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Knots.cpp
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Knots.cpp
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/*
KNOTS.CPP a module to explore 3D knots
Written in Microsoft Visual C++ by Paul de Leeuw.
*/
#include <stdio.h>
#include <time.h>
#include "manp.h"
#include "Fract.h"
#include "resource.h"
#include "fractype.h"
#include "fractalp.h"
#include "menu.h"
#include "anim.h"
#include "OscProcess.h"
extern HWND GlobalHwnd; // This is the main windows handle
extern int user_data(HWND);
extern void PlotExtras(void);
extern void PrintOsc(int); // used for listing oscillator names in d:\temp\OscDump.txt
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 BYTE PerspectiveFlag; // display using perspective
extern double ScreenRatio; // ratio of width / height for the screen
extern int CoordSystem;
extern double mandel_width; // width of display
extern double hor; // horizontal address
extern double vert; // vertical address
extern WORD type; // fractal type
extern int subtype;
extern int curpass, totpasses;
extern double param[];
extern int OscPtrArray[]; // array of pointers to specific oscillators or fractal maps
extern int OscillatorNum;
extern double iterations;
extern double dt; // delta time
extern double VertBias; // allow vertical stretching of the image
extern double zBias; // allow stretching of the image in the z direction
extern int xAxis, yAxis, zAxis; // numerical values for axes for chaotic oscillators
extern BOOL RemoveHiddenPixels;
extern int xdots, ydots;
extern double *wpixels; // an array of doubles holding slope modified iteration counts
extern CTrueCol TrueCol; // palette info
extern RGBTRIPLE OscBackGround;
extern ProcessType OscAnimProc;
extern COscProcess OscProcess;
extern CDib Dib; // Device Independent Bitmap
void InitKnot(double c1[], int dimensions);
int DisplayKnot(double c1[], DWORD colour, int KnotWidth, double i, int dimensions);
void CloseZvaluesKnots(void);
/**************************************************************************
An Introductions to Harmonic Knots - Generic knots - page 359
Corresponding author: [email protected]
***************************************************************************/
int DoAnIntroductions2HarmonicKnots(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor, p, q;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
p = param[2];
q = 4 * p + 1;
KnotWidth = param[3];
ColourFactor = param[4];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = cos(p * i) + 0.25 * cos(p * i) * cos(q * i);
c1[1] = sin(p * i) + 0.25 * sin(p * i) * cos(q * i);
c1[2] = 0.25 * sin(q * i);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Borromean Rings
Meier 2001
http://www.3d-meier.de/ (Representation of knots 6)
***************************************************************************/
int DoBorromeanRings(void)
{
int i, j;
double c1[6], t, gap, Start, End, r, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
r = sqrt(3.0) / 3.0;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 6); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
c1[0] = cos(t); // ring 1
c1[1] = sin(t) + r;
c1[2] = cos(3*t) / 3;
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
c1[0] = cos(t) + 0.5; // ring 2
c1[1] = sin(t) - r/2;
c1[2] = cos(3*t) / 3;
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (DisplayKnot(c1, ((DWORD)(i * 2 / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
c1[0] = cos(t) - 0.5; // ring 3
c1[1] = sin(t) - r/2;
c1[2] = cos(3*t) / 3;
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (DisplayKnot(c1, ((DWORD)(i * 3 / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Cinquefoil Knot
Graphics by Paul Bourke November 2004
http://paulbourke.net/geometry/knots/
***************************************************************************/
int DoCinquefoilKnot(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor, k;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
k = param[2];
KnotWidth = param[3];
ColourFactor = param[4];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = cos(t) * (2 - cos(2*t/(2*k + 1)));
c1[1] = sin(t) * (2 - cos(2*t/(2*k + 1)));
c1[2] = -sin(2*t/(2*k + 1));
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Chrysanthemum Curve
Written by Paul Bourke Attributed to Temple Fay
http://paulbourke.net/geometry/chrysanthemum/
***************************************************************************/
/*
int DoChrysanthemumCurve(void)
{
int i, j;
double c1[6], KnotWidth, ColourFactor, u, r, p4, p8;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
KnotWidth = param[0];
ColourFactor = param[1];
totpasses = 10;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
u = i * 21.0 * PI / iterations;
p4 = sin(17 * u / 3);
p8 = sin(2 * cos(3 * u) - 28 * u);
r = 5*(1 + sin(11*u/5)) - 4*p4*p4*p4*p4 * p8*p8*p8*p8*p8*p8*p8*p8;
c1[0] = r * cos(u);
c1[1] = r * sin(u);
c1[2] = (r/20+0.2)*sin(r*2*PI/7);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
