openjscad-aurora-webapp

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/*
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	License: This code is placed in the public Domain
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	Contributed By: Willliam A Adams
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	August 2011
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*/
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// A couple of useful constants
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Cpi = 3.14159;
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Cphi = 1.61803399;
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Cepsilon = 0.00000001;
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// Function: clean
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//
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// Parameters:
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//	n - A number that might be very close to zero
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// Description:  
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//	There are times when you want a very small number to 
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// 	just be zero, instead of being that very small number.
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//	This function will compare the number to an arbitrarily small 
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//	number.  If it is smaller than the 'epsilon', then zero will be 
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// 	returned.  Otherwise, the original number will be returned.
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//
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function clean(n) = (n < 0) ? ((n < -Cepsilon) ? n : 0) : 
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	(n < Cepsilon) ? 0 : n; 
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// Function: safediv
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//
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// Parameters
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//	n - The numerator
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//	d - The denominator
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//
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// Description:
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//	Since division by zero is generally not a desirable thing, safediv
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//	will return '0' whenever there is a division by zero.  Although this will
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//	mask some erroneous division by zero errors, it is often the case
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//	that you actually want this behavior.  So, it makes it convenient.
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function safediv(n,d) = (d==0) ? 0 : n/d;
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//==================================
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// Degrees
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//==================================
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function DEGREES(radians) = (180/Cpi) * radians;
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function RADIANS(degrees) = Cpi/180 * degrees;
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function deg(deg, min=0, sec=0) = [deg, min, sec];
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function deg_to_dec(d) = d[0] + d[1]/60 + d[2]/60/60;
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//==================================
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//  Spherical coordinates
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//==================================
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// create an instance of a spherical coordinate
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// long - rotation around z -axis
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// lat - latitude, starting at 0 == 'north pole'
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// rad - distance from center
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function sph(long, lat, rad=1) = [long, lat, rad];
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// Convert spherical to cartesian
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function sph_to_cart(s) = [
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	clean(s[2]*sin(s[1])*cos(s[0])),  
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	clean(s[2]*sin(s[1])*sin(s[0])),
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	clean(s[2]*cos(s[1]))
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	];
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// Convert from cartesian to spherical
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function sph_from_cart(c) = sph(
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	atan2(c[1],c[0]), 
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	atan2(sqrt(c[0]*c[0]+c[1]*c[1]), c[2]), 
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	sqrt(c[0]*c[0]+c[1]*c[1]+c[2]*c[2])
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	);
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function sphu_from_cart(c, rad=1) = sph(
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	atan2(c[1],c[0]), 
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	atan2(sqrt(c[0]*c[0]+c[1]*c[1]), c[2]), 
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	rad
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	);
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// compute the chord distance between two points on a sphere
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function sph_dist(c1, c2) = sqrt(
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	c1[2]*c1[2] + c2[2]*c2[2] - 
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	2*c1[2]*c2[2]*
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	((cos(c1[1])*cos(c2[1])) + cos(c1[0]-c2[0])*sin(c1[1])*sin(c2[1]))   
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	);
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//==========================================
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//	Geodesic calculations
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// 
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//  Reference: Geodesic Math and How to Use It
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//  By: Hugh Kenner
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//  Second Paperback Edition (2003), p.74-75
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//  http://www.amazon.com/Geodesic-Math-How-Hugh-Kenner/dp/0520239318
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//
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//  The book was used for reference, so if you want to check the math, 
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//  you can plug in various numbers to various routines and see if you get
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//  the same numbers in the book.
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//
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//  In general, there are enough routines here to implement the various
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//  pieces necessary to make geodesic objects.
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//==========================================
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function poly_sum_interior_angles(sides) = (sides-2)*180;
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function poly_single_interior_angle(pq) = poly_sum_interior_angles(pq[0])/pq[0];
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// Given a set of coordinates, return the frequency
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// Simply calculated by adding up the values of the coordinates
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function geo_freq(xyz) = xyz[0]+xyz[1]+xyz[2];
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// Convert between the 2D coordinates of vertices on the face triangle
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// to the 3D vertices needed to calculate spherical coordinates
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function geo_tri2_tri3(xyf) = [xyf[1], xyf[0]-xyf[1], xyf[2]-xyf[0]];
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// Given coordinates for a vertex on the octahedron face
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// return the spherical coordinates for the vertex
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// class 1, method 1
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function octa_class1(c) = sph(
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	atan(safediv(c[0], c[1])),
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	atan(sqrt(c[0]*c[0]+c[1]*c[1])/c[2]),
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	1 
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	);
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function octa_class2(c) = sph(
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	atan(c[0]/c[1]),
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	atan( sqrt( 2*(c[0]*c[0]+c[1]*c[1])) /c[2]),
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	1 
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	);
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function icosa_class1(c) = octa_class1(
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	[
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		c[0]*sin(72),  
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		c[1]+c[0]*cos(72),  
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		geo_freq(c)/2+c[2]/Cphi
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	]);
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function icosa_class2(c) = sph(
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	atan([c0]/c[1]), 
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	atan(sqrt(c[0]*c[0]+c[1]*c[1]))/cos(36)*c[2],
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	1
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	);
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function tetra_class1(c) = octa_class1(
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	[
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		sqrt(3*c[0]),  
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		2*c[1]-c[0],  
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		(3*c[2]-c[0]-c[1])/sqrt(2)
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	]);
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function class1_icosa_chord_factor(v1, v2, freq) = sph_dist( 
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		icosa_class1(geo_tri2_tri3( [v1[0], v1[1], freq])),
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		icosa_class1(geo_tri2_tri3( [v2[0], v2[1], freq]))
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	);
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