, 03:05 AM
Post: #2
 derekamos Member Posts: 54 Joined: Jan 2015
RE: Geodesic Math
Hi Sliderule,
No one seems to be able to help, but maybe with a bit of programming adaption this info' will help you reconstruct the missing routines. The github reference lists the whole routine.
DA
--[[
//==========================================
// Geodesic calculations
//
// Reference: Geodesic Math and How to Use It
// By: Hugh Kenner
// Second Paperback Edition (2003), p.74-75
// http://www.amazon.com/Geodesic-Math-How-...0520239318
//
// The book was used for reference, so if you want to check the math,
// you can plug in various numbers to various routines and see if you get
// the same numbers in the book.
//
// In general, there are enough routines here to implement the various
// pieces necessary to make geodesic objects.
// https://github.com/Spiritdude/OpenJSCAD....esic.jscad
//==========================================
--]]

function poly_sum_interior_angles(sides) = (sides-2)*180;
function poly_single_interior_angle(pq) = poly_sum_interior_angles(pq[0])/pq[0];

-- Given a set of coordinates, return the frequency
-- Simply calculated by adding up the values of the coordinates
function geo_freq(xyz) = xyz[0]+xyz[1]+xyz[2];

-- Convert between the 2D coordinates of vertices on the face triangle
-- to the 3D vertices needed to calculate spherical coordinates
function geo_tri2_tri3(xyf) = [xyf[1], xyf[0]-xyf[1], xyf[2]-xyf[0]];

-- Given coordinates for a vertex on the octahedron face
-- return the spherical coordinates for the vertex
-- class 1, method 1
function octa_class1(c) = sph(
atan(safediv(c[0], c[1])),
atan(sqrt(c[0]*c[0]+c[1]*c[1])/c[2]),
1
);

function octa_class2(c) = sph(
atan(c[0]/c[1]),
atan( sqrt( 2*(c[0]*c[0]+c[1]*c[1])) /c[2]),
1
);

function icosa_class1(c) = octa_class1(
[
c[0]*sin(72),
c[1]+c[0]*cos(72),
geo_freq(c)/2+c[2]/Cphi
]);

function icosa_class2(c) = sph(
atan([c0]/c[1]),
atan(sqrt(c[0]*c[0]+c[1]*c[1]))/cos(36)*c[2],
1
);

function tetra_class1(c) = octa_class1(
[
sqrt(3*c[0]),
2*c[1]-c[0],
(3*c[2]-c[0]-c[1])/sqrt(2)
]);

function class1_icosa_chord_factor(v1, v2, freq) = sph_dist(
icosa_class1(geo_tri2_tri3( [v1[0], v1[1], freq])),
icosa_class1(geo_tri2_tri3( [v2[0], v2[1], freq]))
);
01-09-2017, 01:52 PM (This post was last modified: 01-09-2017 04:25 PM by SlideRule.)
Post: #3
 SlideRule Senior Member Posts: 1,312 Joined: Dec 2013
RE: Geodesic Math
(01-09-2017 03:05 AM)derekamos Wrote:  No one seems to be able to help ... The github reference lists the whole routine ... https://github.com/Spiritdude/OpenJSCAD....esic.jscad
THANKS!! I will continue to research source(s) for the 65 listings, mostly to glean any special techniques for the 65. You are to be commended for illuminating this reference. I'm very competent in SEO techniques but never even came close to this source. Thanks again ...

BEST!
SlideRule

ps: the Calculator Routines listed on pages 167-168 in Appendix 2 are helpful as well
01-10-2017, 08:32 AM
Post: #4
 derekamos Member Posts: 54 Joined: Jan 2015
RE: Geodesic Math
(01-09-2017 01:52 PM)SlideRule Wrote:  [quote='derekamos' pid='66488' dateline='1483931152']
You are to be commended for illuminating this reference. I'm very competent in SEO techniques but never even came close to this source. Thanks again ...
BEST!
SlideRule
Ah yes, I just used a simple google search, with refined new searches on failure, until the search engine found answers. Its really more like the speed of the human mind to correct its searches, SEO doesn't come even near what brains can do.
DA
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