-- tkz_elements_functions_maths.lua -- date 2024/02/04 -- version 2.00c -- Copyright 2024 Alain Matthes -- This work may be distributed and/or modified under the -- conditions of the LaTeX Project Public License, either version 1.3 -- of this license or (at your option) any later version. -- The latest version of this license is in -- http://www.latex-project.org/lppl.txt -- and version 1.3 or later is part of all distributions of LaTeX -- version 2005/12/01 or later. -- This work has the LPPL maintenance status “maintained”. -- The Current Maintainer of this work is Alain Matthes. -- constant tkzphi = (1+math.sqrt(5))/2 tkzinvphi = (math.sqrt(5)-1)/2 tkzsqrtphi = math.sqrt(tkzphi) --------------------------------------------------------------------------- function round(num, idp) return topoint(string.format("%." .. (idp or 0) .. "f", num)) end function tkzround( num, idp ) local mult = 10 ^ ( idp or 0 ) return math.floor( num * mult + 0.5 ) / mult end function dot_product (a,b,c) return (b-a)..(c-a) end function Cramer33(a1,a2,a3,b1,b2,b3,c1,c2,c3) return a1*b2*c3+a3*b1*c2+a2*b3*c1-a3*b2*c1-a1*b3*c2-a2*b1*c3 end function Cramer22(a1,a2,b1,b2) return a1*b2-a2*b1 end function aligned ( m,a,b ) local z z = (b-a)/(m-b) if math.abs(z.im) < tkz_epsilon then return true else return false end end function islinear (z1,z2,z3) local dp dp = (z2-z1) ^ (z3-z1) if math.abs(dp) < tkz_epsilon then return true else return false end end function isortho (z1,z2,z3) local dp dp = (z2-z1) .. (z3-z1) if math.abs(dp) < tkz_epsilon then return true else return false end end function parabola (a,b,c) local xa,xb,xc,ya,yb,yc xa = a.re ya = a.im xb = b.re yb = b.im xc = c.re yc = c.im D = (xa-xb)*(xa-xc)*(xb-xc) A = (xc*(yb-ya) + xb*(ya-yc)+xa*(yc-yb))/D B = (xc*xc*(ya-yb)+xb*xb*(yc-ya)+xa*xa*(yb-yc))/D C = (xb*xc*(xb-xc)*ya + xc*xa*(xc-xa)*yb +xa*xb*(xa-xb)*yc)/D return A,B,C end function value (v) return scale * v end function real (v) return v/scale end function get_angle (a,b,c) return angle_normalize_(get_angle_( a,b,c )) end function get_angle_( a,b,c ) return point.arg ((c-a)/(b-a)) end function angle_normalize (a) return angle_normalize_ (a) end function angle_normalize_ (a) while a < 0 do a = a + 2*math.pi end while a >= 2*math.pi do a = a - 2*math.pi end return a end function barycenter (...) return barycenter_ (...) end function swap(a,b) local t=a a=b b=t return a,b end function format_number(number, decimal_places) local format_string = string.format("%%.%df", decimal_places) return string.format(format_string, number) end