// $Id: x27c.c 11992 2011-10-20 22:54:16Z andrewross $ // // Drawing "spirograph" curves - epitrochoids, cycolids, roulettes // // Copyright (C) 2007 Arjen Markus // // This file is part of PLplot. // // PLplot is free software; you can redistribute it and/or modify // it under the terms of the GNU Library General Public License as published // by the Free Software Foundation; either version 2 of the License, or // (at your option) any later version. // // PLplot 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 Library General Public License for more details. // // You should have received a copy of the GNU Library General Public License // along with PLplot; if not, write to the Free Software // Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA // // #include "plcdemos.h" // Function prototypes void cycloid( void ); void spiro( PLFLT data[], int fill ); PLINT gcd( PLINT a, PLINT b ); void arcs( void ); //-------------------------------------------------------------------------- // main // // Generates two kinds of plots: // - construction of a cycloid (animated) // - series of epitrochoids and hypotrochoids //-------------------------------------------------------------------------- int main( int argc, const char *argv[] ) { // R, r, p, N // R and r should be integers to give correct termination of the // angle loop using gcd. // N.B. N is just a place holder since it is no longer used // (because we now have proper termination of the angle loop). PLFLT params[9][4] = { { 21.0, 7.0, 7.0, 3.0 }, // Deltoid { 21.0, 7.0, 10.0, 3.0 }, { 21.0, -7.0, 10.0, 3.0 }, { 20.0, 3.0, 7.0, 20.0 }, { 20.0, 3.0, 10.0, 20.0 }, { 20.0, -3.0, 10.0, 20.0 }, { 20.0, 13.0, 7.0, 20.0 }, { 20.0, 13.0, 20.0, 20.0 }, { 20.0, -13.0, 20.0, 20.0 } }; int i; int fill; // plplot initialization // Parse and process command line arguments plparseopts( &argc, argv, PL_PARSE_FULL ); // Initialize plplot plinit(); // Illustrate the construction of a cycloid cycloid(); // Loop over the various curves // First an overview, then all curves one by one // plssub( 3, 3 ); // Three by three window fill = 0; for ( i = 0; i < 9; i++ ) { pladv( 0 ); plvpor( 0.0, 1.0, 0.0, 1.0 ); spiro( ¶ms[i][0], fill ); } pladv( 0 ); plssub( 1, 1 ); // One window per curve for ( i = 0; i < 9; i++ ) { pladv( 0 ); plvpor( 0.0, 1.0, 0.0, 1.0 ); spiro( ¶ms[i][0], fill ); } // Fill the curves fill = 1; pladv( 0 ); plssub( 1, 1 ); // One window per curve for ( i = 0; i < 9; i++ ) { pladv( 0 ); plvpor( 0.0, 1.0, 0.0, 1.0 ); spiro( ¶ms[i][0], fill ); } // Finally, an example to test out plarc capabilities arcs(); // Don't forget to call plend() to finish off! plend(); exit( 0 ); } //-------------------------------------------------------------------------- // Calculate greatest common divisor following pseudo-code for the // Euclidian algorithm at http://en.wikipedia.org/wiki/Euclidean_algorithm PLINT gcd( PLINT a, PLINT b ) { PLINT t; a = abs( a ); b = abs( b ); while ( b != 0 ) { t = b; b = a % b; a = t; } return a; } //-------------------------------------------------------------------------- void cycloid( void ) { // TODO } //-------------------------------------------------------------------------- void spiro( PLFLT params[], int fill ) { #define NPNT 2000 static PLFLT xcoord[NPNT + 1]; static PLFLT ycoord[NPNT + 1]; int windings; int steps; int i; PLFLT phi; PLFLT phiw; PLFLT dphi; PLFLT xmin = 0.0; PLFLT xmax = 0.0; PLFLT xrange_adjust; PLFLT ymin = 0.0; PLFLT ymax = 0.0; PLFLT yrange_adjust; // Fill the coordinates // Proper termination of the angle loop very near the beginning // point, see // http://mathforum.org/mathimages/index.php/Hypotrochoid. windings = (int) ( abs( (int) params[1] ) / gcd( (PLINT) params[0], (PLINT) params[1] ) ); steps = NPNT / windings; dphi = 2.0 * PI / (PLFLT) steps; for ( i = 0; i <= windings * steps; i++ ) { phi = (PLFLT) i * dphi; phiw = ( params[0] - params[1] ) / params[1] * phi; xcoord[i] = ( params[0] - params[1] ) * cos( phi ) + params[2] * cos( phiw ); ycoord[i] = ( params[0] - params[1] ) * sin( phi ) - params[2] * sin( phiw ); if ( i == 0 ) { xmin = xcoord[i]; xmax = xcoord[i]; ymin = ycoord[i]; ymax = ycoord[i]; } if ( xmin > xcoord[i] ) xmin = xcoord[i]; if ( xmax < xcoord[i] ) xmax = xcoord[i]; if ( ymin > ycoord[i] ) ymin = ycoord[i]; if ( ymax < ycoord[i] ) ymax = ycoord[i]; } xrange_adjust = 0.15 * ( xmax - xmin ); xmin -= xrange_adjust; xmax += xrange_adjust; yrange_adjust = 0.15 * ( ymax - ymin ); ymin -= yrange_adjust; ymax += yrange_adjust; plwind( xmin, xmax, ymin, ymax ); plcol0( 1 ); if ( fill ) { plfill( 1 + steps * windings, xcoord, ycoord ); } else { plline( 1 + steps * windings, xcoord, ycoord ); } } void arcs() { #define NSEG 8 int i; PLFLT theta, dtheta; PLFLT a, b; theta = 0.0; dtheta = 360.0 / NSEG; plenv( -10.0, 10.0, -10.0, 10.0, 1, 0 ); // Plot segments of circle in different colors for ( i = 0; i < NSEG; i++ ) { plcol0( i % 2 + 1 ); plarc( 0.0, 0.0, 8.0, 8.0, theta, theta + dtheta, 0.0, 0 ); theta = theta + dtheta; } // Draw several filled ellipses inside the circle at different // angles. a = 3.0; b = a * tan( ( dtheta / 180.0 * M_PI ) / 2.0 ); theta = dtheta / 2.0; for ( i = 0; i < NSEG; i++ ) { plcol0( 2 - i % 2 ); plarc( a * cos( theta / 180.0 * M_PI ), a * sin( theta / 180.0 * M_PI ), a, b, 0.0, 360.0, theta, 1 ); theta = theta + dtheta; } }