1 /**
2 * Mandelbulber v2, a 3D fractal generator _%}}i*<. ______
3 * Copyright (C) 2020 Mandelbulber Team _>]|=||i=i<, / ____/ __ __
4 * \><||i|=>>%) / / __/ /___/ /_
5 * This file is part of Mandelbulber. )<=i=]=|=i<> / /__ /_ __/_ __/
6 * The project is licensed under GPLv3, -<>>=|><|||` \____/ /_/ /_/
7 * see also COPYING file in this folder. ~+{i%+++
8 *
9 * knotv1
10 * Based on DarkBeam formula from this thread:
11 * http://www.fractalforums.com/new-theories-and-research/not-fractal-but-funny-trefoil-knot-routine
12 */
13
14 #include "all_fractal_definitions.h"
15
cFractalKnotV1()16 cFractalKnotV1::cFractalKnotV1() : cAbstractFractal()
17 {
18 nameInComboBox = "Knot V1";
19 internalName = "knot_v1";
20 internalID = fractal::knotV1;
21 DEType = analyticDEType;
22 DEFunctionType = customDEFunction;
23 cpixelAddition = cpixelDisabledByDefault;
24 defaultBailout = 100.0;
25 DEAnalyticFunction = analyticFunctionCustomDE;
26 coloringFunction = coloringFunctionDefault;
27 }
28
FormulaCode(CVector4 & z,const sFractal * fractal,sExtendedAux & aux)29 void cFractalKnotV1::FormulaCode(CVector4 &z, const sFractal *fractal, sExtendedAux &aux)
30 {
31 double polyfoldOrder = fractal->transformCommon.int2;
32
33 if (fractal->transformCommon.functionEnabledAxFalse) z.x = fabs(z.x);
34 if (fractal->transformCommon.functionEnabledAyFalse) z.y = fabs(z.y);
35 if (fractal->transformCommon.functionEnabledAzFalse) z.z = fabs(z.z);
36 z += fractal->transformCommon.offset000;
37
38 CVector4 zc = z;
39 zc.z *= fractal->transformCommon.scaleA1;
40 double mobius =
41 (1.0 * fractal->transformCommon.intA1 + fractal->transformCommon.intB1 / polyfoldOrder)
42 * atan2(zc.y, zc.x);
43
44 zc.x = sqrt(zc.x * zc.x + zc.y * zc.y) - fractal->transformCommon.offsetA2;
45 double temp = zc.x;
46 double c = cos(mobius);
47 double s = sin(mobius);
48 zc.x = c * zc.x + s * zc.z;
49 zc.z = -s * temp + c * zc.z;
50
51 double m = 1.0 * polyfoldOrder / M_PI_2x;
52 double angle1 = floor(0.5 + m * (M_PI_2 - atan2(zc.x, zc.z))) / m;
53
54 temp = zc.x;
55 c = cos(angle1);
56 s = sin(angle1);
57 zc.x = c * zc.x + s * zc.z;
58 zc.z = -s * temp + c * zc.z;
59
60 zc.x -= fractal->transformCommon.offset05;
61
62 double len = sqrt(zc.x * zc.x + zc.z * zc.z);
63
64 if (fractal->transformCommon.functionEnabledCFalse) len = min(len, max(fabs(zc.x), fabs(zc.z)));
65
66 aux.DE0 = len - fractal->transformCommon.offset01;
67
68 if (fractal->transformCommon.functionEnabledJFalse)
69 {
70 if (fractal->transformCommon.functionEnabledDFalse)
71 aux.DE0 = min(aux.dist, aux.DE0);
72 if (fractal->transformCommon.functionEnabledKFalse) aux.DE0 /= aux.DE;
73 if (fractal->transformCommon.functionEnabledEFalse) z = zc;
74 }
75 double colorDist = aux.dist;
76 aux.dist = aux.DE0;
77
78 // aux.color
79 if (fractal->foldColor.auxColorEnabled)
80 {
81 double colorAdd = 0.0;
82 double ang = (M_PI - 2.0 * fabs(atan(zc.x / zc.z))) * 2.0 / M_PI;
83
84 if (fmod(ang, 2.0) < 1.0) colorAdd += fractal->foldColor.difs0000.x;
85 colorAdd += fractal->foldColor.difs0000.y * fabs(ang);
86 colorAdd += fractal->foldColor.difs0000.z * fabs(ang * zc.x);
87 colorAdd += fractal->foldColor.difs0000.w * angle1;
88
89 colorAdd += fractal->foldColor.difs1;
90 if (fractal->foldColor.auxColorEnabledA)
91 {
92 if (colorDist != aux.dist) aux.color += colorAdd;
93 }
94 else
95 aux.color += colorAdd;
96 }
97
98 // DE tweak
99 if (fractal->analyticDE.enabledFalse) aux.dist = aux.dist * fractal->analyticDE.scale1;
100 }
101