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Curves.cpp
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Curves.cpp
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/*
CURVES.CPP a module to explore 3D curves
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 double sech(double x);
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 BYTE PerspectiveFlag; // display using perspective
extern int CoordSystem;
extern double param[];
extern int curpass, totpasses;
extern long threshold;
extern double ScreenRatio; // ratio of width / height for the screen
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 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 int OscPtrArray[]; // array of pointers to specific oscillators or fractal maps
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 InitCurve(double c1[], int dimensions);
int DisplayCurve(double c1[], DWORD colour, int CurveWidth, double i, int dimensions);
void CloseZvaluesCurves(void);
/**************************************************************************
Abdank-Abakanowicz Quadratrix
https://www.mathcurve.com/courbes2d.gb/abdank/abdank.shtml
***************************************************************************/
int DoAbdankAbakanowiczQuadratrix(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, frequency, amplitude;
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];
a = param[2];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = a * sin(t);
c1[1] = a * a / 2 * (t + sin(t) * cos(t));
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Ampersand Curve
http://mathworld.wolfram.com/AmpersandCurve.html
***************************************************************************/
int DoAmpersandCurve(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, b, c, r, frequency, amplitude;
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];
CurveWidth = param[2];
ColourFactor = param[3];
amplitude = param[4];
frequency = param[5];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
a = 2 * cos(2 * t) + cos(4 * t) + 9;
b = -37 * cos(t) - 5 * cos(3 * t);
c = 22 * cos(2 * t) + 16;
r = (-b + sqrt(fabs(b * b - 4 * a * c))) / 2 / a;
c1[0] = r * cos(t);
c1[1] = r * sin(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Anguinea
https://www.mathcurve.com/courbes2d.gb/anguinee/anguinee.shtml
***************************************************************************/
int DoAnguinea(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, d, frequency, amplitude;
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];
a = param[2];
d = param[3];
CurveWidth = param[4];
ColourFactor = param[5];
amplitude = param[6];
frequency = param[7];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = d * tan(t / 2);
c1[1] = a / 2 * sin(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Archimedean Spiral
http://www.3d-meier.de/
***************************************************************************/
int DoArchimedeanSpiralCurve(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, frequency, amplitude;
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];
CurveWidth = param[2];
ColourFactor = param[3];
amplitude = param[4];
frequency = param[5];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = t * cos(t);
c1[1] = t * sin(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Astroid
http://www.3d-meier.de/
***************************************************************************/
int DoAstroid(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, frequency, amplitude;
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];
a = param[2];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = a * pow(cos(t), 3);
c1[1] = a * pow(sin(t), 3);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Bean Curve
http://www.2dcurves.com/quartic/quarticbn.html
***************************************************************************/
int DoBeanCurve(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, s, c, r, frequency, amplitude;
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];
CurveWidth = param[2];
ColourFactor = param[3];
amplitude = param[4];
frequency = param[5];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
s = sin(t);
c = cos(t);
r = s * s * s + c * c * c;
c1[0] = r * cos(t);
c1[1] = r * sin(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Besace
https://www.mathcurve.com/courbes2d.gb/besace/besace.shtml
***************************************************************************/
int DoBesace(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, b, frequency, amplitude;
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];
a = param[2];
b = param[3];
CurveWidth = param[4];
ColourFactor = param[5];
amplitude = param[6];
frequency = param[7];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = a * cos(t) - b * sin(t);
c1[1] = -sin(t) * c1[0];
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Bicorn Curve
http://www.3d-meier.de/
***************************************************************************/
int DoBicornCurve(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, frequency, amplitude;
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];
CurveWidth = param[2];
ColourFactor = param[3];
amplitude = param[4];
frequency = param[5];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = sin(t);
c1[1] = COSSQR(t) * (2 + cos(t))/(3 + SINSQR(t));
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Bifoliate Curve
http://mathworld.wolfram.com/Bifoliate.html
***************************************************************************/
int DoBifoliate(void)
{
int i, j;
double c1[6], t, gap, Start, End, a, r, CurveWidth, ColourFactor, frequency, amplitude;
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];
a = param[2];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
r = a * 8 * cos(t) * sin(t) * sin(t) / (3 + cos(4 * t));
c1[0] = r * cos(t);
c1[1] = r * sin(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Biquartic-Carlos Sacre
https://www.mathcurve.com/courbes2d.gb/biquartic/biquartic.shtml
