// HypTriangle.java (part of FunDomain java program) /* -------------------------------------------------------------- FunDomain: Program for drawing fundamental domains of subgroups of SL_2(Z) Copyright (C) 2001 Helena A. Verrill This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. Helena A. Verrill UK address: 23 Roper Close Rugby CV21 4PF England email: verrill@math.ku.dk see web page: http://hverrill.net for most recent address and email address. more information about the GPL can be found at: http://www.gnu.org/copyleft/gpl.html ------------------------------------------------------------------ */ import java.awt.*; public class HypTriangle{ //object data public IntMat M; // measures transform from identity triangle public int translation; public int length; public double[][] Triangle = new double [200][2]; public ArcSection Arc1, Arc2, Arc3; int[] X = new int [200]; int[] Y = new int [200]; int Ma, Mc; double Scale; public double MaxY=0; public Polygon Poly = new Polygon(); private double x0im, X0im, y0im, x1im, y1im, x2im, y2im; private double radius1, radius2, radius3; private double center1, center2, center3; private int top; static final double sqrt3 = 1.7320508075688772; private static Polygon[] triangle_list = new Polygon [200]; private static HypTriangle[] hyp_triangle_list = new HypTriangle [200]; private static IntMat[] hyp_matrix_list = new IntMat [200]; private static int number_of_stored_triangles=0; //constructor public HypTriangle(int top, int width, int scale, IntMat N){ this.top = top; this.Scale = 0; if (N.c==0) { IntMat MMM = new IntMat(1,0,0,1); this.M = MMM; this.translation = N.b/N.d;} else { this.translation = N.a/N.c; IntMat MMM = new IntMat(1,-translation,0,1).mult(N); M = MMM; } boolean found = false; int i=0; while ((found==false) && (i< number_of_stored_triangles)){ if (hyp_matrix_list[i].equal(M) || hyp_matrix_list[i].equal(M.negate())) found = true; i++; } if (number_of_stored_triangles==0) i=0; if (found == true) { this.Poly = triangle_list[i-1]; this.length = hyp_triangle_list[i-1].length; this.Triangle = hyp_triangle_list[i-1].Triangle; this.radius1 = hyp_triangle_list[i-1].radius1; this.radius2 = hyp_triangle_list[i-1].radius2; this.radius3 = hyp_triangle_list[i-1].radius3; this.MaxY = hyp_triangle_list[i-1].MaxY; this.Scale = hyp_triangle_list[i-1].Scale; this.Ma = hyp_triangle_list[i-1].Ma; this.Mc = hyp_triangle_list[i-1].Mc; } else{ find_double_triangle(scale); find_Poly(scale, top, width); if (i<199) { hyp_triangle_list[i] = this; triangle_list[i] = this.Poly; IntMat MMM = new IntMat(M.a,M.b,M.c,M.d); hyp_matrix_list[i] = MMM; number_of_stored_triangles++; } } } private void find_double_triangle(int scale){ IntMat N = new IntMat(); double max = (double)(this.top)/(double)(scale); if (M.c!=0) {Ma = M.a; Mc=M.c;} else {Ma = M.b; Mc=M.d;} N = new IntMat(Mc,-Ma,0,Mc).mult(M); // image of infinity x0im = N.XIm("infinity",-1); X0im = N.XIm("infinity",1); y0im = N.YIm("infinity",max); // image of first elliptic point x1im = N.XIm(-0.5,sqrt3/2); y1im = N.YIm(-0.5,sqrt3/2); // image of second elliptic point x2im = N.XIm(0.5,sqrt3/2); y2im = N.YIm(0.5,sqrt3/2); if (M.c==0) {x0im = x1im; X0im = x2im;} radius1 = Math.abs((x0im - N.XIm(-0.5,0))/2); radius2 = Math.abs((N.XIm(1,0) - N.XIm(-1,0))/2); radius3 = Math.abs((X0im - N.XIm(0.5,0))/2); center1 = (x0im + N.XIm(-0.5,0))/2; center2 = ((double)(N.a*N.c-N.b*N.d))/((double)(N.c*N.c-N.d*N.d)); center3 = (X0im + N.XIm(0.5,0))/2; Arc1 = new ArcSection(x0im,y0im,x1im,y1im,radius1,center1); IntMat NS = new IntMat(); NS = N.mult(IntMat.S); boolean nbr = false; int i=0; while ((i 1000){ Polygon P = new Polygon(X,Y,0); Poly = P; } } else { double MaxRadius = Math.max(Math.max(radius1,radius2),radius3); double max = (double)top/Scale; double Size = MaxRadius*Scale; double lft_lim = -(double)2*width/Scale-2*MaxRadius; double rt_lim = (double)2*width/Scale+2*MaxRadius; // the left and rt limits here for X values are assumnig we've // moved so the image of infinity is on the screen. // these values could be made more accurate. // have cut this out until done properly for(i=0;i<=length;i++){ X[i] =(int)Math.round((Triangle[i][0]*Scale)); Y[i] =top - (int)Math.round((Math.max(Math.min(Triangle[i][1],max),-max)*Scale)); } Polygon P = new Polygon(X,Y,length); Poly = P; Poly.translate((Ma*scale)/Mc,0); } } public boolean appears_on_Screen(int scale, int x0, int width){ return true; } }