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KnotOsc.cpp
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KnotOsc.cpp
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/*
KNOTOSC.CPP a module to explore Knots interpreted as oscillators
Written in Microsoft Visual C++ by Paul de Leeuw.
*/
#include <stdio.h>
#include <time.h>
#include <math.h>
#include "manp.h"
#include "Fract.h"
#include "resource.h"
#include "fractype.h"
#include "fractalp.h"
#include "menu.h"
#include "anim.h"
extern HWND GlobalHwnd; // This is the main windows handle
extern int user_data(HWND);
extern void InitOscillator(double c1[], int dimensions);
extern int DisplayOscillator(double c1[], double cn[], double dt, DWORD colour, double i, int dimensions, int FindCentre);
extern void PlotExtras(void);
extern double x_rot; /* angle display plane to x axis */
extern double y_rot; /* angle display plane to y axis */
extern double z_rot; /* angle display plane to z axis */
extern long threshold;
extern double mandel_width; /* width of display */
extern double hor; /* horizontal address */
extern double vert; /* vertical address */
extern double ScreenRatio; // ratio of width / height for the screen
extern double param[];
extern WORD type; // fractal type
extern int subtype; // A - E
extern int curpass, totpasses;
extern CFract Fractal; // current fractal stuff
//extern double VertBias; // allow vertical stretching of the image
extern BOOL DisplayAxes;
extern double dt; // delta time
static double xscale, yscale;
extern double iterations;
static double xMax, yMax, zMax, xMin, yMin, zMin;
///////////////////////////////////////////////////////////////////////////
// Knot Oscillators start here
///////////////////////////////////////////////////////////////////////////
/**************************************************************************
Eight Knot as an Oscillator
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2:5)
***************************************************************************/
int DoEightKnotOsc(void)
{
double t, c1[3], cn[3], dt2;
c1[0] = cn[0] = param[10]; // x
c1[1] = cn[1] = param[11]; // y
c1[2] = cn[2] = param[12]; // z
dt2 = param[0];
totpasses = 10;
InitOscillator(c1, 3); // pass in number of dimensions
for (t = 0; t < iterations; t += dt2)
{
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
curpass = (int)(t * totpasses / iterations);
c1[0] = 10*cos(t) + 10*cos(3*t);
c1[1] = 6*sin(t) + 10*sin(3*t);
c1[2] = 4*sin(3*t) - 10*sin(6*t);
if (DisplayOscillator(c1, cn, dt, ((DWORD)t % threshold), t, 3, 0) < 0)
break;
cn[0] = c1[0];
cn[1] = c1[1];
cn[2] = c1[2];
}
PlotExtras();
return 0;
}
/**************************************************************************
Granny Knot as an Oscillator
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.3)
***************************************************************************/
int DoGrannyKnotOsc(void)
{
double t, c1[3], cn[3], dt2;
c1[0] = cn[0] = param[10]; // x
c1[1] = cn[1] = param[11]; // y
c1[2] = cn[2] = param[12]; // z
dt2 = param[0];
totpasses = 10;
InitOscillator(c1, 3); // pass in number of dimensions
for (t = 0; t < iterations; t += dt2)
{
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
curpass = (int)(t * totpasses / iterations);
c1[0] = -22*cos(t) - 128*sin(t) - 44*cos(3*t) - 78*sin(3*t);
c1[1] = -10*cos(2*t) - 27*sin(2*t) + 38*cos(4*t) + 46*sin(4*t);
c1[2] = 70*cos(3*t) - 40*sin(3*t);
if (DisplayOscillator(c1, cn, dt, ((DWORD)t % threshold), t, 3, 0) < 0)
break;
cn[0] = c1[0];
cn[1] = c1[1];
cn[2] = c1[2];
}
PlotExtras();
return 0;
}
/**************************************************************************
~Knot Universes in Bianchi Type I Cosmology - Tempestuous as an Oscillator
Ratbay Myrzakulov 15 July 2012
https://arxiv.org/abs/1204.1093
***************************************************************************/
int DoKnotUniversesITempestuousOsc(void)
{
double c1[4], cn[4], t, s21, s22, s23, s31, s32, s33, c21, c22, c23, c31, c32, c33, dt2;