*/
/**************************************************************************
Decorative Knot Patterns - Compound Pattern 3
Prof. Y. F. Chen 2011
History of Knot Theory / Definition of Knot Theory & Knots
***************************************************************************/
int DoDecorativeKnotPatternsCompoundPattern3(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = cos(t) + 0.2 * cos(3 * t) + 0.98 * cos(-5 * t);
c1[1] = 1.875 * sin(t) + 0.665 * sin(3 * t) + 0.45 * sin(-5 * t);
c1[2] = 0.35 * sin(8 * t) + 0.15 * sin(2 * t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Decorative Knot Patterns - Four Main Loops
Prof. Y. F. Chen 2011
History of Knot Theory / Definition of Knot Theory & Knots
***************************************************************************/
int DoDecorativeKnotPatternsFourMainLoops(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = 0.6 * cos(t) + 0.25 * cos(-3 * t) - 0.26 * cos(-9 * t);
c1[1] = 0.6 * sin(t) + 0.25 * sin(-3 * t) - 0.26 * sin(-9 * t);
c1[2] = 0.12 * sin(16 * t) + 0.06 * sin(4 * t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Decorative Knot Patterns - Inner Loop Pattern 3
Prof. Y. F. Chen 2011
History of Knot Theory / Definition of Knot Theory & Knots
***************************************************************************/
int DoDecorativeKnotPatternsInnerLoopPattern3(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = cos(4*t) + 0.875 * cos(7 * t);
c1[1] = sin(4*t) + 0.875 * sin(7 * t);
c1[2] = 0.35 * sin(12 * t) - 0.15 * sin(3 * t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Decorative Knot Patterns - Inner Loop Pattern 5
Prof. Y. F. Chen 2011
History of Knot Theory / Definition of Knot Theory & Knots
***************************************************************************/
int DoDecorativeKnotPatternsInnerLoopPattern5(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = cos(2*t) + 0.67 * cos(7 * t);
c1[1] = sin(2*t) + 0.67 * sin(7 * t);
c1[2] = 0.2 * sin(10 * t) - 0.1 * sin(5 * t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Decorative Knot Patterns - Inner Loop Pattern 6
Prof. Y. F. Chen 2011
History of Knot Theory / Definition of Knot Theory & Knots
***************************************************************************/
int DoDecorativeKnotPatternsInnerLoopPattern6(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = 1.5 * cos(t) + 0.35 * cos(3 * t) - 0.9 * cos(5 * t);
c1[1] = 1.5 * sin(t) + 0.35 * sin(3 * t) - 0.9 * sin(5 * t);
c1[2] = 0.35 * sin(8 * t) - 0.2 * sin(2 * t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Decorative Knot Patterns - Three Main Loops
Prof. Y. F. Chen 2011
History of Knot Theory / Definition of Knot Theory & Knots
***************************************************************************/
int DoDecorativeKnotPatternsThreeMainLoops(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = 0.59 * cos(t) + 0.3 * cos(-2 * t) - 0.45 * cos(-5 * t);
c1[1] = 0.59 * sin(t) + 0.3 * sin(-2 * t) - 0.45 * sin(-5 * t);
c1[2] = 0.1 * sin(9 * t) + 0.25 * sin(6 * t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Eight Knot
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2:5)
***************************************************************************/
int DoEightKnot(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
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);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Fibonacci Fourier Knots
Louis H. Kauffman 3 Dec 1997
https://arxiv.org/pdf/q-alg/9711013.pdf
***************************************************************************/
int DoFibonacciFourierKnots(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor, n, fn, fn1, fn2, sqrt5;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
n = param[2];
KnotWidth = param[3];
ColourFactor = param[4];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
sqrt5 = sqrt(5.0);
fn = (pow((1 + sqrt5), n) - pow((1 - sqrt5), n)) / (pow(2, n)) / sqrt5;
fn1 = (pow((1 + sqrt5), (n + 1)) - pow((1 - sqrt5), (n + 1))) / pow(2, (n + 1)) / sqrt5;
fn2 = (pow((1 + sqrt5), (n + 2)) - pow((1 - sqrt5), (n + 2))) / pow(2, (n + 2)) / sqrt5;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = cos(fn * t);
c1[1] = sin(fn1 * t + 0.5);
c1[2] = 0.5 * cos(fn2 * t + 0.5) + 0.5 * sin(fn1 * t + 0.5);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Fourier Knot
Louis H. Kauffman 3 Dec 1997
https://arxiv.org/pdf/q-alg/9711013.pdf
***************************************************************************/
int DoFourierKnot(int variety)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
if (variety == 0)
c1[0] = cos(2 * t);
else
c1[0] = sin(2 * t);
c1[1] = cos(3 * t + 0.5);
c1[2] = 0.5 * cos(5 * t + 0.5) + 0.5 * sin(3 * t + 0.5);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
int DoFourierKnotI()
{
return (DoFourierKnot(0));
}
int DoFourierKnotIII()
{
return (DoFourierKnot(1));
}
/**************************************************************************
Granny Knot