***************************************************************************/
int DoBiquarticCarlosSacre(void)
{
int i, j;
double c1[6], t, gap, Start, End, n, CurveWidth, ColourFactor, frequency, amplitude;
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];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = sin(3 * t) * cos(t);
c1[1] = pow(sin(3 * t) * sin(t), n);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Booth's Curve
https://www.mathcurve.com/courbes2d.gb/booth/booth.shtml
***************************************************************************/
int DoBoothsCurve(void)
{
int i, j;
double c1[6], t, gap, Start, End, a, b, e, r, CurveWidth, ColourFactor, frequency, amplitude;
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];
a = param[2];
b = param[3];
e = param[4];
CurveWidth = param[5];
ColourFactor = param[6];
amplitude = param[7];
frequency = param[8];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
r = sqrt(a * a * cos(t) * cos(t) + fabs(e * b * b * sin(t) * sin(t)));
c1[0] = r * cos(t);
c1[1] = r * sin(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Brachistochrone Curve
https://www.mathcurve.com/courbes2d.gb/brachistochrone/brachistochrone.shtml
***************************************************************************/
int DoBrachistochroneCurve(void)
{
int i, j;
double c1[6], t, gap, Start, End, a, CurveWidth, ColourFactor, frequency, amplitude;
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];
a = param[2];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = a * (t - sin(t));
c1[1] = a * (cos(t) - 1);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Butterfly Curve
https://en.wikipedia.org/wiki/Butterfly_curve_(transcendental)
***************************************************************************/
int DoButterflyCurve(void)
{
int i, j;
double c1[6], t, gap, Start, End, r, CurveWidth, ColourFactor, frequency, amplitude;
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];
CurveWidth = param[2];
ColourFactor = param[3];
amplitude = param[4];
frequency = param[5];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
r = exp(cos(t)) - 2 * cos(4 * t) + pow(sin(t / 24), 5);
c1[0] = r * sin(t);
c1[1] = r * cos(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Cassinian Oval
http://www.3d-meier.de/
***************************************************************************/
int DoCassinianOval(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, b, M, frequency, amplitude;
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];
a = param[2];
b = param[3];
CurveWidth = param[4];
ColourFactor = param[5];
amplitude = param[6];
frequency = param[7];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
M = 2 * a*a * cos(2*t) + 2 * sqrt((-a*a*a*a + b*b*b*b) + a*a*a*a * COSSQR(2*t));
c1[0] = sqrt(M/2) * cos(t);
c1[1] = sqrt(M/2) * sin(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Catenary Curve
http://astrowww.phys.uvic.ca/~tatum/classmechs/class18.pdf
***************************************************************************/
int DoCatenary(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, frequency, amplitude;
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];
a = param[2];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = t;
c1[1] = a * cosh(t / a);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Cayley's Sextic
http://mathworld.wolfram.com/CayleysSextic.html
***************************************************************************/
int DoCayleysSextic(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, r, frequency, amplitude;
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];
a = param[2];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
r = 4 * a * pow(cos(t / 3), 3);
c1[0] = r * cos(t);
c1[1] = r * sin(t);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
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], CurveWidth, 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
CurveWidth = param[0];
ColourFactor = param[1];
totpasses = 10;
InitCurve(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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Cissoid
http://www.3d-meier.de/
***************************************************************************/
int DoCissoid(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, frequency, amplitude;
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];
a = param[2];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = a * t*t*t / (t*t + 1);
c1[1] = a * t*t / (t*t + 1);
c1[2] = amplitude*sin(frequency*t) + amplitude*sin(frequency*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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Clelie Curve
https://en.wikipedia.org/wiki/Clelie
***************************************************************************/
int DoClelieCurve(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, m;
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];
a = param[2];
m = param[3];
CurveWidth = param[4];
ColourFactor = param[5];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
c1[0] = a * sin(m * t) * cos(t);
c1[1] = a * sin(m * t) * sin(t);
c1[2] = a * cos(m * 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 (DisplayCurve(c1, ((DWORD)(i / ColourFactor) % threshold), (int)CurveWidth, i, 6) < 0)
break;
t += gap;
}
PlotExtras();
CloseZvaluesCurves();
return 0;
}
/**************************************************************************
Cochleoid
https://www.mathcurve.com/courbes2d.gb/cochleoid/cochleoid.shtml
***************************************************************************/
int DoCochleoid(void)
{
int i, j;
double c1[6], t, gap, Start, End, CurveWidth, ColourFactor, a, r, frequency, amplitude;
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];
a = param[2];
CurveWidth = param[3];
ColourFactor = param[4];
amplitude = param[5];
frequency = param[6];
totpasses = 10;
gap = (End - Start) / iterations;
t = Start;
InitCurve(c1, 3); // pass in number of dimensions
for (i = 0; i < iterations; i++)
{
curpass = (int)(i * totpasses);
r = a * sin(t) / t;
c1[0] = r * cos(t);
c1[1] = r * sin(t);