HueStripes_MagnHeight.pov

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/*

https://github.com/t-o-k/POV-Ray-complex-functions

Copyright (c) 2022-2024 Tor Olav Kristensen, http://subcube.com

Use of this source code is governed by the GNU Lesser General Public License version 3,
which can be found in the LICENSE file.

*/
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#version 3.7;

global_settings { assumed_gamma 1.0 }

#include "colors.inc"
#include "../Complex_Functions.inc"
#include "../Color_Functions.inc"
#include "../Function_Meshes.inc"

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/*
The function below is from Kurtz le pirate in this POV-Ray newsgroup post:

    Subject: How to ...
    From: kurtz le pirate
    Date: Nov 2021-11-28 10:46:21
    Newsgroup: povray.general
    http://news.povray.org/povray.general/message/%3C61a3a44d%241%40news.povray.org%3E


Prefix/Infix:

    Fn(Z) = (-Z^3.0 + Z^2.0*j + 1.0)/(Z - 1.0 + 1.0*j)^2.0


Prefix:

    Fn(Z) =
        Div(
            Add(
                Add(
                    Neg(
                        Pow(
                            Z,
                            +3.0
                        ),
                    ),
                    Mul(
                        Sqr(
                            Z
                        ),
                        +1.0*j
                    )
                ),
                +1.0
            ),
            Sqr(
                Add(
                    Z,
                    -1.0 +1.0*j
                )
            )
        )


Postfix:

    (Z)Fn =
        (
            (
                (
                    (
                        (
                            Z,
                            +3.0
                        )Pow
                    )Neg,
                    (
                        (
                            Z
                        )Sqr,
                        +1.0*j
                    )Mul
                )Add,
                +1.0
            )Add,
            (
                (
                    Z,
                    -1.0 +1.0*j
                )Add
            )Sqr
        )Div
*/

#declare No = 16;

#declare PartTypes = array[No];
#declare Arguments = array[No];

#declare PartTypes[0] = "Z";
#declare Arguments[0] = ZFn();

#declare PartTypes[1] = "Const";
#declare Arguments[1] = RealConstFn(+3.0);

#declare PartTypes[2] = "Pow";
#declare Arguments[2] = Arg2Fn(0, 1);

#declare PartTypes[3] = "Neg";
#declare Arguments[3] = Arg1Fn(2);

#declare PartTypes[4] = "Z";
#declare Arguments[4] = ZFn();

#declare PartTypes[5] = "Sqr";
#declare Arguments[5] = Arg1Fn(4);

#declare PartTypes[6] = "Const";
#declare Arguments[6] = ImagConstFn(+1.0);

#declare PartTypes[7] = "Mul";
#declare Arguments[7] = Arg2Fn(5, 6);

#declare PartTypes[8] = "Add";
#declare Arguments[8] = Arg2Fn(3, 7);

#declare PartTypes[9] = "Const";
#declare Arguments[9] = RealConstFn(+1.0);

#declare PartTypes[10] = "Add";
#declare Arguments[10] = Arg2Fn(8, 9);

#declare PartTypes[11] = "Z";
#declare Arguments[11] = ZFn();

#declare PartTypes[12] = "Const";
#declare Arguments[12] = ComplexConstFn(-1.0, +1.0);

#declare PartTypes[13] = "Add";
#declare Arguments[13] = Arg2Fn(11, 12);

#declare PartTypes[14] = "Sqr";
#declare Arguments[14] = Arg1Fn(13);

#declare PartTypes[15] = "Div";
#declare Arguments[15] = Arg2Fn(10, 14);


#declare ReFunctions = array[No];
#declare ImFunctions = array[No];

AssembleFunctions(PartTypes, Arguments, ReFunctions, ImFunctions)

#declare RealFn = FinalFunction(ReFunctions);
#declare ImagFn = FinalFunction(ImFunctions);

#declare MagnitudeFn = MagnitudeFunction(RealFn, ImagFn);
#declare PhaseFn = PhaseFunction(RealFn, ImagFn);

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#declare HueFn = HueFunction(PhaseFn);

#declare HueRampFn =
    RampFunction(
        15.00, // Ramp interval (Degrees)
        0.00   // Shift fraction
    )
;

#declare HueStripeFn =
    StripeFunction(
        2.00,  // Stripe width (Degrees)
        0.50,  // Outside value
        0.00   // Inside value
    )
;
                                                                       
#declare LnMagnitudeFn = function(re, im) { ln(MagnitudeFn(re, im)) };

#declare LightnessFn = function(re, im) { HueStripeFn(HueRampFn(HueFn(re, im))) };

#declare Saturation = 1.00;

#declare MinX = -8.0;
#declare MaxX = +8.0;

#declare MinZ = -8.0;
#declare MaxZ = +8.0;

#declare NoOfIntervalsX = 1600;
#declare NoOfIntervalsZ = 1600;

object {
    FunctionMesh2(LnMagnitudeFn, MinX, MaxX, MinZ, MaxZ, NoOfIntervalsX, NoOfIntervalsZ)
    FunctionsPigmentRGB(
        function { HSL_RD_FN(HueFn(x, z), Saturation, LightnessFn(x, z)) },
        function { HSL_GN_FN(HueFn(x, z), Saturation, LightnessFn(x, z)) },
        function { HSL_BU_FN(HueFn(x, z), Saturation, LightnessFn(x, z)) }
    )
}

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background { color Blue/6 + Green/12 }

light_source {
    100*<+2, +3, -4>
    color 1.2*White
    shadowless
    rotate +210*y
}

camera {
    angle 48
    location <0, 8, -26>
    look_at <1, 3, 0>
    rotate +210*y
}

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