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.3)
***************************************************************************/
int DoGrannyKnot(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 6); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
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);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Knot 3-1
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.6)
***************************************************************************/
int DoKnot3_1(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 6); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = 41*cos(t) - 18*sin(t) - 83*cos(2*t) - 83*sin(2*t) - 11*cos(3*t) + 27*sin(3*t);
c1[1] = 36*cos(t) + 27*sin(t) - 113*cos(2*t) + 30*sin(2*t) + 11*cos(3*t) - 27*sin(3*t);
c1[2] = 45*sin(t) - 30*cos(2*t) + 113*sin(2*t) - 11*cos(3*t) + 27*sin(3*t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Knot 4-1
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.7)
***************************************************************************/
int DoKnot4_1(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 6); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = 32*cos(t) - 51*sin(t) - 104*cos(2*t) - 34*sin(2*t) + 104*cos(3*t) - 91*sin(3*t);
c1[1] = 94*cos(t) + 41*sin(t) + 113*cos(2*t) - 68*cos(3*t) - 124*sin(3*t);
c1[2] = 16*cos(t) + 73*sin(t) - 211*cos(2*t) - 39*sin(2*t) - 99*cos(3*t) - 21*sin(3*t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Knot 5-1
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.8)
***************************************************************************/
int DoKnot5_1(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 6); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = 88*cos(t) + 115*sin(t) - 475*cos(2*t) - 127*sin(2*t) - 87*cos(3*t) + 36*sin(3*t) + 11*cos(4*t) - 19*sin(4*t);
c1[1] = 89*cos(t) - 32*sin(t) - 172*cos(2*t) + 294*sin(2*t) + 76*cos(3*t) + 102*sin(3*t) - 61*cos(4*t) + 113*sin(4*t);
c1[2] = 44*cos(t) - 69*sin(t) + 34*cos(2*t) + 223*sin(2*t) + 16*cos(3*t)+ 120*sin(3*t) + 42*cos(4*t) - 125*sin(4*t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Knot 5-2
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.9)
***************************************************************************/
int DoKnot5_2(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 6); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = -33*cos(t) + 43*sin(t) + 214*sin(2*t) - 101*cos(3*t) - 47*sin(3*t) + 11*sin(4*t);
c1[1] = -57*cos(t) + 99*sin(t) - 54*cos(2*t) - 159*sin(2*t) - 117*cos(3*t) - 5*sin(3*t) - 31*cos(4*t) - 45*sin(4*t);
c1[2] = 34*cos(t) - 21*sin(t) - 100*cos(2*t) - 93*sin(2*t) - 27*cos(3*t) - 16*sin(3*t) + 52*cos(4*t) + 84*sin(4*t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Knot 6-1
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.10)
***************************************************************************/
int DoKnot6_1(void)
{
int i, j;
double c1[6], t, gap, Start, End, e, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
e = atan(1.0);
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 6); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = 12*cos(t*e) + 20*sin(t) - 163*cos(2*t) + 76*sin(2*t) - 87*cos(3*t) - 15*sin(3*t) - 21*cos(4*t) + 14*sin(4*t) + 24*cos(5*t) - 50*sin(5*t);
c1[1] = 29*cos(t*e) + 78*sin(t) - 180*cos(2*t) + 58*sin(2*t) + 88*cos(3*t) + 72*sin(3*t) - 14*sin(4*t);
c1[2] = -30*cos(t*e) - 78*sin(t) - 111*cos(2*t) + 37*sin(2*t) - 67*cos(3*t) - 51*sin(3*t) + 31*cos(4*t) + 8*sin(4*t) -11*cos(5*t) + 65*sin(5*t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************
Knot 6-2
Meier 2001
http://www.3d-meier.de/ (Representation of knots 2.11)
***************************************************************************/
int DoKnot6_2(void)
{
int i, j;
double c1[6], t, gap, Start, End, KnotWidth, ColourFactor;
c1[0] = c1[3] = param[10]; // x
c1[1] = c1[4] = param[11]; // y
c1[2] = c1[5] = param[12]; // z
Start = param[0];
End = param[1];
KnotWidth = param[2];
ColourFactor = param[3];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitKnot(c1, 6); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = -6*cos(t) - 21*sin(t) - 195*cos(2*t) + 92*sin(2*t) - 64*cos(3*t) - 23*sin(3*t) - 6*cos(4*t) + 13*sin(4*t) +24*cos(5*t) + 15*sin(5*t) + 41*sin(6*t);
c1[1] = -21*cos(t) - 24*sin(t) - 207*cos(2*t) - 72*sin(2*t) + 112*cos(3*t) - 7*sin(3*t) - 13*cos(4*t) - 40*sin(4*t) -27*cos(5*t) - 3*sin(5*t) - 17*cos(6*t);
c1[2] = -18*cos(t) - 13*sin(t) + 113*cos(2*t) - 107*sin(2*t) + 86*cos(3*t) - 9*sin(3*t) - 26*cos(4*t) - 7*sin(4*t) +24*cos(5*t) + 33*sin(5*t) + 21*cos(6*t) + 31*sin(6*t);
for (j = 0; j < 3; j++)
c1[j + 3] += c1[j] * dt;
if (user_data(GlobalHwnd) == -1) // user pressed a key?
return -1;
if (DisplayKnot(c1, ((DWORD)(i / ColourFactor) % threshold), (int)KnotWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesKnots();
return 0;
}
/**************************************************************************