c1[0] = cn[0] = param[10]; // x
c1[1] = cn[1] = param[11]; // y
c1[2] = cn[2] = param[12]; // z
c1[3] = cn[3] = param[13]; // z
dt2 = param[0];
totpasses = 10;
InitOscillator(c1, 4); // pass in number of dimensions
for (t = -iterations; t < iterations; t += dt2)
{
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
curpass = (int)(t * totpasses / iterations);
s21 = sin(2 * t);
s22 = s21 * s21;
s23 = s21 * s22;
s31 = sin(3 * t);
s32 = s31 * s31;
s33 = s31 * s32;
c21 = cos(2 * t);
c22 = c21 * c21;
c23 = c21 * c22;
c31 = cos(3 * t);
c32 = c31 * c31;
c33 = c31 * c32;
c1[0] = (-12 * s32 + 36 * c31 + 18 * c32) * c21 - 49 * s21 * (26 / 49 + c31) * s31;
c1[1] = -18 * s21 * c32 + (-49 * s31 * c21 - 36 * s21) * c31 - 26 * s31 * c21 + 12 * s32 * s21;
c1[2] = -30 * s31 * (2 + c31) * c22 - 38 * s21 * (c32 - 27 / 38 * s32 + 58 / 19 * c31 + 40 / 19) * c21 + 30 * s31 * s22 * (2 + c31);
c1[3] = (6 * c22 - 6 * s22) * c33 + (24 * c22 - 22 * s31 * s21 * c21 - 24 * s22) * c32
+ ((6 * s32 - 24) * s22) * c31 - (12 * (c21 - 3 / 4 * s31 * s21)) * (s31 * c21 + 4 / 3 * s21) * s31;
if (DisplayOscillator(c1, cn, dt, ((DWORD)(t * 30.0) % threshold), t, 4, 0) < 0)
break;
cn[0] = c1[0];
cn[1] = c1[1];
cn[2] = c1[2];
cn[3] = c1[3];
}
PlotExtras();
return 0;
}
/**************************************************************************
Marcus Torus Knot
Marcus Rezende August 2018
***************************************************************************/
int DoMarcusTorusKnotOsc(void)
{
double t, c1[3], cn[3], dt2, R, r, p, q;
c1[0] = cn[0] = param[10]; // x
c1[1] = cn[1] = param[11]; // y
c1[2] = cn[2] = param[12]; // z
dt2 = param[0];
R = param[1];
r = param[2];
p = param[3];
q = param[4];
totpasses = 10;
InitOscillator(c1, 3); // pass in number of dimensions
for (t = -iterations; t < iterations; t += dt2)
{
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
curpass = (int)(t * totpasses / iterations);
cn[0] = (R + r * cos(p * t)) * cos(q * t);
cn[1] = (R + r * cos(p * t)) * sin(q * t);
cn[2] = R * cos(p * t);
if (DisplayOscillator(c1, cn, dt, ((DWORD)(t * 30.0) % threshold), t, 3, 0) < 0)
break;
}
PlotExtras();
return 0;
}
/**************************************************************************
Torus Knot
Meier 2001
http://www.3d-meier.de/ (Representation of knots 4.1-13)
***************************************************************************/
int DoTorusKnotOsc(void)
{
double t, c1[3], cn[3], dt2, R, r, p, q;
c1[0] = cn[0] = param[10]; // x
c1[1] = cn[1] = param[11]; // y
c1[2] = cn[2] = param[12]; // z
dt2 = param[0];
R = param[1];
r = param[2];
p = param[3];
q = param[4];
totpasses = 10;
InitOscillator(c1, 3); // pass in number of dimensions
for (t = 0; t < iterations; t += dt2)
{
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
curpass = (int)(t * totpasses / iterations);
c1[0] = (R + r * cos(p * t)) * cos(q * t);
c1[1] = (R + r * cos(p * t)) * sin(q * t);
c1[2] = r * sin(p * t);
if (DisplayOscillator(c1, cn, dt, ((DWORD)t % threshold), t, 3, 0) < 0)
break;
cn[0] = c1[0];
cn[1] = c1[1];
cn[2] = c1[2];
}
PlotExtras();
return 0;
}
/**************************************************************************
Trefoil Knot A as an Oscillator
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.1)
***************************************************************************/
int DoTrefoilKnotAOsc(void)
{
double t, c1[3], cn[3], dt2;
c1[0] = cn[0] = param[10]; // x
c1[1] = cn[1] = param[11]; // y
c1[2] = cn[2] = param[12]; // z
dt2 = param[0];
totpasses = 10;
InitOscillator(c1, 3); // pass in number of dimensions
for (t = 0; t < iterations; t += dt2)
{
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
curpass = (int)(t * totpasses / iterations);
c1[0] = (2 + cos(1.5*t))*cos(t);
c1[1] = (2 + cos(1.5*t))*sin(t);
c1[2] = sin(1.5*t);
if (DisplayOscillator(c1, cn, dt, ((DWORD)t % threshold), t, 3, 0) < 0)
break;
cn[0] = c1[0];
cn[1] = c1[1];
cn[2] = c1[2];
}
PlotExtras();
return 0;
}